Now You Try

<p>Find each product or quotient. Express your answers in lowest terms.</p><p><code class='latex inline'>\displaystyle \frac{5}{12} \times \frac{3}{10} </code></p>

<p> Find each difference.</p><p><code class='latex inline'>
\displaystyle
-\frac{2}{3} + (- \frac{3}{4})
</code></p>

<p>Choose two fractions to make each statement true.</p><p>The sum is less than the product. </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 each product or quotient. Express your answers in lowest terms.</p><p><code class='latex inline'>\displaystyle 2 \frac{7}{8} \times 6 \frac{1}{2} </code></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>Express each rational number in decimal form.</p><p><code class='latex inline'>\displaystyle \frac{2}{5} </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>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>Five friends shared two pizzas. Fran ate <code class='latex inline'>\displaystyle \frac{1}{3} </code> of a pizza, Abdul ate <code class='latex inline'>\displaystyle \frac{3}{8} </code> of a pizza, Hannah ate <code class='latex inline'>\displaystyle \frac{1}{4} </code> of a pizza, and Siva ate <code class='latex inline'>\displaystyle \frac{1}{2} </code> of a pizza. What fraction of the pizza remains for Brad?</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>Name the coordinates of the points graphed on each number line.</p><img src="/qimages/24102" />

<p>Use a diagram to show which fraction is greater. Describe the pattern in the two fractions being compared. Make a general statement about the pattern and which fraction is greater.</p><p><code class='latex inline'>\displaystyle \frac{4}{5}</code> or <code class='latex inline'>\displaystyle \frac{5}{6}</code></p>

<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>Evaluate.</p><p><code class='latex inline'>
\displaystyle
-\frac{5}{6} \times \frac{3}{10}
</code></p>

<p>Find each sum.</p><p><code class='latex inline'>
\displaystyle
-\frac{2}{3} + \frac{3}{8}
</code></p>

<p>Find the least common denominator for the fractions in each set. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle \frac{1}{4}, \frac{5}{6} </code></p>

<p>Explain how the diagram illustrates the fact that <code class='latex inline'>
\displaystyle
\frac{2}{3} \times \frac{3}{4} = \frac{1}{2}
</code></p><img src="/qimages/1651" />

<p>Use a diagram to show which fraction is greater. Describe the pattern in the two fractions being compared. Make a general statement about the pattern and which fraction is greater.</p><p><code class='latex inline'>\displaystyle \frac{2}{3}</code> or <code class='latex inline'>\displaystyle \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>Seismology An earthquake of magnitude <code class='latex inline'>\displaystyle 7.7 </code> occurred in 2001 in Gujarat, India. It was about 4900 times as strong as the greatest earthquake ever to hit Pennsylvania. What is the magnitude of the Pennsylvania earthquake? (Hint: Refer to the Richter scale on page 453.)</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'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>Find each product.</p><p><code class='latex inline'>(\frac{3}{7})(\frac{3}{7})</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>Find each sum.</p><p><code class='latex inline'>
\displaystyle
-\frac{1}{2} + (-\frac{1}{2})
</code></p>

<p>Choose two fractions to make each statement true.</p><p>The sum is greater than the product. </p>

<p>Choose two fractions to make each statement true.</p><p>The quotient is greater than the sum.</p>

<p>Find each product.</p><p><code class='latex inline'>(-\frac{8}{9})(\frac{9}{8})</code></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>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>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>How can Jordan'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>Express each rational number in decimal form.</p><p><code class='latex inline'>\displaystyle \frac{-12}{5} </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>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>

<p>Express each rational number in decimal form.</p><p><code class='latex inline'>\displaystyle -\frac{7}{10} </code></p>

<p>Evaluate.</p><p><code class='latex inline'>
\displaystyle
(-\frac{5}{12}) \div (-\frac{3}{8})
</code></p>

<p> Find each difference.</p><p><code class='latex inline'>
\displaystyle
(-\frac{4}{5}) - (-\frac{3}{10})
</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>In each part, decide which rational number is not equivalent to the others.</p><p><code class='latex inline'>\displaystyle -0.5, \frac{1}{-2}, \frac{-1}{-2}, \frac{-1}{2} </code></p>

