Question

Name
Add and Subtrac
Finding equivalent tu
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As you work on the problem, draw a model if you
Problem
Derek and Ryan each made a 12-inch pizza. Derek cut his into 12 equal slices. Ryan also cut
his into equal slices, but he cut fewer pieces. If both boys ended up eating the same amount
of pizza and had some left over, what are some fractions that could describe how much of
their pizzas they ate? Name at least three different pairs.
Answer​

Answer 1

Answer:

1. ¹⁰/₁₂ and ⅚;

2. ⁸/₁₂ and ⁴/₆;

3. ⁶/₁₂ and ³/₆

Step-by-step explanation:

The question is asking what fractions of 12 are equivalent to fractions of some smaller number.

Derek cut his pizza into 12 slices. Let's say that Ryan cut his into 6 slices.

Scheme 1

Derek eats 10 slices, and Ryan eats 5 (Fig A )

Then Derek has eaten ¹⁰/₁₂ = ⅚ of a pizza and Ryan has eaten ⅚ of a pizza.

They each have ⅙ of a pizza left over.

The fractions here are ¹⁰/₁₂ and ⅚.

Scheme 2

Derek eats 8 slices, and Ryan eats 4 (Fig. B)

Then Derek has eaten ⁸/₁₂ = ⅔ of a pizza and Ryan has eaten ⁴/₆ = ⅔ of a pizza.

They each have ⅓ of a pizza left over.

The fractions here are ⁸/₁₂ and ⁴/₆.

Scheme 3

Derek eats 6 slices, and Ryan eats 3 (Fig. C)

Then Derek has eaten ⁶/₁₂ = ½ of a pizza and Ryan has eaten ³/₆ = ½ of a pizza.

They each have ½ of a pizza left over.

The fractions here are ⁶/₁₂ and ³/₆.