7. Q6
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Similar Question 1
<p>Show each multiplication using a different model. Determine the product.</p><p><code class='latex inline'>\displaystyle \frac{2}{9} \times 4 \frac{1}{4} </code></p>
Similar Question 2
<p>Order the fractions in each set from least to greatest. </p><p><code class='latex inline'>\displaystyle\frac{5}{2}, \frac{6}{3}, \frac{7}{4}</code></p>
Similar Question 3
<p>Calculate each quotient using equivalent fractions. </p><p><code class='latex inline'>\frac{3}{5}\div\frac{5}{6}</code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Add.</p><p><code class='latex inline'>\frac{1}{2} + \frac{2}{3} + \frac{3}{4}</code></p>
<p>Reilly has exactly enough white sugar for five batches of cherry cookies. He decides to make five batches of chocolate cookies instead. How much more white sugar does he need?</p><p><code class='latex inline'>\displaystyle \begin{array}{llllllll} &\text{Chocolate Cookies} & \text{Cherry Cookies} \\ & 1 \frac{1}{3}\text{cups white sugar} &\frac{1}{2} \text{white sugar} \end{array} </code></p>
<p>Why does finding out how many <code class='latex inline'>\frac{3}{4}</code> strips fit along the length of 4 whole strips help you solve the problem?</p>
<p>Why does a common denominator make adding or subtracting fractions easier?</p>
<p>Order the fractions in each set from least to greatest. </p><p><code class='latex inline'>\displaystyle\frac{3}{8}, \frac{4}{5}, \frac{1}{2}</code></p>
<p>Calculate. </p><p><code class='latex inline'>\frac{5}{6}\div\frac{1}{4}</code></p>
<p>Explain why you can calculate <code class='latex inline'>2\div\frac{2}{3}</code> using each method below. Use the Communication Checklist and the picture to help you.</p><img src="/qimages/25791" /><p>Multiply 2 by 3 and then divide by 2. </p>
<p>In each pair, which fraction is greater? How do you know?</p><p><code class='latex inline'>\displaystyle\frac{2}{3}, \frac{5}{6}</code></p>
<p>Show each multiplication using a different model. Determine the product.</p><p><code class='latex inline'>\displaystyle 4\frac{2}{5} \times 3 \frac{3}{5} </code></p>
<p>Sketch a model to show <code class='latex inline'>\frac{5}{6}\div\frac{1}{3}=2\frac{1}{2}</code>.</p>
<p>Sketch a model and calculate. </p><p><code class='latex inline'>\frac{3}{5}+\frac{2}{7}</code></p>
<p>What is the value of each expression?</p><p><code class='latex inline'>\frac{2}{3}</code> of <code class='latex inline'>\frac{6}{8}</code></p>
<p>Susan stated that <code class='latex inline'>\displaystyle\frac{5}{6}</code> is between <code class='latex inline'>\displaystyle\frac{4}{5}</code> and <code class='latex inline'>\displaystyle\frac{6}{7}</code>.</p><p>Do you agree? Give reasons for your answer.</p>
<p>Write each fraction as the difference of two proper fractions with different denominators. </p><p><code class='latex inline'>\frac{1}{2}</code></p>
<p>Write each fraction as the sum of two different unit fractions. </p><p><code class='latex inline'>\frac{5}{12}</code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{9}{5} - \frac{1}{2}</code></p>
<p>a) Draw a picture to show that <code class='latex inline'>\frac{2}{5} \times \frac{3}{8} = \frac{6}{40}</code>.</p><p>b) List two other pairs of fractions with a product of <code class='latex inline'>\frac{6}{40}</code>.</p>
<p>Choose two fractions to make each statement true.</p><p>The sum is less than the product. </p>
<p>Tai calculated <code class='latex inline'>3\frac{1}{3} \times 4\frac{3}{8}</code>. He multiplied the whole number parts together and then multiplied the fraction parts together. He got an incorrect product of <code class='latex inline'>12 \frac{3}{24}</code>.</p><p>a) Why would estimation not help Tai realize that he had made a mistake?</p><p>b) How could you show Tai that his answer is incorrect?</p>
<p>Which quotients are <code class='latex inline'>1\frac{1}{4}</code>? How do you know?</p><p><code class='latex inline'>\frac{3}{5}\div\frac{3}{4}</code></p>
<p>About <code class='latex inline'>\frac{3}{4}</code> of the students in the drama club are girls. About <code class='latex inline'>\frac{3}{4}</code> of these girls are in Grade 8. What fraction of the students in the drama club are Grade 8 girls?</p>
<p>Find the fraction that is halfway between each pair of numbers. Use a number line if it helps. </p><p><code class='latex inline'>0</code> and <code class='latex inline'>1</code></p>
<p>Calculate.</p><p><code class='latex inline'>\frac{5}{8}+\frac{1}{3}</code></p>
<p>Printers print at different rates. How many pages does each printer print per minute?</p><p>20 pages in <code class='latex inline'>1\frac{1}{3}</code> min</p>
<p>Each fraction below is <code class='latex inline'>\displaystyle \frac{2}{3} </code> of another fraction. What is the other fraction?</p><p><code class='latex inline'>\displaystyle \frac{6}{15} </code></p>
<p>Andrea&#39;s bedroom is <code class='latex inline'>1\frac{1}{3}</code> times as long as Kit’s bedroom and <code class='latex inline'>1 \frac{2}{3}</code> times as wide. What fraction of the area of Kit’s bedroom is the area ofAndrea’s bedroom?</p>
<p>Calculate each quotient using equivalent fractions. </p><p><code class='latex inline'>2\frac{1}{2}\div\frac{3}{8}</code></p>
<p>Which quotients are <code class='latex inline'>1\frac{1}{4}</code>? How do you know?</p><p><code class='latex inline'>\frac{5}{2}\div\frac{1}{2}</code></p>
<p>Jeff painted <code class='latex inline'>1\frac{3}{4}</code> walls in the computer room. How many walls does he still have to paint if the computer room has 4 walls?</p>
<p>Which quotients are greater than 2? Calculate these quotients only.</p><p><code class='latex inline'>\frac{7}{8}\div\frac{1}{3}</code></p>
<p>Draw each rectangle on grid paper. Use the rectangle to find each product.</p><p><code class='latex inline'>\frac{5}{6} \times \frac{1}{2}</code></p><img src="/qimages/23010" />
<p>Timo says that you can divide <code class='latex inline'>\frac{15}{16}\div\frac{3}{4}</code> by calculating <code class='latex inline'>\frac{15\div3}{16\div4}</code>.</p><p>a) Do you agree with Timo?</p><p>b) Does Timo&#39;s method work with other fractions?</p>
<p>How much greater is the first shaded fraction than the second shaded fraction?</p><img src="/qimages/9649" />