<p>Why did Tamara and Jordan divide by <code class='latex inline'>\frac{2}{3}</code> to solve their problems?</p>

<p>Find the least common denominator for the fractions in each set. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle \frac{1}{5}, \frac{3}{10} </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>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>Half of a number, decreased by <code class='latex inline'>\displaystyle \frac{3}{4} </code>, gives <code class='latex inline'>\displaystyle \frac{7}{12} . </code> What is the number?</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> Find each difference.</p><p><code class='latex inline'>
\displaystyle
(-\frac{1}{4}) - \frac{1}{6}
</code></p>

<p>Find each sum or difference. Express your answers in lowest terms.</p><p><code class='latex inline'>
\begin{array}{lllll}
a) & \frac{3}{10}+ \frac{9}{10} &&b) & \frac{3}{8} + \frac{1}{4} \\
c) & \frac{5}{6} &&d) & 1\frac{7}{9} - \frac{2}{5}
\end{array}
</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>Find each sum.</p><p><code class='latex inline'>
\displaystyle
\frac{1}{7} + (-\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>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{4}{10}+\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>How does the pattern, <code class='latex inline'>\frac{1}{9}, \frac{2}{9}, \frac{3}{9}</code>, change if the denominator is 99?</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>In each part, decide which rational number is not equivalent to the others.</p><p><code class='latex inline'>\displaystyle \frac{3}{4}, 0.75, \frac{-3}{4}, \frac{-3}{-4} </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>In each part, decide which rational number is not equivalent to the others.</p><p><code class='latex inline'>\displaystyle -2.5,-2 \frac{1}{2}, \frac{-5}{2}, \frac{5}{2} </code></p>

<ol>
<li>Measurement The height of a triangle is <code class='latex inline'>\displaystyle 2 \mathrm{~m} </code> more than the base. The area is <code class='latex inline'>\displaystyle 17.5 \mathrm{~m}^{2} </code>. Find the length of the base.</li>
</ol>

<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>Find the least common denominator for the fractions in each set. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle \frac{3}{4}, \frac{5}{8}, \frac{1}{16} </code></p>

<p>Find each product or quotient. Express your answers in lowest terms.</p><p><code class='latex inline'>\displaystyle \frac{2}{9} \div 2 \frac{2}{7} </code></p>

<p>The top floor of an apartment building has eight apartments. Each of the other floors below it has <code class='latex inline'>1\frac{1}{2}</code> times as many apartments as the floor above. Use a diagram and a numeric representation to help determine the maximum number of floors that this building can have.</p>

<p>Express the fractions <code class='latex inline'>\frac{1}{9}, \frac{2}{9}, \frac{3}{9}</code>, and so on as decimals. Describe the pattern.</p>

<p>Evaluate.</p><p><code class='latex inline'>
\displaystyle
(-\frac{1}{8}) \times \frac{6}{11}
</code></p>

<p>Find each product or quotient. Express your answers in lowest terms.</p><p><code class='latex inline'>\displaystyle \left(\frac{3}{4} \div \frac{2}{3}\right) </code></p>

<p>Find the least common denominator for the fractions in each set. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle \frac{5}{6}, \frac{1}{2}, \frac{2}{9} </code></p>

<p>Find each sum.</p><p><code class='latex inline'>
\displaystyle
-\frac{2}{3} + (-\frac{3}{4})
</code></p>

<p>Think About a Plan An earthquake of magnitude <code class='latex inline'>\displaystyle 9.1 </code> occurred in 2004 in the Indian Ocean near Indonesia. It was about 74,900 times as strong as the greatest earthquake ever to hit Texas. Find the magnitude of the Texas earthquake. (Remember that an increase of <code class='latex inline'>\displaystyle 1.0 </code> on the Richter scale means an earthquake is 30 times stronger.)</p>
<ul>
<li><p>Can you write an exponential or logarithmic equation?</p></li>
<li><p>How does the solution of your equation help you find the magnitude?</p></li>
</ul>

<p> Find each difference.</p><p><code class='latex inline'>
\displaystyle
\frac{3}{8} - \frac{5}{6}
</code></p>

