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Jenny completed four-fifths of her summer reading assignment. Her classmate Antonio completed seven-eighths of his assignment, and classmate Jerry completed three-fourths of his assignment. Which student read the least? Which student read the most? Which student fell in the middle? (Show all work.)

User Latkin
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Answer:

Jerry, Antonio, Jenny

Explanation:

To solve this, we can represent the numbers as fractions, make them have one common denominator, and go from there

First, we can represent these as fractions:

Jenny:

four-fifths = 4/5

Antonio:

seven-eighths = 7/8

Jerry:

three-fourths = 3/4

Next, we can find the lowest common multiple. We can do this by listing the multiples of each number until something is in common for all 3

4:

4, 8, 12, 16, 20, 24, 28 ,32, 36, 40, 44, 48

8:

8, 16, 24, 32, 40, 48, 56, 64

5:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

One number that is in common is 40.

Our next step is to find out what we need to multiply each number by to equal 40. We can do this via division.

4:

40/4 = 10

8:

40/8 = 5

5:

40/5 = 8

Next, we can multiply the numerator and denominator by the same number, essentially multiplying it by 1. For example, 4/5 * 5/5 = 20/25, which is still equal to 4/5 because 5/5 = 1 and multiplying any number by 1 keeps it the same.

3/4 * 10/10 = 30/40

7/8 * 5/5 = 35/40

4/5 * 8/8 = 32/40

We can see that 3/4 (Jerry) is the lowest, 7/8 (Antonio) is the highest, and 4/5 (Jenny) is in the middle

User Harish Ganesan
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