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:
Question: Write [beautiful math coming... please be patient] $\,\displaystyle\frac{3}{7}\,$ with a denominator of $\,14\,$.

Solution: [beautiful math coming... please be patient] $\displaystyle\frac{3}{7} = \frac{6}{14}$

The key is to multiply by [beautiful math coming... please be patient] $\,1\,$ 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 [beautiful math coming... please be patient] $\,7\,$ be multiplied by, to get $\,14\,$?   Answer: $\,2\,$

Thus, you multiply by [beautiful math coming... please be patient] $\,1\,$ in the form of $\,\displaystyle\frac{2}{2}\,$, as shown below:

[beautiful math coming... please be patient] $\displaystyle\frac{3}{7} \ = \ \frac{3}{7}\cdot\frac{2}{2} \ = \ \frac{6}{14}$

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 $\,14\,$:

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)