zMath 160  - Unit 2: Rational Numbers, GCF, and LCM

Rational Numbers


1)

Complete. Write the answer as a fraction using the form in the example. Example: two-thirds is written as 2/3.


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2)

Complete.


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3)

Complete.


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4)

Complete.


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5)

Complete.


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Greatest Common Factor (GCF)


6)

Find the GCF for 20 and 25.


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7)

Find the GCF for 27 and 36.


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8)

Find the GCF for 15 and 22.


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9)

Find the GCF for 42 and 56.


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10) Use the distributive property to show the GCF of 36 + 8.

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11)

Use the distributive property to show the GCF of 60 + 96.


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12)

Solve 7 (5 – 3)


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13)

Solve 2 (5 + 8)


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14) For her birthday party, Tausha is preparing bags of treats to share with her friends. She has 18 candy bars and 12 packs of gum. Tausha wants to use all of her candy and gum. What is the greatest number of bags of treats that Tausha can make if each of the bags has the same number of candy bars and packs of gum in it? How many candy bars and how many packs of gum will be in each bag? Explain how you found the answer.

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Least Common Multiple (LCM)

15)

Find the LCM for 6 and 4.


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16)

Find the LCM for 12 and 18.


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17)

Find the LCM for 6 and 8.


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18)

Find the LCM for 16 and 20.


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19)

Eggs can be packaged 12 (1 dozen) to a carton while English muffins are generally sold in packages of 8. How many of each would you buy to make egg muffin sandwiches (1 egg per muffin) so that you would use the same number of eggs and muffins with no extra eggs or muffins left over. Explain how you solved the problem.


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Review


20)

List the prime numbers between 20 and 50. There are seven.


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21)

Let’s examine division by zero. What do you think the solution to this division problem is? Explain how you solved it. You can check your answer by multiplying by the divisor, which in this case is 0, and then comparing it to the dividend which is 8.


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22)

Evaluate. 5-cubed


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23)

Evaluate. 12-squared


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24)

Evaluate.  27


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25)

Evaluate.  7 × (5 – 3) + 62


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26)

Evaluate.  8 – 15 ÷ 5 × 2


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27)

I am a counting number. All three of my digits are even and different. The sum of my digits is 12. The product of my digits is less than 40. The sum of my hundred’s digit, plus my one’s digit, is less than my ten’s digit. Who am I?


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28)

Anna is shopping. She found three shirts that she wants to purchase, each costing $8.99. There is no tax on clothing in her state. Approximately how much money does Anna need to purchase the shirts?


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29)

Fill in the diamond with <, >, or = to make the sentence true. 


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