Simplify 4 1/5-2 2/3

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

Step 1

Convert

$4 \frac{1}{5}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$4 + \frac{1}{5} - 2 \frac{2}{3}$

Add

$4$ and

$\frac{1}{5}$ .

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$4 \cdot \frac{5}{5} + \frac{1}{5} - 2 \frac{2}{3}$

Combine

$4$ and

$\frac{5}{5}$ .

$\frac{4 \cdot 5}{5} + \frac{1}{5} - 2 \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{4 \cdot 5 + 1}{5} - 2 \frac{2}{3}$

Simplify the numerator.

Multiply

$4$ by

$5$ .

$\frac{20 + 1}{5} - 2 \frac{2}{3}$

Add

$20$ and

$1$ .

$\frac{21}{5} - 2 \frac{2}{3}$

Step 2

Convert

$2 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{21}{5} - (2 + \frac{2}{3})$

Add

$2$ and

$\frac{2}{3}$ .

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{21}{5} - (2 \cdot \frac{3}{3} + \frac{2}{3})$

Combine

$2$ and

$\frac{3}{3}$ .

$\frac{21}{5} - (\frac{2 \cdot 3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$\frac{21}{5} - \frac{2 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply

$2$ by

$3$ .

$\frac{21}{5} - \frac{6 + 2}{3}$

Add

$6$ and

$2$ .

$\frac{21}{5} - \frac{8}{3}$

Step 3

To write

$\frac{21}{5}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{21}{5} \cdot \frac{3}{3} - \frac{8}{3}$

Step 4

To write

$- \frac{8}{3}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{21}{5} \cdot \frac{3}{3} - \frac{8}{3} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of

$15$ , by multiplying each by an appropriate factor of

$1$ .

Multiply

$\frac{21}{5}$ by

$\frac{3}{3}$ .

$\frac{21 \cdot 3}{5 \cdot 3} - \frac{8}{3} \cdot \frac{5}{5}$

Multiply

$5$ by

$3$ .

$\frac{21 \cdot 3}{15} - \frac{8}{3} \cdot \frac{5}{5}$

Multiply

$\frac{8}{3}$ by

$\frac{5}{5}$ .

$\frac{21 \cdot 3}{15} - \frac{8 \cdot 5}{3 \cdot 5}$

Multiply

$3$ by

$5$ .

$\frac{21 \cdot 3}{15} - \frac{8 \cdot 5}{15}$

Step 6

Combine the numerators over the common denominator.

$\frac{21 \cdot 3 - 8 \cdot 5}{15}$

Step 7

Simplify the numerator.

Multiply

$21$ by

$3$ .

$\frac{63 - 8 \cdot 5}{15}$

Multiply

$- 8$ by

$5$ .

$\frac{63 - 40}{15}$

Subtract

$40$ from

$63$ .

$\frac{23}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{15}$

Decimal Form:

$1.5\overline{3}$

Mixed Number Form:

$1 \frac{8}{15}$

Simplify 4 1/5-2 2/3

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