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In step 3, how did the fractions come to multiplying with those particular numbers?

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- MHB
- Thread starter bobisaka
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View attachment 9462

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MHB

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The denominator of the first fraction is $6$ and the of the second one it is $9$. We expand both fractions to make their denominators the same as the least common denominator.

The Least Common Multiple of $6$ and $9$ is $18$. It holds that $6\cdot 3=18$ and $9\cdot 2=18$. Therefore we expand the first fraction by $3$ : $\frac{11}{6}=\frac{11\cdot 3}{6\cdot 3}=\frac{33}{18}$ and the second fraction by $2$: $\frac{7}{9}=\frac{7\cdot 2}{9\cdot 2}=\frac{14}{18}$.

Now we can do the subtraction by subtracting the numerators: $$\frac{11}{6}-\frac{7}{9}=\frac{33}{18}-\frac{14}{18}=\frac{19}{18}$$

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