How do you write fractions with a common denominator?

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How do you write fractions with a common denominator?

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Answer 1 · 2014-11-17T04:06:59

To write fractions with a common denominator, you will most likely need to scale some numbers up! I will explain how.

Let's try it with the fractions $\frac{2}{3}$ $2/3$ and $\frac{3}{12}$ $3/12$

12 is larger than 3, so we will have to multiply the 3 by some number to equal 12. (We are really finding the Least Common Multiple of the two denominators!) To do this, you have to multiply the 3 by 4, because 3x4=12. But now the numerator doesn't match the denominator. When you scale the denominator up, you have to scale the numerator up too! So the 2 must be multiplied by 4 also.

Now you have the following: $\frac{8}{12}$ $8/12$ and $\frac{3}{12}$ $3/12$

These fractions now have common denominators! Now they're all set for adding or subtracting fractions.

Try another: $\frac{2}{6}$ $2/6$ and $\frac{3}{5}$ $3/5$ : The least common multiple of 6 and 5 is 30. (the product of the denominators)

Transform each fraction by multiplying by "1":
$\frac{2}{6} \cdot \frac{5}{5}$ $2/6*5/5$ = $\frac{10}{30}$ $10/30$ and $\frac{3}{5} \cdot \frac{6}{6}$ $3/5*6/6$ = $\frac{18}{30}$ $18/30$

One last problem: $\frac{4}{9}$ $4/9$ and $\frac{7}{6}$ $7/6$ What is the least common multiple of 9 and 6? Could you use 54? Absolutely, but it is not the LEAST number that you could use. How about 18? YES!

$\frac{4}{9} \cdot \frac{2}{2}$ $4/9*2/2$ = $\frac{8}{18}$ $8/18$ and $\frac{7}{6} \cdot \frac{3}{3}$ $7/6*3/3$ = $\frac{21}{18}$ $21/18$ Ready to go...

Hope this helped!

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How do you write fractions with a common denominator?

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