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All courses Math Foundations · MF.RN.1 7 of 60
Generate, compare, and simplify equivalent fractions in numeric and contextual settings.

Generate equivalent fractions

Problem
Generate \(\text{two}\) fractions equivalent to \(3/5\) using scale factors \(2\) and \(3\), in that order.
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
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Hint

Apply scale factor 2 to both numerator and denominator first, then repeat with factor 3.

Equivalent fractions are made by multiplying the numerator and denominator by the same nonzero whole number, so the value stays the same.

Solution walkthrough

01

Use the equivalence rule

\[a/b~=~(a~x~k)/(b~x~k)\]

Multiplying numerator and denominator by the same nonzero scale factor preserves a fraction's value.

02

Apply scale factor two

\[(3~x~2)/(5~x~2)~=~6/10\]

The first required scale factor is 2. Multiplying both 3 and 5 by 2 gives 6 and 10.

03

Check the first fraction

\[6/10~=~(6~/~2)/(10~/~2)~=~3/5\]

Dividing both parts of 6/10 by 2 returns the original fraction, confirming equivalence.

04

Apply scale factor three

\[(3~x~3)/(5~x~3)~=~9/15\]

The second required scale factor is 3. Multiplying numerator and denominator by 3 gives 9 and 15.

05

Check the second fraction

\[9/15~=~(9~/~3)/(15~/~3)~=~3/5\]

Dividing both parts of 9/15 by 3 returns the original fraction.

06

Give the fractions in order

\[6/10~\text{and}~9/15\]

Scale factors 2 and 3 produce 6/10 and 9/15, respectively. This matches the correct choice.

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Another way

  1. Use cross-products to check: 3 × 10 = 5 × 6 and 3 × 15 = 5 × 9.

!

Common mistake

Do not multiply only the numerator or only the denominator. The same scale factor must be applied to both parts.

Solution walkthrough video