<p>Draw a fraction strip model to show the number of times <code class='latex inline'>\frac{1}{4}</code> fits into <code class='latex inline'>\frac{7}{8}</code>. </p>
<p> How does the product of two fractions less than 1 compare with the two fractions being multiplied? Is the product greater than, less than, or equal to each fraction? How do you know?</p>
<p>Fabienne said that she now understands why she needs to multiply the numerator and denominator of a fraction by the same amount to get an equivalent fraction. Explain her reasoning, shown below. </p><p><code class='latex inline'>\displaystyle \frac{3}{5} \times 1=\frac{3}{5} </code></p><p><code class='latex inline'>\displaystyle 1=\frac{2}{2} </code></p><p><code class='latex inline'>\displaystyle \frac{3}{5} \times \frac{2}{2}=\frac{3}{5} </code></p><p><code class='latex inline'>\displaystyle \frac{3 \times 2}{5 \times 2}=\frac{3}{5} </code></p>
<p>What is the value of each expression?</p><p><code class='latex inline'>\frac{3}{8}</code> of <code class='latex inline'>\frac{8}{9}</code></p>
<p>Why might using a diagram to calculate <code class='latex inline'>\frac{1}{3}</code> of <code class='latex inline'>\frac{3}{5}</code> be better than multiplying <code class='latex inline'>0.333 33...</code> by <code class='latex inline'>0.6</code>?</p>
<p>Calculate. </p><p><code class='latex inline'>\frac{5}{6}\div\frac{1}{6}</code></p>
<p>What section of the fraction strip tower shows each value?</p><p><code class='latex inline'>\displaystyle \frac{4}{5}</code> of <code class='latex inline'>\frac{1}{2} </code></p>
<p>Calculate. </p><p><code class='latex inline'>\frac{1}{5}\div\frac{2}{5}</code></p>
<p>Sketch a model, and calculate the answer. </p><p><code class='latex inline'>7\frac{3}{10}-2\frac{1}{4}</code></p>
<img src="/qimages/9654" /><p>Which section of the fraction strip tower shows each value?</p><p>a) <code class='latex inline'>\displaystyle \frac{2}{3} </code> of <code class='latex inline'>\displaystyle \frac{3}{7} </code></p><p>b) <code class='latex inline'>\displaystyle \frac{1}{3} </code> of <code class='latex inline'>\displaystyle \frac{2}{3} </code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{10}{3} - \frac{3}{4}</code></p>
<p>What division expression does this picture represent?</p><img src="/qimages/25785" />
<p>Fredreka wrote <code class='latex inline'>\frac{2}{5}</code> of her report in 1 h. How much time will she need to complete the entire report at this rate?</p>
<p>The fraction below is written as the sum of two unit fractions. Are they correct? How do you know?</p><p><code class='latex inline'>\frac{5}{12} = \frac{1}{3} + \frac{1}{4}</code></p>
<p>This picture models a fraction of a fraction. Complete the sentence: <code class='latex inline'>\bigcirc</code> of <code class='latex inline'>\bigcirc</code> is<code class='latex inline'>\bigcirc</code>.</p><img src="/qimages/9656" />
<p><code class='latex inline'>\frac{2}{12}</code> of the container is filled with water. How much more of the container must be filled so that only <code class='latex inline'>\displaystyle \frac{1}{4} </code> is empty?</p>
<p>Order the fractions in each set from least to greatest. </p><p><code class='latex inline'>\displaystyle\frac{5}{2}, \frac{6}{3}, \frac{7}{4}</code></p>
<p>Order the fractions in each set from least to greatest. </p><p><code class='latex inline'>\displaystyle\frac{7}{10}, \frac{6}{8}, \frac{3}{5}</code></p>
<p>Draw each rectangle on grid paper. Use the rectangle to find each product.</p><p><code class='latex inline'>\frac{2}{5} \times \frac{1}{2}</code></p><img src="/qimages/23009" />
<p>Which answer is closest to <code class='latex inline'>\frac{1}{2}</code> ? How close is it?</p><p>A. <code class='latex inline'>\displaystyle \frac{3}{4}-\frac{2}{10} </code></p><p>C. <code class='latex inline'>\displaystyle \frac{1}{3}+\frac{1}{5}+\frac{1}{10} </code></p><p>B. <code class='latex inline'>\displaystyle \frac{4}{5}-\frac{1}{3}+\frac{1}{15} </code></p><p>D. <code class='latex inline'>\displaystyle \frac{2}{9}+\frac{1}{6}+\frac{1}{3} </code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{7}{2} - \frac{3}{5}</code></p>
<p>Write each fraction as the difference of two proper fractions with different denominators. </p><p><code class='latex inline'>\frac{1}{10}</code></p>
<p>Which quotients are greater than 2? Calculate these quotients only.</p><p><code class='latex inline'>\frac{8}{9}\div\frac{3}{4}</code></p>
<p>Sketch a model, and calculate the answer. </p><p><code class='latex inline'>2\frac{4}{5}+3\frac{1}{2}</code></p>
<p>Which difference is greater?</p><p><code class='latex inline'>\displaystyle \begin{array}{llllllll} &(a) \phantom{.} 5 \frac{1}{3} - 4\frac{1}{2} &(b) \phantom{.} 6 \frac{1}{2} - 3\frac{2}{9} \end{array} </code></p>
<p> Matthew’s bed takes up <code class='latex inline'>\frac{1}{3}</code> of the width of his bedroom and <code class='latex inline'>\frac{3}{5}</code> of the length. What fraction of the area of the floor does Matthew’s bed take up?</p>
<p>What is the value of each expression?</p><p><code class='latex inline'>\frac{1}{5}</code> of <code class='latex inline'>\frac{1}{2}</code></p>
<p>Sketch an appropriate fraction strip, and shade the fraction <code class='latex inline'>\frac{4}{11}</code>. Then use your sketch to show the expression.</p><p><code class='latex inline'>\displaystyle \frac{1}{4} </code> of <code class='latex inline'>\displaystyle \frac{4}{11} </code></p>
<p>Aviv cut out the ads on 5 pages of a newspaper. He discovered that when he put the ads together, they filled <code class='latex inline'>1 \frac{1}{3}</code> pages. How many pages would the non-advertising parts of these pages fill if Aviv put them together?</p>
<p>Shakira says that <code class='latex inline'>0.4\div0.08</code> is <code class='latex inline'>\frac{1}{10}</code> of <code class='latex inline'>4\div8</code>. Do you agree? Explain.</p>
<p>What is the missing fraction in each sentence?</p><p><code class='latex inline'>\square</code> of <code class='latex inline'>\displaystyle \frac{5}{6} </code> is <code class='latex inline'>\displaystyle \frac{1}{12} </code></p>
<p>Alana is cooking a turkey. It take <code class='latex inline'>4\frac{1}{2}</code>h to cook. She check it every 20 mins, or <code class='latex inline'>\frac{1}{3}</code>h. How many times will she check it before it is cooked?</p>
