Multiplying mixed numbers means to convert mixed numbers into a form where multiplication is possible.

## Multiplying Fractions:

Multiplying fractions is easier than adding or subtracting. Follow this single step below:

**Step 1:** Multiply numerator to numerator and denominator to denominator.

Consider this multiplication problem

1/2 • 3/4

multiplying the numerators together, and then multiply the denominators together. So we have,

(1•3) /(2•4) = 3/8

## Multiplying Mixed Numbers:

To multiply mixed numbers convert the mixed numbers into fractions which can be proper or improper fraction:

1^{1}⁄_{2} . ^{1}/_{2}

We convert 1^{1}⁄_{2}to the improper fraction ^{3}⁄_{2}, so now have^{3}⁄_{2}•^{1}⁄_{2}=^{3}⁄_{4}

Consider another example, multiplying factors that are both mixed numbers:

3^{1}⁄_{3}• 2^{1}⁄_{2}

Again, we convert both mixed numbers to improper fractions and perform the multiplication:

^{10}⁄_{3} •^{5}⁄_{2}=^{10•5}⁄_{3•2}

= ^{50}⁄_{6}= 8^{1}⁄_{3}

## Multiplying Fractions that consist of Variables in the numerator and denominator:

We treat fractions with variables no differently than if we were working with constants—the numerators are multiplied together, and the denominators are multiplied together as shown in this example:

𝑚/𝑥 • 𝑐/𝑑 = mc/xd or cm/dx

As another example consider this problem:

m/n • 1/2

Multiplying the numerators together and the denominators, we obtain the answer:

m•1 / n •2 = 𝑚/𝑛•2

= 𝑚/2n

## Cancellation Method:

A little shortcut for how to multiply fractions is what is called “cancelling.” Watch how it works. Let’s begin with the multiplication of two fractions. We note that 5 is the greatest common factor of 5 in the numerator and 10 in the denominator. So we divide 5 into both the numerator and denominator to obtain:

Now we have simplified the problem through cross-cancelling to this:

7•1/2•4 = 7/8

By pulling out the common factors (in this case, “5”) the expression is much easier to simplify and reduce to lowest terms.

The same is true when variables are present in the fractions. Consider this multiplication problem:

𝑚/3 • 9/𝑛

We now cross-cancel in a similar manner we have final result as 3m/n

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