Renaming Fractions with a Specified Denominator

To add or subtract fractions, the denominators must be the same.

This lesson gives you practice renaming fractions with a desired denominator.

Example

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:

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: $\displaystyle\,\frac 37 =\frac{3\cdot 2}{7\cdot 2} = \frac{6}{14}\,$

Practice