<p>Find the fraction that is halfway between each pair of numbers. Use a number line if it helps. </p><p><code class='latex inline'>\displaystyle\frac{3}{2}</code> and <code class='latex inline'>2</code></p>
<p>What is the missing fraction in each sentence?</p><p><code class='latex inline'>\displaystyle \frac{5}{12} </code> is <code class='latex inline'>\displaystyle \frac{1}{2} </code> of <code class='latex inline'>\square</code></p>
<p>This circle graph shows the number of sports programs that students participate in.</p><img src="/qimages/9650" /><p>a) What fraction of students participate in one or more programs?</p><p>b) What fraction of students participate in more than one program?</p>
<p> Mei used a number line to model each calculation. Explain how you know that her model is correct.</p><p><code class='latex inline'>\displaystyle 2 \frac{1}{3} + 3 \frac{1}{6} = 5 \frac{1}{2} </code></p><img src="/qimages/9652" />
<p>Write each fraction as the difference of two proper fractions with different denominators. </p><p><code class='latex inline'>\frac{1}{6}</code></p>
<p>Jeff added two fractions. Lydia subtracted the same two fractions. Jeff’s answer was <code class='latex inline'>\frac{3}{4}</code> greater than Lydia&#39;s. What could the fractions be?</p>
<p>Calculate. </p><p><code class='latex inline'>6\frac{1}{4}-3\frac{5}{6}</code></p>
<p>Draw each rectangle on grid paper. Use the rectangle to find each product.</p><p><code class='latex inline'>\frac{4}{5} \times \frac{3}{4}</code></p><img src="/qimages/23012" />
<p>This picture models a fraction of a fraction. Complete the sentence: <code class='latex inline'>\bigcirc</code> of <code class='latex inline'>\bigcirc</code> is<code class='latex inline'>\bigcirc</code>.</p><img src="/qimages/9655" />
<p>The result when Tamara divided <code class='latex inline'>1</code> by <code class='latex inline'>\frac{2}{3}</code> was the reciprocal of <code class='latex inline'>\frac{2}{3}</code>. What happens when you multiply <code class='latex inline'>\frac{2}{3}</code> by its reciprocal?</p>
<p>Calculate. </p><p><code class='latex inline'>\frac{1}{2}\div\frac{1}{3}</code></p>
<p>The fraction below is <code class='latex inline'>\frac{2}{3}</code> of another fraction. What is the other fraction?</p><p><code class='latex inline'>\displaystyle \frac{2}{7} </code></p>
<p>One store offers a discount of 20% on a price. Another store offers a <code class='latex inline'>\frac{1}{3}</code> discount on the same price. What fraction of the higher sale price is the lower sale price?</p>
<p>In each pair, which fraction is greater? How do you know?</p><p><code class='latex inline'>\displaystyle\frac{1}{2}, \frac{2}{3}</code></p>
<p>What multiplication expression does this model represent?</p><img src="/qimages/9663" />
<p>Subtract.</p><p><code class='latex inline'>\frac{5}{3} - \frac{2}{6}</code></p>
<p>Explain how you know that <code class='latex inline'>\frac{2}{3}</code> of <code class='latex inline'>\frac{4}{5}</code> is the same as each expression below.</p><p>twice as much as <code class='latex inline'>\frac{1}{3}</code> of <code class='latex inline'>\frac{4}{5}</code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{7}{4} - \frac{3}{5}</code></p>
<p>What section of the fraction strip tower shows each value?</p><p><code class='latex inline'>\displaystyle \frac{1}{3}</code> of <code class='latex inline'>\frac{1}{4} </code></p>
<p>This year, <code class='latex inline'>\frac{3}{5}</code> of the students in Fiona’s class are girls. Fiona notices that <code class='latex inline'>\frac{2}{3}</code> of these girls wear braces. Only <code class='latex inline'>\frac{1}{2}</code> of the boys wear braces. </p><p>What fraction of all the students in Fiona’s class wear braces?</p>
<p>Calculate each quotient using equivalent fractions. </p><p><code class='latex inline'>1\frac{3}{4}\div\frac{5}{6}</code></p>
<p>Use each digit from 1 to 4 once to make this equation true.</p><p><code class='latex inline'>\displaystyle \frac{\bigcirc}{6} + \frac{\bigcirc}{5} + \frac{\bigcirc}{\bigcirc} = \frac{49}{30} </code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{7}{2} - \frac{5}{4}</code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{3}{4} - \frac{3}{5}</code></p>
<p>Sketch an appropriate fraction strip, and shade the fraction <code class='latex inline'>\frac{4}{11}</code>. Then use your sketch to show the expression.</p><p><code class='latex inline'>\displaystyle \frac{1}{2} </code> of <code class='latex inline'>\displaystyle \frac{4}{11} </code></p>
<p>What is the value of each expression?</p><p><code class='latex inline'>\frac{4}{6}</code> of <code class='latex inline'>\frac{1}{2}</code></p>
<p>Calculate. </p><p><code class='latex inline'>\frac{7}{8}\div\frac{1}{3}</code></p>
<p>The fraction below is written as the sum of two unit fractions. Are they correct? How do you know?</p><p><code class='latex inline'>\frac{7}{12} = \frac{1}{2} + \frac{1}{6}</code></p>
<p>Calculate. </p><p><code class='latex inline'>\frac{3}{8}\div\frac{2}{9}</code></p>
<p>Calculate.</p><p><code class='latex inline'>\frac{2}{5}-\frac{1}{10}</code></p>
<p>What is the missing fraction in each sentence?</p><p><code class='latex inline'>\displaystyle \frac{2}{12} </code> is <code class='latex inline'>\displaystyle \frac{1}{4} </code> of <code class='latex inline'>\square</code></p>
<p>Calculate each quotient using equivalent fractions. </p><p><code class='latex inline'>5\div\frac{1}{3}</code></p>
<p>In each pair, which fraction is greater? How do you know?</p><p><code class='latex inline'>\displaystyle\frac{1}{4}, \frac{1}{3}</code></p>
<p>What section of the fraction strip tower shows each value?</p><p><code class='latex inline'>\displaystyle \frac{1}{2}</code> of <code class='latex inline'>\frac{1}{6} </code></p>
<p>Draw a circle. Show that </p><p><code class='latex inline'> \frac{1}{2} </code> of <code class='latex inline'>\frac{1}{2}</code> of <code class='latex inline'>\frac{1}{2}</code> is <code class='latex inline'>\frac{1}{8}</code>.</p>
<p>How can you calculate <code class='latex inline'>\frac{3}{5}\div\frac{1}{2}</code> using equivalent fractions with a common denominator?</p>
<p>What multiplication expression does this model represent?</p><img src="/qimages/9662" />
