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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
Starting with 3/5, make one equivalent fraction using scale factor 2 and another using scale factor 3. Write them in that order.
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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 equivalent-fraction rule

\[\frac{3}{5}=\frac{3\times~n}{5\times~n}\)~\text{for}~\text{any}~\text{nonzero}~\text{whole}~\text{number}~\(n\]

Equivalent fractions are made by multiplying the numerator and denominator by the same whole number. That keeps the value of \(\frac{3}{5}\) the same.

02

Make one equivalent fraction with 2

\[\frac{3}{5}\times\frac{2}{2}=\frac{6}{10}\]

Since \(\frac{2}{2}=1\), multiplying by it does not change the value. It only changes the form, so \(\frac{3}{5}\) becomes \(\frac{6}{10}\).

03

Make a second equivalent fraction with 3

\[\frac{3}{5}\times\frac{3}{3}=\frac{9}{15}\]

Again, \(\frac{3}{3}=1\), so the fraction keeps the same value. Multiplying both parts by 3 gives another equivalent fraction, \(\frac{9}{15}\).

04

State the two fractions

\[\text{Two}~\text{fractions}~\text{equivalent}~\text{to}~\(\frac{3}{5}\)~\text{are}~\(\frac{6}{10}\)~\text{and}~\(\frac{9}{15}\).\]

The problem asks for two examples, and both answers were made by multiplying the top and bottom of \(\frac{3}{5}\) by the same number.

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Another way

  1. Verify by simplifying 6/10 by 2 and 9/15 by 3; both return to 3/5.

!

Common mistake

A common mistake is to add the same number to the numerator and denominator, like changing \(\frac{3}{5}\) into \(\frac{5}{7}\). That changes the value. To make an equivalent fraction, you must multiply both the numerator and denominator by the same whole number.