audio read-through 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.


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:

$$\cssId{s17}{\frac{3}{7} \ = \ \frac{3}{7}\cdot\frac{2}{2} \ = \ \frac{6}{14}}$$

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 $\,14\,$:


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


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