1.10 Chapter Review
Textbook
7 Math Nelson
Chapter
Chapter 1
Section
1.10
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Solutions 20 Videos

Explain how to determine two numbers whose common multiple is 120.

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Q1

a) If Kyle has only $2 coins, $5 bills, and $20 bills, what is the least amount he can pay using only $2s, only $5s, and only $20s? What is the LCM of 2, 5, and 20?

b) What is the LCM of 2, 3, and 9?

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Q2

Show at least one method you can use to list the common factors of 128 and 192.

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Q3

The number 272 is a multiple of 16. Explain how to use this information to determine the GCF of 16 and 272.

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Q4

a) Draw a factor rainbow for each number.

i) 4 ii) 9 iii) 16 iv) 25 v) 36

b) Write another number whose factor rainbow will have a similar shape to those in part a). Explain your thinking.

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Q5

Find a number that has these properties. Show your work or give a reason for your answer.

a number that is divisible by 2 and 3 and is greater than 100

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Q6a

Find a number that has these properties. Show your work or give a reason for your answer.

a number that has only 2 factors and is between 90 and 100

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Q6b

Find a number that has these properties. Show your work or give a reason for your answer.

a number that can be divided by 2 three times in a row with no remainder, has 5 as a factor, and is greater than 40

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Q6c

Calculate 2^5 without using a calculator.

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Q7a

Explain how you know that 2^{10} is twice 2^9.

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Q7b

If 9 is a factor of a number, explain why 3 is also a factor.

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Q8a

Explain why 3 is a factor of 3^{10}.

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Q8b

The number 3^{12} is equal to 531 441. Explain how to use this answer to calculate 3^{11}.

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Q8c

On Monday, Zach sends an e-mail message to 4 friends. On Tuesday, each of these friends forwards the message to 4 people. On Wednesday, each of these people forwards the message to 4 other people.

a) How many people were sent the message on Wednesday? Explain how you know.

b) Show how to use powers to describe the number of messages sent on Wednesday.

c) How many people will be sent the message on Sunday if this daily process of forwarding continues? Explain your reasoning.

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Q9

Winnie used her calculator to calculate the square root of a number. She then found the square root of the number displayed. The calculator then showed 3. What number did Winnie first enter into her calculator? Explain your reasoning.

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Q10

A rectangular ice rink measures 25 m by 64 m. What are the dimensions of a square with the same area? Show the steps you used.

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Q11

Use the rules for order of operations to evaluate each expression. Show your steps.

2\times5+5\div1+10^2

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Q12a

Use the rules for order of operations to evaluate each expression. Show your steps.

5+(5-1)^2+5\times3

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Q12b

Use the rules for order of operations to evaluate each expression. Show your steps.

2^2+120\div2\div2\div2

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Q12c

What is the last digit of 445^{12}? Explain how you know.

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Q13