Simplify (-4 2/5)÷3 6/7

$- 4 \frac{2}{5} \div 3 \frac{6}{7}$

Step 1

Convert

$4 \frac{2}{5}$ to an improper fraction.

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

$- (4 + \frac{2}{5}) \div 3 \frac{6}{7}$

Add

$4$ and

$\frac{2}{5}$ .

To write

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

$\frac{5}{5}$ .

$- (4 \cdot \frac{5}{5} + \frac{2}{5}) \div 3 \frac{6}{7}$

Combine

$4$ and

$\frac{5}{5}$ .

$- (\frac{4 \cdot 5}{5} + \frac{2}{5}) \div 3 \frac{6}{7}$

Combine the numerators over the common denominator.

$- \frac{4 \cdot 5 + 2}{5} \div 3 \frac{6}{7}$

Simplify the numerator.

Multiply

$4$ by

$5$ .

$- \frac{20 + 2}{5} \div 3 \frac{6}{7}$

Add

$20$ and

$2$ .

$- \frac{22}{5} \div 3 \frac{6}{7}$

Step 2

Convert

$3 \frac{6}{7}$ to an improper fraction.

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

$- \frac{22}{5} \div (3 + \frac{6}{7})$

Add

$3$ and

$\frac{6}{7}$ .

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{7}{7}$ .

$- \frac{22}{5} \div (3 \cdot \frac{7}{7} + \frac{6}{7})$

Combine

$3$ and

$\frac{7}{7}$ .

$- \frac{22}{5} \div (\frac{3 \cdot 7}{7} + \frac{6}{7})$

Combine the numerators over the common denominator.

$- \frac{22}{5} \div \frac{3 \cdot 7 + 6}{7}$

Simplify the numerator.

Multiply

$3$ by

$7$ .

$- \frac{22}{5} \div \frac{21 + 6}{7}$

Add

$21$ and

$6$ .

$- \frac{22}{5} \div \frac{27}{7}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$- \frac{22}{5} \cdot \frac{7}{27}$

Step 4

Multiply

$- \frac{22}{5} \cdot \frac{7}{27}$ .

Multiply

$\frac{7}{27}$ by

$\frac{22}{5}$ .

$- \frac{7 \cdot 22}{27 \cdot 5}$

Multiply

$7$ by

$22$ .

$- \frac{154}{27 \cdot 5}$

Multiply

$27$ by

$5$ .

$- \frac{154}{135}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{154}{135}$

Decimal Form:

$- 1.1\overline{407}$

Mixed Number Form:

$- 1 \frac{19}{135}$

Simplify (-4 2/5)÷3 6/7

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