<p>This week. Anita spent <code class='latex inline'>3 \frac{1}{2}</code> h practising the piano. She also spent <code class='latex inline'>6 \frac{1}{4}</code> h at soccer practice and <code class='latex inline'>4 \frac{1}{3}</code> h on the telephone.</p><p>a) How much time. in total. did Anita spend on the piano and at soccer?</p><p>b) How much more time did Anita spend at soccer than on the phone?</p>
<p>Write each fraction as the sum of two different unit fractions. </p><p><code class='latex inline'>\frac{3}{4}</code></p>
<p>A large popcorn bag holds four times as much as a small popcorn bag. At the end of a party, <code class='latex inline'>3 \frac{1}{3}</code> small bags and <code class='latex inline'>2 \frac{1}{4}</code> large bags were left. </p><p>a) How many small bags would be leftover popcorn fill?</p><p>b) How many large bags would the leftover popcorn fill?</p>
<p>Sketch a model for this calculation.</p><p><code class='latex inline'>\frac{3}{4}\times\frac{2}{5}=\frac{6}{20}</code></p>
<p>The values of a, b, and c are all improper fractions. What could the values be?</p><p><code class='latex inline'>\displaystyle a \times b \times c = \frac{14}{3} </code></p>
<p>Calculate. </p><p><code class='latex inline'>\frac{3}{4}\div6</code></p>
<p>Calculate. </p><p><code class='latex inline'>\frac{5}{8}\div\frac{3}{4}</code></p>
<p>a) Calculate the sum of <code class='latex inline'>\frac{3}{5}</code> and <code class='latex inline'>\frac{2}{3}</code>. </p><p>b) Calculate the difference of <code class='latex inline'>\frac{3}{5}</code> and <code class='latex inline'>\frac{2}{3}</code>. </p><p>c) How much greater is the sum than the difference?</p>
<p>Four students added <code class='latex inline'>\frac{3}{4} + \frac{5}{6}</code> and got these answers:</p><p><code class='latex inline'>\displaystyle \frac{38}{24}, 1 \frac{14}{24}, 1 \frac{7}{12}, </code> and <code class='latex inline'>\displaystyle \frac{19}{12} </code>.</p><p>a) Are they all correct? How do you know?</p><p>b) Which answer is in simplest form?</p>
<p>Calculate. </p><p><code class='latex inline'>\frac{3}{9}\div\frac{2}{9}</code></p>
<p>a) Calculate <code class='latex inline'>0.4 \times 0.3</code>.</p><p>b) Rename each decimal as a fraction, and multiply. What do you notice?</p>
<p>a) What is the probability of landing in the red A section.</p><img src="/qimages/9665" /><p>b) Why does it make sense that the probability is <code class='latex inline'>\frac{1}{2} \times \frac{1}{3}</code>?</p>
<p>If Kyle divides <code class='latex inline'>4\frac{2}{3}</code> by a fraction less than 1, the answer is a whole number. List three possible fractions. </p>
<p>Explain why you can calculate <code class='latex inline'>2\div\frac{2}{3}</code> using each method below. Use the Communication Checklist and the picture to help you.</p><img src="/qimages/25791" /><p>Divide equivalent fractions with the same denominator.</p>
<p>The fraction below is <code class='latex inline'>\frac{2}{3}</code> of another fraction. What is the other fraction?</p><p><code class='latex inline'>\displaystyle \frac{1}{4} </code></p>
<p>Add.</p><p><code class='latex inline'>\frac{5}{4} + \frac{3}{5} + \frac{1}{6}</code></p>
<p>Eileen used to be on the phone <code class='latex inline'>3\frac{1}{2}</code> times as much as her sister every day. As a New Year&#39;s resolution, she decided to cut down to about <code class='latex inline'>\frac{2}{5}</code> of the time she used to be on the phone. About how many times as much as her sister is Eileen now on the phone? </p>
<p>Which products are greater than <code class='latex inline'>\frac{1}{2}</code>?</p><p>a) <code class='latex inline'>\frac{3}{4}\times\frac{5}{6}</code></p><p>b) <code class='latex inline'>\frac{1}{6}\times\frac{7}{8}</code></p><p>c) <code class='latex inline'>\frac{3}{9}\times\frac{8}{9}</code></p><p>d) <code class='latex inline'>\frac{3}{5}\times\frac{2}{3}</code></p>
<p>Calculate. </p><p><code class='latex inline'>\frac{3}{8}\div\frac{1}{2}</code></p>
<p>David multiplied <code class='latex inline'>3 \frac{1}{5}</code> by another mixed number. The product was a whole number. What are two possibilities for the mixed number?</p>
<p>Which section of the fraction strip tower shows each value? <code class='latex inline'>\displaystyle \frac{1}{3} </code> of <code class='latex inline'>\displaystyle \frac{2}{3} </code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{11}{12} - \frac{5}{6}</code></p>
<p>A pail of water was <code class='latex inline'>\frac{1}{4}</code> full. Kassia added some water until the pail was <code class='latex inline'>\frac{2}{3}</code> full. How much water did she add? Express your answer as afraction ofthe total capacity of the pail.</p>
<p>One fraction divides into another fraction <code class='latex inline'>3\frac{1}{3}</code> times. list two possible pairs of fractions. </p>
<p>The fraction below is written as the sum of two unit fractions. Are they correct? How do you know?</p><p><code class='latex inline'>\frac{5}{6} = \frac{1}{3} + \frac{1}{3}</code></p>
<p>Every ratio can be described as a fraction. Why can you describe the ratio of the can sizes as any of the following?</p><p><code class='latex inline'>3:2</code></p><p><code class='latex inline'>1:\frac{2}{3}</code></p><p><code class='latex inline'>\frac{3}{2}:1</code></p>
<p>Calculate. </p><p><code class='latex inline'>5\frac{1}{2}-3\frac{1}{3}</code></p>
<p>The fraction below is written as the sum of two unit fractions. Are they correct? How do you know?</p><p><code class='latex inline'>\frac{11}{8} = \frac{1}{2} + \frac{1}{9}</code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{7}{10} - \frac{1}{2}</code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{7}{8} - \frac{3}{4}</code></p>
<p>Mirim is making <code class='latex inline'>3 \frac{1}{2}</code> dozen cookies. If <code class='latex inline'>\frac{2}{7}</code> of the cookies have icing, how many dozen cookies have icing?</p>
<p>The fraction below is written as the sum of two unit fractions. Are they correct? How do you know?</p><p><code class='latex inline'>\frac{2}{5} = \frac{1}{3} + \frac{1}{15}</code></p>
<p>Which expression has the greatest value? How do you know?</p><p>a) <code class='latex inline'>\frac{4}{5}\times\frac{2}{3}-\frac{1}{5}\times\frac{5}{8}</code></p><p>b) <code class='latex inline'>\frac{4}{5}\times(\frac{2}{3}-\frac{1}{5})\times\frac{5}{8}</code></p><p>c) <code class='latex inline'>(\frac{4}{5}\times\frac{2}{3}-\frac{1}{5})\times\frac{5}{8}</code></p>
