﻿ Renaming Fractions with a Specified Denominator
RENAMING FRACTIONS WITH A SPECIFIED DENOMINATOR

by Dr. Carol JVF Burns (website creator)
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• PRACTICE (online exercises and printable worksheets)
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To add or subtract fractions, the denominators must be the same.
This lesson gives you practice renaming fractions with a desired denominator.

EXAMPLE:
Question: Write $\,\displaystyle\frac{3}{7}\,$ with a denominator of $\,14\,$.

Solution: $\displaystyle\frac{3}{7} = \frac{6}{14}$

The key is to multiply by $\,1\,$ in the correct way!
Multiplying a number by $\,1\,$ just changes the name of the number (not where it lives on a number line)!

The original denominator is $\,7\,$; the desired denominator is $\,14\,$.
What must $\,7\,$ be multiplied by, to get $\,14\,$?   Answer: $\,2\,$

Thus, you multiply by $\,1\,$ in the form of $\,\displaystyle\frac{2}{2}\,$, as shown below:

$\displaystyle\frac{3}{7} \ = \ \frac{3}{7}\cdot\frac{2}{2} \ = \ \frac{6}{14}$

The fraction $\displaystyle\,\frac{6}{14}\,$ is just a different name for the number $\,\displaystyle\frac 3 7\,$ (and it's a better name for some situations)!

So, here's the thought process for writing $\displaystyle\frac 37\,$ with a denominator of $\,14\,$:

• What must $\,7\,$ (the original denominator) be multiplied by to get $\,14\,$? Answer: $\,2\,$
• If the denominator gets multiplied by $\,2\,$, the numerator must also be multiplied by $\,2\,$.
Thus, the ‘net effect’ is to multiply the number by $\,1\,$ (which only changes the name, not the number).
• Thus: $\displaystyle\,\frac 37 =\frac{3\cdot 2}{7\cdot 2} = \frac{6}{14}\,$

Master the ideas from this section