# Multiplying Mixed Numbers

You can multiply Mixed numbers in few simple steps.

## Step by step guide to multiply mixed numbers

1. Convert the mixed numbers to improper fractions. (improper fraction is a fraction in which the top number is bigger than bottom number). $$a \ \frac{c}{ \color{ blue }{b} }= a \ \color{blue}{+} \ \frac{c}{\color{ blue }{b}}=\frac{a \color{ blue }{b} \ \color{blue}{+} \ c}{ \color{ blue }{b} }$$
2. Multiply fractions and simplify if necessary.

### Example 1:

Multiply mixed numbers. $$2 \ \frac{1}{4} \ \times \ 3 \ \frac{1}{2}=$$

Converting mixed numbers to fractions, $$2 \ \frac{1}{4}=\frac{9}{4}$$ and $$3 \ \frac{1}{2}=\frac{7}{2}$$.
$$\frac{9}{4} \ \times \ \frac{7}{2}$$,

Applying the fractions rule for multiplication, $$\frac{9 \ \times \ 7}{4 \ \times \ 2}=\frac{63}{8}=7 \ \frac{7}{8}$$

### Example 2:

Multiply mixed numbers. $$5 \ \frac{2}{3} \ \times \ 3 \ \frac{3}{4}=$$

Converting mixed numbers to fractions, $$\frac{17}{3} \ \times \ \frac{15}{4}$$,

Applying the fractions rule for multiplication, $$\frac{17 \ \times \ 15}{3 \ \times \ 4}=\frac{255}{12}=21 \ \frac{1}{4}$$

### Example 3:

Multiply mixed numbers. $$3 \ \frac{2}{3} \ \times \ 2 \ \frac{1}{2}=$$

Converting mixed numbers to fractions, $$3 \ \frac{2}{3}=\frac{11}{3}$$ and $$2 \ \frac{1}{2}=\frac{5}{2}$$.
$$\frac{11}{3}×\frac{5}{2}$$,

Applying the fractions rule for multiplication, $$\frac{11×5}{3×2}=\frac{55}{6}=9 \ \frac{1}{6}$$

### Example 4:

Multiply mixed numbers. $$4 \ \frac{3}{5} \ \times \ 2 \ \frac{1}{3}=$$

Converting mixed numbers to fractions, $$\frac{23}{5}×\frac{7}{3}$$,

Applying the fractions rule for multiplication, $$\frac{23×7}{5×3}=\frac{161}{15}=10 \ \frac{11}{15}$$

## Exercises

### Find each product.

• $$\color{blue}{1\frac{2}{3} \times 1\frac{1}{4}}$$
• $$\color{blue}{1\frac{3}{5} \times 1\frac{2}{3}}$$
• $$\color{blue}{1\frac{2}{3} \times 3\frac{2}{7}}$$
• $$\color{blue}{4\frac{1}{8} \times 1\frac{2}{5}}$$
• $$\color{blue}{2\frac{2}{5} \times 3\frac{1}{5}}$$
• $$\color{blue}{1\frac{1}{3} \times 1\frac{2}{3}}$$

• $$\color{blue}{2\frac{1}{12}}$$
• $$\color{blue}{2\frac{2}{3}}$$
• $$\color{blue}{5\frac{10}{21}}$$
• $$\color{blue}{5\frac{31}{40}}$$
• $$\color{blue}{7\frac{17}{25}}$$
• $$\color{blue}{2\frac{2}{9}}$$