<p>The fraction below is written as the sum of two unit fractions. Are they correct? How do you know?</p><p><code class='latex inline'>\frac{4}{15} = \frac{1}{5} + \frac{1}{15}</code></p>
<p>a) Why can you calculate 60% of 1.5 by multiplying <code class='latex inline'>\frac{3}{5}\times\frac{3}{2}</code>?</p><p>b) Which calculation do. you find easier? Why?</p>
<p>Add.</p><p><code class='latex inline'>\frac{7}{10} + \frac{7}{5} + \frac{7}{2}</code></p>
<p>Jake mowed about <code class='latex inline'>\frac{3}{5}</code> of the school lawn yesterday. He mowed another <code class='latex inline'>\frac{1}{4}</code> of the lawn this morning. How much is left to mow?</p>
<p>a) How does this picture show that</p><p><code class='latex inline'>\displaystyle \frac{1}{2} </code> of <code class='latex inline'>\displaystyle \frac{3}{4} </code> is <code class='latex inline'>\displaystyle \frac{3}{8} </code> ?</p><img src="/qimages/9657" /><p> Draw a picture to show that <code class='latex inline'>\displaystyle \frac{3}{4} </code> of <code class='latex inline'>\displaystyle \frac{1}{2} </code></p>
<p>Two students, George and Mason, worked on a project. </p><p>George worked for <code class='latex inline'>3\frac{2}{3}</code>h.</p><p>Mason worked for <code class='latex inline'>2\frac{4}{5}</code>h</p><p>What was the total time spent on the project?</p>
<p>Subtract.</p><p><code class='latex inline'>\frac{13}{6} - \frac{8}{12}</code></p>
<p>Calculate. </p><p><code class='latex inline'>3\frac{1}{5}\times6\frac{3}{8}</code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{7}{5} - \frac{4}{10}</code></p>
<p>Explain how you know that <code class='latex inline'>\frac{2}{3}</code> of <code class='latex inline'>\frac{4}{5}</code> is the same as each expression below.</p><p>four times as much as <code class='latex inline'>\frac{1}{3}</code> of <code class='latex inline'>\frac{6}{7}</code></p>
<p>In each pair, which fraction is greater? How do you know?</p><p><code class='latex inline'>\displaystyle\frac{3}{4}, \frac{5}{8}</code></p>
<p>What is the missing fraction in each sentence?</p><p><code class='latex inline'>\bigcirc</code> is <code class='latex inline'>\frac{1}{4}</code> of <code class='latex inline'>\frac{2}{5}</code> .</p>
<p>How do you know that dividing by <code class='latex inline'>\frac{1}{6}</code> is the same as multiplying by 6?</p>
<p>Calculate. </p><p><code class='latex inline'>\frac{4}{5}\div\frac{2}{3}</code></p>
<p>Write each fraction as the difference of two proper fractions with different denominators. </p><p><code class='latex inline'>\frac{3}{4}</code></p>
<p>Jasleen goes to bed 3 h after dinner. Yesterday, she spent <code class='latex inline'>1 \frac{1}{2}</code> h on her homework and <code class='latex inline'>\frac{2}{3}</code> h on the telephone after dinner. How much time did she have left before bedtime?</p>
<p>Subtract.</p><p><code class='latex inline'>\frac{7}{8} - \frac{1}{3}</code></p>
<p>How does this picture show that <code class='latex inline'>\frac{2}{3}</code> of <code class='latex inline'>\frac{1}{2}</code> is <code class='latex inline'>\frac{1}{3}</code>?</p><img src="/qimages/9658" />
<p>Choose two fractions to make each statement true.</p><p>The sum is greater than the product. </p>
<p>Calculate. </p><p><code class='latex inline'>2\frac{1}{2}\div\frac{2}{3}</code></p>
<p>Which quotients are greater than 1?</p><p>i) <code class='latex inline'>\frac{3}{5}\div\frac{2}{3}</code></p><p>ii) <code class='latex inline'>\frac{9}{2}\div\frac{5}{6}</code></p><p>iii) <code class='latex inline'>\frac{3}{7}\div\frac{1}{8}</code></p><p>b) How could you have predicted the answer to part (a) without calculating the quotients?</p>
<p>Write each fraction as the sum of two different unit fractions. </p><p><code class='latex inline'>\frac{7}{10}</code></p>
<p>Use the fractions <code class='latex inline'>\displaystyle\frac{19}{10}, \frac{11}{3}, \frac{9}{4}</code></p><p>Order the fractions from least to greatest. </p>
<p>What division expression does each picture represent?</p><img src="/qimages/25787" />
<p>Choose two fractions to make each statement true.</p><p>The quotient is greater than the sum.</p>
<p>Write each fraction as a fraction of another fraction (not 1).</p><p>a) <code class='latex inline'>\displaystyle \frac{1}{5} </code></p><p>b) <code class='latex inline'>\displaystyle \frac{2}{8} </code></p><p>c) <code class='latex inline'>\displaystyle \frac{5}{12} </code></p><p>d) <code class='latex inline'>\displaystyle \frac{3}{7} </code></p>
<p>Which quotients are greater than 2? Calculate these quotients only.</p><p><code class='latex inline'>3\frac{1}{3}\div\frac{4}{5}</code></p>
<p>What is the missing fraction in each sentence?</p><p><code class='latex inline'>\square</code> of <code class='latex inline'>\displaystyle \frac{4}{9} </code> is <code class='latex inline'>\displaystyle \frac{1}{3} </code></p>
<p>Draw a picture to show that <code class='latex inline'>\frac{2}{3}</code> of <code class='latex inline'>1 \frac{1}{2}</code> is <code class='latex inline'>1</code>.</p>
<p>Why does it make sense that <code class='latex inline'>\frac{7}{8}\div\frac{3}{4}</code> is greater than <code class='latex inline'>\frac{7}{8}</code>?</p>
<p>About <code class='latex inline'>\frac{2}{11}</code> of Canadian downhill skiers are from British Columbia. Recall that about <code class='latex inline'>\frac{1}{10}</code> of Canadians downhill ski. What fraction of all Canadian downhill skiers are from British Columbia?</p>
<p>Which quotients are <code class='latex inline'>1\frac{1}{4}</code>? How do you know?</p><p><code class='latex inline'>\frac{3}{4}\div\frac{3}{5}</code></p>
<p>Calculate.</p><p><code class='latex inline'>\frac{2}{5}+\frac{1}{7}</code></p>
<p>Order the fractions in each set from least to greatest. </p><p><code class='latex inline'>\displaystyle\frac{10}{3}, \frac{7}{5}, \frac{13}{6}</code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{13}{6} - \frac{2}{5}</code></p>
<p>A sports store placed an order for shoes. Three-eighths of the order was basketball shoes; one quarter was running shoes, and the rest were golf shoes. </p><p>What fraction of the order was golf shoes?</p>
<p>Calculate each quotient using equivalent fractions. </p><p><code class='latex inline'>\frac{3}{5}\div\frac{5}{6}</code></p>
