# Multiplication of integers by a fraction and a mixed number - Examples, Exercises and Solutions

Multiplying a whole number by a fraction and a mixed number is solved in the following steps:

The first step:

Convert each whole number and mixed number into a similar fraction and rewrite the problem.

The second stage:

Multiply the numerators and the denominators separately.

The multiplication of numerators will be written in the new numerator.

The multiplication of denominators will be written in the new denominator.

## Practice Multiplication of integers by a fraction and a mixed number

### Exercise #1

$4.1\cdot1.6\cdot3.2+4.7=\text{?}$

### Step-by-Step Solution

We convert decimal numbers into mixed fractions:

$4\frac{1}{10}\times1\frac{6}{10}\times3\frac{2}{10}+4\frac{7}{10}=$

Now, we convert mixed fractions into simple fractions:

$\frac{41}{10}\times\frac{16}{10}\times\frac{32}{10}+\frac{47}{10}=$

We solve the exercise from left to right:

$\frac{41\times16}{10\times10}=\frac{656}{100}$

Now we get the exercise:

$\frac{656}{100}\times\frac{32}{10}+\frac{47}{10}=$

We solve the multiplication exercise:

$\frac{656\times32}{100\times10}=\frac{20,992}{1,000}$

Now we get the exercise:

$\frac{20,992}{1,000}+\frac{47}{10}=$

We multiply the fraction on the right so that its denominator is also 1000:

$\frac{47\times100}{10\times100}=\frac{4,700}{1,000}$

We get the exercise:

$\frac{20,992}{1,000}+\frac{4,700}{1,000}=\frac{20,992+4,700}{1,000}=\frac{25,692}{1,000}$

We convert the simple fraction into a decimal number:

$\frac{25,692}{1,000}=25.692$

25.692

### Exercise #2

$2\times\frac{5}{7}=$

### Video Solution

$1\frac{3}{7}$

### Exercise #3

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

### Video Solution

$1\frac{1}{2}$

### Exercise #4

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

### Video Solution

$2\frac{2}{3}$

### Exercise #5

$6\times\frac{3}{4}=$

### Video Solution

$4\frac{1}{2}$

### Exercise #1

$7\times\frac{2}{5}=$

### Video Solution

$2\frac{4}{5}$

### Exercise #2

$3\times\frac{6}{7}=$

### Video Solution

$2\frac{4}{7}$

### Exercise #3

Solve:

$7\times\frac{3}{8}=$

### Video Solution

$2\frac{5}{8}$

### Exercise #4

$8\times\frac{1}{2}=$

### Video Solution

$4$

### Exercise #5

$3\times\frac{8}{12}=$

### Video Solution

$2$

### Exercise #1

$8\times\frac{5}{9}=$

### Video Solution

$4\frac{4}{9}$

### Exercise #2

$3\times1\frac{1}{2}=$

### Video Solution

$4\frac{1}{2}$

### Exercise #3

$3\times1\frac{1}{3}=$

### Video Solution

$4$

### Exercise #4

$2\times2\frac{1}{3}=$

### Video Solution

$4\frac{2}{3}$

### Exercise #5

$4\times1\frac{1}{5}=$

### Video Solution

$4\frac{4}{5}$