8.08 Multiply fractions and mixed numbers

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Do you remember how to multiply fractions?

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To multiply two fractions, we multiply the numerators (top numbers) to get the new numerator, and we multiply the denominators (bottom number) to get the new denominator.

When the multiplication involves one or more mixed numbers we can still use this method, but we first take one extra step to rewrite the mixed numbers as improper fractions.

For example, let's look at the product $1\frac{3}{8}\times2\frac{1}{3}$138​×213​. We start by rewriting the mixed numbers as improper fractions:

$1\frac{3}{8}\times2\frac{1}{3}$138​×213​

$=$=

$\frac{11}{8}\times\frac{7}{3}$118​×73​

Now that we have written both values as improper fractions, we can multiply them using our usual method:

$\frac{11}{8}\times\frac{7}{3}$118​×73​	$=$=	$\frac{11\times7}{8\times3}$11×78×3​
	$=$=	$\frac{77}{24}$7724​

So we have that $1\frac{3}{8}\times2\frac{1}{3}=\frac{77}{24}$138​×213​=7724​. We could also rewrite this as the mixed number $3\frac{5}{24}$3524​.

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