<p>What is the missing fraction in each sentence?</p><p><code class='latex inline'>\frac{2}{3}</code> is <code class='latex inline'>\bigcirc</code> of <code class='latex inline'>\frac{3}{4}</code> .</p>
<p>Draw a model to show each calculation. Then determine the sum or difference.</p><p><code class='latex inline'>\displaystyle 2 - \frac{3}{4} </code></p>
<p>A recipe calls for <code class='latex inline'>1\frac{2}{3}</code> cups of flour and <code class='latex inline'>\frac{3}{4}</code> cup of sugar. These are the only dry ingredients. What is the total measure of the dry ingredients?</p>
<p>What is the missing fraction in each sentence?</p><p><code class='latex inline'>\displaystyle \frac{2}{5} </code> is <code class='latex inline'>\displaystyle \frac{2}{3} </code> of <code class='latex inline'>\square</code></p>
<p>How did dividing each whole strip into fourths help you solve the problem?</p>
<p>Where can you place brackets to make this equation true?</p><p><code class='latex inline'>\frac{3}{5}+\frac{1}{4}\div\frac{2}{3}+\frac{1}{3}=\frac{193}{120}</code></p>
<p>How can Jordan&#39;s strategy be used to show that a fraction divided by <code class='latex inline'>\frac{2}{3}</code> is the product of this fraction and <code class='latex inline'>\frac{3}{2}</code>? Use examples to support your explanation. </p>
<p>Mereille showed that <code class='latex inline'>\frac{6}{5}\times10\frac{1}{2}</code> equals <code class='latex inline'>10\frac{1}{2}+2\frac{1}{10}</code>. Complete her explanation. </p><img src="/qimages/25793" />
<p>Sketch a model and calculate. </p><p><code class='latex inline'>\frac{3}{5}-\frac{2}{7}</code></p>
<p>What is the missing fraction in each sentence?</p><p><code class='latex inline'>\displaystyle \frac{3}{8} </code> is <code class='latex inline'>\displaystyle \frac{3}{4} </code> of <code class='latex inline'>\square</code></p>
<p>In each pair, which fraction is greater? How do you know?</p><p><code class='latex inline'>\displaystyle\frac{1}{2}, \frac{2}{5}</code></p>
<p>Calculate.</p><p><code class='latex inline'>\frac{5}{9}-\frac{2}{7}</code></p>
<p>How could you solve the problem using equivalent fractions for <code class='latex inline'>4</code> and <code class='latex inline'>\frac{3}{4}</code>, and then dividing the numerators?</p>
<p>Find the fraction that is halfway between each pair of numbers. Use a number line if it helps. </p><p><code class='latex inline'>1</code> and <code class='latex inline'>2</code></p>
<p>Find the fraction that is halfway between each pair of numbers. Use a number line if it helps. </p><p><code class='latex inline'>\displaystyle\frac{1}{2}</code> and <code class='latex inline'>1</code></p>
<p>Write each fraction as the difference of two proper fractions with different denominators. </p><p><code class='latex inline'>\frac{1}{4}</code></p>
<p>More than <code class='latex inline'>\frac{3}{4}</code> of Americans eat ice cream at least once a month. About <code class='latex inline'>\frac{3}{10}</code> of these people eat vanilla ice cream.</p><p>a) What fraction of Americans eat vanilla ice cream at least once a month?</p><p>b) According to recent statistics, there are about 300 million Americans. About how many of them eat vanilla ice cream at least once a month?</p>
<p>Add.</p><p><code class='latex inline'>\frac{5}{6} + \frac{4}{5} + \frac{4}{3}</code></p>
<p>Calculate.</p><p><code class='latex inline'>\frac{7}{8}-\frac{2}{3}</code></p>
<p>What section of the fraction strip tower shows each value?</p><p><code class='latex inline'>\displaystyle \frac{3}{4}</code> of <code class='latex inline'>\frac{4}{9} </code></p>
<p>Find the fraction that is halfway between each pair of numbers. Use a number line if it helps. </p><p><code class='latex inline'>0</code> and <code class='latex inline'>\displaystyle\frac{1}{2}</code></p>
<p>The highest point in Alberta is Mount Columbia. Mount Columbia is about <code class='latex inline'>\displaystyle 4 \frac{3}{5} </code> times as high as the highest point in New Brunswick, Mount Carleton. Mount Carleton is about <code class='latex inline'>\displaystyle 5 \frac{3}{4} </code> times as high as the highest point in Prince Edward Island. Compare the height of Mount Columbia with the height of the highest point in Prince Edward Island.</p>
<img src="/qimages/83427" /><p>Each picture models a fraction of a fraction. Complete this sentence for each picture: <code class='latex inline'>\displaystyle \square </code> of <code class='latex inline'>\displaystyle \square </code> is \square.</p><img src="/qimages/83428" />
<p>Subtract.</p><p><code class='latex inline'>\frac{2}{3} - \frac{7}{12}</code></p>
<p>Use fractions to explain why <code class='latex inline'>4.5\times0.5</code> equals <code class='latex inline'>2.25</code>. </p>
<p>What is the missing fraction in each sentence?</p><p><code class='latex inline'>\square</code> of <code class='latex inline'>\displaystyle \frac{1}{2} </code> is <code class='latex inline'>\displaystyle \frac{1}{8} </code></p>
<p>To calculate <code class='latex inline'>7 \frac{1}{8} - 2\frac{2}{3}</code>, Lee added <code class='latex inline'>\frac{1}{3}</code> to <code class='latex inline'>4 \frac{1}{8}</code>. Why do you think that Lee did this?</p>
<p>Use words and these pictures to explain why <code class='latex inline'>\frac{3}{5}</code> of <code class='latex inline'>\frac{2}{3}</code> is the same as <code class='latex inline'>\frac{2}{3}</code> of <code class='latex inline'>\frac{3}{5}</code>.</p><img src="/qimages/25790" />
<p>a) Complete this pattern, and continue it for three more products.</p><p><code class='latex inline'>\displaystyle 4 \times \frac{1}{2}= </code></p><p><code class='latex inline'>\displaystyle 2 \times \frac{1}{2}= </code></p><p><code class='latex inline'>\displaystyle 1 \times \frac{1}{2}= </code></p><p><code class='latex inline'>\displaystyle \frac{1}{2} \times \frac{1}{2}= </code></p><p>b) How does this pattern explain the product of <code class='latex inline'>\frac{1}{2} \times \frac{1}{2}</code>?</p>
<p>Which is easier to determine, <code class='latex inline'>\frac{1}{6}</code> of <code class='latex inline'>\frac{6}{7}</code> or <code class='latex inline'>\frac{1}{6}</code> of <code class='latex inline'>\frac{5}{7}</code>? Why?</p>