<p>Find the least common denominator for the fractions in each set. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle \frac{1}{3}, \frac{4}{5}, \frac{7}{12} </code></p>

<p>The gold content of jewelry is given in karats. For example, 24-karat gold is pure gold, and 18-karat gold is <code class='latex inline'>\frac{18}{24}</code> or <code class='latex inline'>0.75</code> gold. </p><p>If a piece of jewelry is <code class='latex inline'>\frac{2}{3}</code> gold, how would you describe it using karats?</p>

<p>Evaluate.</p><p><code class='latex inline'>
\displaystyle
(-\frac{1}{7}) \times (-\frac{3}{5})
</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>Use a diagram to show which fraction is greater. Describe the pattern in the two fractions being compared. Make a general statement about the pattern and which fraction is greater.</p><p><code class='latex inline'>\displaystyle \frac{1}{2}</code> or <code class='latex inline'>\displaystyle \frac{2}{3}</code></p>

<p>Express each rational number in decimal form.</p><p><code class='latex inline'>\displaystyle \frac{-35}{40} </code></p>

<p>About <code class='latex inline'>\frac{1}{3}</code> of Canadians regularly read news online. Another 12% rarely read news online. What fraction of Canadians never read news online?</p>

<p>Find the least common denominator for the fractions in each set. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle \frac{1}{10}, \frac{1}{6} </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>How did dividing each whole strip into fourths help you solve the problem?</p>

<p>How does the pattern, <code class='latex inline'>\frac{1}{9}, \frac{2}{9}, \frac{3}{9}</code>, change if the denominator is 99 999?</p>

<p>Evaluate.</p><p>a) <code class='latex inline'>\displaystyle
\frac{2}{3}- \frac{3}{4} \times \frac{1}{2}
</code></p><p>b) <code class='latex inline'>\displaystyle
(\frac{2}{3} - \frac{3}{4}) \times \frac{1}{2}
</code></p><p>c) <code class='latex inline'>\displaystyle
\frac{3}{4} - \frac{2}{3} \times \frac{1}{2}
</code></p><p>\d) <code class='latex inline'>\displaystyle
(\frac{3}{4} - \frac{2}{3}) \times \frac{1}{2}
</code></p>

<p>Evaluate.</p><p><code class='latex inline'>
\displaystyle
\frac{7}{8} \div (-\frac{5}{6})
</code></p>

<p>Use a diagram to show which fraction is greater. Describe the pattern in the two fractions being compared. Make a general statement about the pattern and which fraction is greater.</p><p><code class='latex inline'>\displaystyle \frac{3}{4}</code> or <code class='latex inline'>\displaystyle \frac{4}{5}</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>The owners of Mooses, Gooses, and Juices are considering an increase in the price of their frozen fruit smoothies. At the current price of <code class='latex inline'>\$1.75</code>, they sell on average 150 smoothies a day. Their research shows that every <code class='latex inline'>\$0.25</code> increase in the price of a smoothie will result in a decrease of 10 sales per day.</p>
<ul>
<li>Compare the rate of change of revenue when the price increases by <code class='latex inline'>\$0.25, \$0.75, \$1.00, \$1.25</code>, and <code class='latex inline'>\$1.50</code>.</li>
</ul>

<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>Which ratio is not equal to <code class='latex inline'>\frac{9}{12}</code>?</p><p>A. <code class='latex inline'>\frac{18}{24}</code></p><p>B. <code class='latex inline'>\frac{3}{4}</code></p><p>C. <code class='latex inline'>\frac{15}{20}</code></p><p>D. <code class='latex inline'>\frac{18}{27}</code></p>

<p>Find the least common denominator for the fractions in each set. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle \frac{5}{6}, \frac{7}{18} </code></p>

<p>Find the least common denominator for the fractions in each set. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle \frac{2}{3}, \frac{1}{2} </code></p>

<p>Evaluate.</p><p><code class='latex inline'>
\displaystyle
(-4\frac{2}{5}) \div (1\frac{4}{7})
</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>Perform each integer operation.</p><p><code class='latex inline'>\displaystyle -28 \div 7 </code></p>