To add or subtract fractions, the denominators must be the same.
This lesson gives you practice renaming fractions with a desired denominator.
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 $\,14\,$:
Type in your answer as a diagonal fraction (like 2/7),
since you can't type horizontal fractions.