<p><code class='latex inline'>\displaystyle \frac{16}{\square} \div \frac{2}{\square}=8 </code></p><p>Explain why this is true no matter what the denominator is, as long as both denominators are the same. </p>
<p>The fraction below is <code class='latex inline'>\frac{2}{3}</code> of another fraction. What is the other fraction?</p><p><code class='latex inline'>\displaystyle \frac{2}{9} </code></p>
<p>Which quotients are <code class='latex inline'>1\frac{1}{4}</code>? How do you know?</p><p><code class='latex inline'>5\div4</code></p>
<p>Describe a situation in which you might calculate <code class='latex inline'>\frac{3}{4}</code> of <code class='latex inline'>\frac{8}{10}</code>.</p>
<p>Lynnsie has <code class='latex inline'>1\frac{1}{2}</code> large cans of paint. Each small can holds <code class='latex inline'>\frac{3}{5}</code> as much paint as a large can. How many small cans will Lynnsie be able to fill?</p>
<p>Calculate. </p><p><code class='latex inline'>\frac{1}{4}\div\frac{5}{6}</code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{5}{3} - \frac{2}{9}</code></p>
<p>What multiplication expression does this model represent?</p><img src="/qimages/9659" />
<p>Printers print at different rates. How many pages does each printer print per minute?</p><p>20 pages in <code class='latex inline'>1\frac{1}{2}</code> min</p>
<p>In each pair, which fraction is greater? How do you know?</p><p><code class='latex inline'>\displaystyle\frac{3}{4}, \frac{2}{5}</code></p>
<p>What is the missing fraction in each sentence?</p><p><code class='latex inline'>\square</code> of <code class='latex inline'>\displaystyle \frac{5}{7} </code> is <code class='latex inline'>\displaystyle \frac{3}{7} </code></p>
<p>Calculate. </p><p><code class='latex inline'>\frac{5}{8}\div\frac{1}{4}</code></p>
<p>Explain how you know that <code class='latex inline'>\frac{2}{3}</code> of <code class='latex inline'>\frac{4}{5}</code> is the same as each expression below.</p><p>twice as much as <code class='latex inline'>\frac{2}{3}</code> of <code class='latex inline'>\frac{2}{5}</code></p>
<p>The fraction below is written as the sum of two unit fractions. Are they correct? How do you know?</p><p><code class='latex inline'>\frac{7}{10} = \frac{1}{5} + \frac{1}{2}</code></p>
<p>Add.</p><p><code class='latex inline'>\frac{1}{3} + \frac{3}{4} + \frac{2}{5}</code></p>
<p>Suppose that Manuel had only <code class='latex inline'>\displaystyle \frac{3}{4} </code> of a large bag of popcorn. How would each student change his or her solution to calculate the number of small bags the popcorn would fill?</p>
<p>Subtract.</p><p><code class='latex inline'>\frac{17}{10} - \frac{5}{6}</code></p>
<p>Jim and Mike had to shovel snow from their driveway.</p><p>Jim shovelled about <code class='latex inline'>\frac{3}{10}</code> of the driveway. </p><p>Mike shovelled about <code class='latex inline'>\frac{2}{3}</code> of the driveway.</p><p>About what fraction of the driveway was cleared of snow?</p>
<p><code class='latex inline'>\frac{a}{b}</code> is a fraction. The sum of <code class='latex inline'>\frac{a}{b}</code> and <code class='latex inline'>\frac{b}{a}</code> is close to 2. List two possible possible values for <code class='latex inline'>\frac{a}{b}</code>. </p>
<p>What fraction calculation can you use to determine the number of quarters in \$4.50?</p>
<p>What multiplication expression does this model represent?</p><img src="/qimages/9660" />
<p>What division expression does each picture represent?</p><img src="/qimages/25786" />
<p>Draw each rectangle on grid paper. Use the rectangle to find each product.</p><p><code class='latex inline'>\frac{1}{2} \times \frac{3}{4}</code></p><img src="/qimages/23007" />
<p>Why did Tamara and Jordan divide by <code class='latex inline'>\frac{2}{3}</code> to solve their problems?</p>
<p>Explain how you know that <code class='latex inline'>\frac{4}{6}\div\frac{3}{6}</code> has the same quotient as <code class='latex inline'>\frac{4}{5}\div\frac{3}{5}</code>.</p>
<p>Draw each rectangle on grid paper. Use the rectangle to find each product.</p><p><code class='latex inline'>\frac{3}{4} \times \frac{2}{3}</code></p><img src="/qimages/23008" />
<p>Calculate. </p><p><code class='latex inline'>(\frac{2}{3})^3</code></p>
<p>How much greater is the first product than the second product?</p><p><code class='latex inline'>\frac{3}{4}\times\frac{5}{6}</code> than <code class='latex inline'>\frac{1}{4}\times\frac{5}{6}</code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{7}{5} - \frac{2}{3}</code></p>
<p>Sketch a model, and calculate the answer. </p><p><code class='latex inline'>8-2\frac{1}{3}</code></p>
<p>Calculate.</p><p><code class='latex inline'>\frac{3}{4}+\frac{5}{6}</code></p>
<p>A muesli recipe requires <code class='latex inline'>1\frac{1}{4}</code> cups of oatmeal. How many cups of oatmeal do you need for <code class='latex inline'>3 \frac{1}{3}</code>?</p>
<p>Calculate. </p><p><code class='latex inline'>\frac{4}{7}\div\frac{1}{10}</code></p>
<p>Calculate. </p><p><code class='latex inline'>2\frac{1}{5}+3\frac{1}{6}</code></p>
<p>In each pair, which fraction is greater? How do you know?</p><p><code class='latex inline'>\displaystyle\frac{2}{3}, \frac{3}{4}</code></p>
<p>Each car on a commuter train holds 20 people. On a particular morning. 5 cars were 90% full and 3 cars were 65% full. If the people were rearranged to fill as many cars as possible. how many cars would be filled?</p>
<p> Craig needs to measure <code class='latex inline'>2 \frac{3}{8}</code> cups. How many times must he fill a <code class='latex inline'>\frac{1}{3}</code> cup measuring cup?</p>
<p>Craig needs to measure <code class='latex inline'>3\frac{1}{3}</code> cups. How many times must he fill a <code class='latex inline'>\frac{1}{2}</code> cup measuring cup?</p>
<p>Arrange these values in order from least to greatest.</p><p>a) <code class='latex inline'>\frac{2}{3}</code> of <code class='latex inline'>\displaystyle \frac{9}{10}</code></p><p>b) <code class='latex inline'>\displaystyle \frac{3}{5} </code> of <code class='latex inline'>\frac{5}{9}</code></p><p>c) <code class='latex inline'>\displaystyle \frac{1}{3} </code> of <code class='latex inline'>\displaystyle \frac{6}{9} </code></p>
<p>How much greater is the first product than the second product?</p><p><code class='latex inline'>\frac{3}{4}\times\frac{5}{6}</code> than <code class='latex inline'>\frac{3}{4}\times\frac{1}{2}</code></p>
