Section B Practice Problems

Problem 1

Pens are sold in packages of 5 and also in packages of 6.

  1. Jada wants to buy 60 pens for her class. Which packages of pens and how many should Jada buy if she doesn't want any extras? Explain or show your reasoning.
  2. Han wants to buy 55 pens for his class. Which packages of pens and how many should Han buy? Explain or show your reasoning.
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Solution
  1. Sample responses:
    • 10 packages of 6 pens, because 10× 6=6010 \times 6 = 60. That is fewer packages than 12 packages of 5.
    • 12 packages of 5 pens, because her classmates are seated in groups of 5.
  2. Sample responses:
    • 11 packages of 5 pens, because 11× 5=55.11 \times 5 = 55.
    • 10 packages of 6 pens because 10× 6=6010 \times 6 = 60. He will have 5 extra pens.

Problem 2

  1. Find the factor pairs of 36.
  2. How many factors does 36 have?
  3. List the factors of 15.
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Solution
  1. 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6 
  2. 9
  3. 1, 3, 5, 15

Problem 3

Select all numbers that are multiples of 8.

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Solution
A,C,F,H

Problem 4

  1. List the multiples of 2 from 1 to 30.
  2. List the multiples of 3 from 1 to 30.
  3. What do you notice about the numbers in the two lists?
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Solution
  1. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
  2. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
  3. Sample responses:
    • Each multiple of 3 is greater than the multiple of 2 in the same position on the list.
    • Some numbers are on both lists.
    • Every third number on the list of multiples of 2 is the same as every second number on the list of multiples of 3.

Problem 5

Which number(s) from 1 to 100 have the most factors? Explain or show how you know.

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Solution

The numbers 60, 72, 84, 90, and 96 all have 12 factors each. For example, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.