# Multiplying Fractions with Whole Numbers (Mixed Fractions)

To multiply two or more mixed fractions, we have to start by converting the mixed fractions to improper fractions. Then, we simply multiply the numerators and denominators separately. Finally, we simplify the resulting fraction if possible.

Here, we will learn to multiply mixed fractions step by step. In addition, we will solve some practice problems to apply everything learned.

##### ARITHMETIC

Relevant for

Learning to multiply two or more mixed fractions.

See steps

##### ARITHMETIC

Relevant for

Learning to multiply two or more mixed fractions.

See steps

## Steps to multiply mixed fractions

Mixed fractions are fractions that are made up of a fractional part and a whole number part. On the other hand, improper fractions only have the fractional part.

Mixed fractions can be converted to improper fractions and vice versa. Therefore, we follow the steps below to multiply mixed fractions:

Step 1: Convert the mixed fractions to improper fractions.

To convert mixed fractions to improper fractions, we multiply the integer part by the denominator and add the result to the numerator.

Step 2: Multiply the numerators.

Step 3: Multiply the denominators.

Step 4: Simplify the resulting fraction if possible.

## Multiplying mixed fractions – Examples with answers

The steps used to multiply mixed fractions seen above are used to solve the following examples. Try to solve the problems before looking at the solution.

### EXAMPLE 1

Solve the multiplication of fractions $latex 1\frac{1}{2}\times \frac{1}{3}$.

Step 1: Convert the first mixed fraction to improper fraction:

$$1\frac{1}{2}\times \frac{1}{3}$$

$$=\frac{3}{2}\times \frac{1}{3}$$

Step 2: Multiplying the numerators, we have:

$$=\frac{3\times 1}{2\times 3}$$

$$=\frac{3}{2\times 3}$$

Step 3: Multiplying the denominators, we have:

$$=\frac{3}{6}$$

Step 4: We can simplify by dividing by 3:

$$=\frac{1}{2}$$

### EXAMPLE 2

Find the product of the multiplication $latex 2\frac{2}{3}\times 1\frac{1}{5}$.

Step 1: We convert both mixed fractions to improper fractions:

$$2\frac{2}{3}\times 1\frac{1}{5}$$

$$=\frac{8}{3}\times \frac{6}{5}$$

Step 2: By multiplying the numerators, we have:

$$=\frac{8\times 6}{3\times 5}$$

$$=\frac{48}{3\times 5}$$

Step 3: By multiplying the denominators, we have:

$$=\frac{48}{15}$$

Step 4: We divide by 3 to simplify and then convert to a mixed fraction:

$$=\frac{16}{5}$$

$$=3\frac{1}{5}$$

### EXAMPLE 3

Solve the multiplication of fractions $latex 1\frac{4}{5}+3\frac{1}{7}$.

Step 1: We convert both mixed fractions to improper fractions:

$$1\frac{4}{5}\times 3\frac{1}{7}$$

$$=\frac{9}{5}\times \frac{22}{7}$$

Step 2: Multiplying the numerators, we have:

$$=\frac{9\times 22}{5\times 7}$$

$$=\frac{198}{5\times 7}$$

Step 3: Multiplying the denominators, we have:

$$=\frac{198}{35}$$

Step 4: Converting to a mixed fraction, we have:

$$=5\frac{23}{35}$$

### EXAMPLE 4

Solve the multiplication of mixed fractions $latex \frac{1}{4}\times 1\frac{1}{2} \times \frac{1}{3}$.

Step 1: Convert the mixed fraction to an improper fraction:

$$\frac{1}{4}\times 1\frac{1}{2} \times \frac{1}{3}$$

$$=\frac{1}{4}\times \frac{3}{2} \times \frac{1}{3}$$

Step 2: By multiplying the numerators, we have:

$$=\frac{1\times 3 \times 1}{4\times 2 \times 3}$$

$$=\frac{3}{4\times 2 \times 3}$$

Step 3: By multiplying the denominators, we have:

$$=\frac{3}{24}$$

Step 4: We can simplify by dividing by 3:

$$=\frac{1}{8}$$

### EXAMPLE 5

Find the product of the mixed fractions $latex 1\frac{2}{3}\times \frac{3}{4}\times 2\frac{1}{5}$.

Step 1: We convert both mixed fractions to improper fractions:

$$1\frac{2}{3}\times \frac{3}{4}\times 2\frac{1}{5}$$

$$=\frac{5}{3}\times \frac{3}{4}\times \frac{11}{5}$$

Step 2: Multiplying the numerators, we have:

$$=\frac{5\times 3 \times 11}{3\times 4 \times 5}$$

$$=\frac{165}{3\times 4 \times 5}$$

Step 3: Multiplying the denominators, we have:

$$=\frac{165}{60}$$

Step 4: We simplify by dividing by 15 and converting to a mixed fraction:

$$=\frac{11}{4}$$

$$=2\frac{3}{4}$$

### EXAMPLE 6

Solve the multiplication of fractions $latex 2\frac{3}{4} \times 1\frac{2}{3}\times 1\frac{2}{5}$.

Step 1: We convert the mixed fractions to improper fractions:

$$2\frac{3}{4}\times 1\frac{2}{3}\times 1\frac{2}{5}$$

$$=\frac{11}{4}\times \frac{5}{3}\times \frac{7}{5}$$

Step 2: By multiplying the numerators, we have:

$$=\frac{11\times 5 \times 7}{4\times 3 \times 5}$$

$$=\frac{385}{4\times 3 \times 5}$$

Step 3: By multiplying the denominators, we have:

$$=\frac{385}{60}$$

Step 4: We can simplify by dividing by 5 and converting to a mixed fraction:

$$=\frac{77}{12}$$

$$=6\frac{5}{12}$$

## Multiplying mixed fractions – Practice problems

Apply everything you have learned about the multiplication of mixed fractions to solve the following practice problems.