<p>Describe a situation in which you might add <code class='latex inline'>\displaystyle \frac{1}{3} + \frac{1}{4} + \frac{1}{2} </code>.</p>
<p>What section of the fraction strip tower shows each value?</p><p><code class='latex inline'>\displaystyle \frac{1}{6}</code> of <code class='latex inline'>\frac{1}{2} </code></p>
<p>Pia used <code class='latex inline'>\frac{2}{3}</code> of her sugar to make <code class='latex inline'>\frac{3}{4}</code> of a batch of cookies. How much of her sugar would she need to make the whole batch?</p>
<p>Calculate. </p><p><code class='latex inline'>\frac{9}{20}\div\frac{3}{5}</code></p>
<p>Calculate. </p><p><code class='latex inline'>\frac{4}{8}\div\frac{7}{8}</code></p>
<p>the highest point in Alberta is Mount Columbia. Mount Columbia is about <code class='latex inline'>4 \frac{3}{5}</code> times as high as the highest point in New Brunswick, Mount Carleton. Mount Carleton is about <code class='latex inline'>5 \frac{3}{4}</code> times as high as the highest point in Prince Edward Island. Compare the height of Mount Columbia with the height of the highest point in Prince Edward Island.</p>
<p>In each pair, which fraction is greater? How do you know?</p><p><code class='latex inline'>\displaystyle\frac{2}{5}, \frac{3}{10}</code></p>
<p>Each picture models a fraction of a fraction. Complete this sentence for each picture: <code class='latex inline'>\displaystyle \quad </code> of <code class='latex inline'>\displaystyle \quad </code> is</p><img src="/qimages/83429" />
<p>What is the missing fraction in each sentence?</p><p><code class='latex inline'>\frac{3}{8}</code> is <code class='latex inline'>\frac{3}{5}</code> of <code class='latex inline'>\bigcirc</code>.</p>
<p>A muesli recipe requires <code class='latex inline'>1\frac{1}{4}</code> cups of oatmeal. How many cups of oatmeal do you need for each number of batches?</p><p><code class='latex inline'>2 \frac{1}{2}</code> batches</p>
<p>Two fractions with different denominators are being added using this grid model. Identify the fractions, Danna and explain your reasoning.</p><img src="/qimages/9648" />
<p>At a school party, <code class='latex inline'>\frac{2}{3}</code> of the students are wearing T—shirts and <code class='latex inline'>\frac{1}{5}</code> are wearing long- sleeved shirts. Which fraction is greater? By how much is it greater?</p>
<p>Sketch a model, and calculate the answer. </p><p><code class='latex inline'>2\frac{1}{5}+3\frac{3}{5}</code></p>
<p>Teo made a video that was <code class='latex inline'>2\frac{1}{2}</code>h long. He made it by clipping together sections that were each about <code class='latex inline'>\frac{1}{3}</code>h long. </p><p>a) About how many sections did Teo clip together?</p><p>b) How do you know that the sections were not all exactly <code class='latex inline'>\frac{1}{3}</code>h long?</p>
<p>Find the fraction that is halfway between each pair of numbers. Use a number line if it helps. </p><p><code class='latex inline'>1</code> and <code class='latex inline'>\displaystyle\frac{3}{2}</code></p>
<p>Show each multiplication using a different model. Determine the product.</p><p><code class='latex inline'>\displaystyle \frac{2}{9} \times 4 \frac{1}{4} </code></p>
<p>Subtract.</p><p><code class='latex inline'>\frac{7}{2} - \frac{2}{4}</code></p>
<p>Calculate. </p><p><code class='latex inline'>1\frac{1}{5}\div\frac{2}{5}</code></p>
<p>About <code class='latex inline'>\frac{2}{5}</code> of the students in a school were invited to participate in a special Videoconferencing program. Only <code class='latex inline'>\frac{1}{3}</code> of these students brought in their permlssion forms by the first day of the program. What fraction of the students were permitted to participate in the first day of the program?</p>
<p>Kevin added two mixed numbers, <code class='latex inline'>4 \frac{\bigcirc}{\bigcirc}</code> and <code class='latex inline'>3 \frac{\bigcirc}{\bigcirc}</code>. What could the whole number part of the answer be? Why?</p>
<p>The fraction below is written as the sum of two unit fractions. Are they correct? How do you know?</p><p><code class='latex inline'>\frac{2}{15} = \frac{1}{10} + \frac{1}{30}</code></p>
<p>Calculate. </p><p><code class='latex inline'>8-1\frac{3}{5}</code></p>
<p>Add.</p><p><code class='latex inline'>\frac{5}{12} + \frac{6}{5} + \frac{3}{4}</code></p>
<p>a) Continue this addition pattern to get three more terms in each row. </p><img src="/qimages/25810" /><p><code class='latex inline'>\displaystyle \frac{4}{5}+\frac{\frac{4}{10}}{y}+\frac{4}{20} </code></p><p><code class='latex inline'>\displaystyle \frac{12}{10} \quad \frac{12}{20} \quad \frac{12}{40} \quad \ldots </code></p><p>b) What is the 10th number in the 2nd row?</p><p>c) Why does it make sense that all the numerators in the 2nd row are 12?</p>
<p>In each pair, which fraction is greater? How do you know?</p><p><code class='latex inline'>\displaystyle\frac{22}{32}</code> or <code class='latex inline'>\displaystyle\frac{43}{65}</code></p>
<p>Complete Diane&#39;s explanation for calculating <code class='latex inline'>1.2\times3.55</code>. </p><img src="/qimages/25789" />
<p> Mei used a number line to model each calculation. Explain how you know that her model is correct.</p><p><code class='latex inline'>\displaystyle 3 \frac{1}{4} - 3 \frac{1}{2} = 1 \frac{3}{4} </code></p><img src="/qimages/9653" />
<p>Calculate. </p><p><code class='latex inline'>(\frac{3}{5})^2</code></p>
<p> Jessica is awake <code class='latex inline'>\frac{2}{3}</code> of the day. She spends <code class='latex inline'>\frac{5}{8}</code> of this time at home.</p><p>a) What fraction of the day is Jessica awake at home?</p><p>b) How many hours is Jessica awake at home?</p>
<p>Calculate. </p><p><code class='latex inline'>\frac{2}{9}\times\frac{2}{7}</code></p>
<p>Which quotients are greater than 2? Calculate these quotients only.</p><p><code class='latex inline'>\frac{5}{9}\div\frac{1}{4}</code></p>
<p>Does order matter in division of fractions? For example, is <code class='latex inline'>\frac{2}{3}\div\frac{1}{5}</code> the same as <code class='latex inline'>\frac{1}{5}\div\frac{2}{3}</code>? Explain.</p>
<p>Subtract.</p><p><code class='latex inline'>\frac{8}{5} - \frac{2}{3}</code></p>
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