Simplify 4 1/5-22/3

$4 \frac{1}{5} - \frac{22}{3}$

Step 1

Convert

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

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

$4 + \frac{1}{5} - \frac{22}{3}$

Add

$4$ and

$\frac{1}{5}$ .

To write

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

$\frac{5}{5}$ .

$4 \cdot \frac{5}{5} + \frac{1}{5} - \frac{22}{3}$

Combine

$4$ and

$\frac{5}{5}$ .

$\frac{4 \cdot 5}{5} + \frac{1}{5} - \frac{22}{3}$

Combine the numerators over the common denominator.

$\frac{4 \cdot 5 + 1}{5} - \frac{22}{3}$

Simplify the numerator.

Multiply

$4$ by

$5$ .

$\frac{20 + 1}{5} - \frac{22}{3}$

Add

$20$ and

$1$ .

$\frac{21}{5} - \frac{22}{3}$

Step 2

To write

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

$\frac{3}{3}$ .

$\frac{21}{5} \cdot \frac{3}{3} - \frac{22}{3}$

Step 3

To write

$- \frac{22}{3}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{21}{5} \cdot \frac{3}{3} - \frac{22}{3} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of

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

$1$ .

Multiply

$\frac{21}{5}$ by

$\frac{3}{3}$ .

$\frac{21 \cdot 3}{5 \cdot 3} - \frac{22}{3} \cdot \frac{5}{5}$

Multiply

$5$ by

$3$ .

$\frac{21 \cdot 3}{15} - \frac{22}{3} \cdot \frac{5}{5}$

Multiply

$\frac{22}{3}$ by

$\frac{5}{5}$ .

$\frac{21 \cdot 3}{15} - \frac{22 \cdot 5}{3 \cdot 5}$

Multiply

$3$ by

$5$ .

$\frac{21 \cdot 3}{15} - \frac{22 \cdot 5}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{21 \cdot 3 - 22 \cdot 5}{15}$

Step 6

Simplify the numerator.

Multiply

$21$ by

$3$ .

$\frac{63 - 22 \cdot 5}{15}$

Multiply

$- 22$ by

$5$ .

$\frac{63 - 110}{15}$

Subtract

$110$ from

$63$ .

$\frac{- 47}{15}$

Step 7

Move the negative in front of the fraction.

$- \frac{47}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{47}{15}$

Decimal Form:

$- 3.1\overline{3}$

Mixed Number Form:

$- 3 \frac{2}{15}$

Simplify 4 1/5-22/3

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