﻿ Renaming Fractions with a Specified Denominator
RENAMING FRACTIONS WITH A SPECIFIED DENOMINATOR
• PRACTICE (online exercises and printable worksheets)
• This page gives an in-a-nutshell discussion of the concepts.
Want more details, more exercises? Read the full text!

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
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Practice with Factors

Type in your answer as a diagonal fraction (like 2/7),
since you can't type horizontal fractions.

 (an even number, please)