Evaluate 3/4*16/9-(7/10)÷(7/20)

$\frac{3}{4} \cdot \frac{16}{9} - \frac{7}{10} \div \frac{7}{20}$

Step 1

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{3}{4} \cdot \frac{16}{3 (3)} - \frac{7}{10} \div \frac{7}{20}$

Cancel the common factor.

$\frac{3}{4} \cdot \frac{16}{3 \cdot 3} - \frac{7}{10} \div \frac{7}{20}$

Rewrite the expression.

$\frac{1}{4} \cdot \frac{16}{3} - \frac{7}{10} \div \frac{7}{20}$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

$\frac{1}{4} \cdot \frac{4 (4)}{3} - \frac{7}{10} \div \frac{7}{20}$

Cancel the common factor.

$\frac{1}{4} \cdot \frac{4 \cdot 4}{3} - \frac{7}{10} \div \frac{7}{20}$

Rewrite the expression.

$\frac{4}{3} - \frac{7}{10} \div \frac{7}{20}$

To divide by a fraction, multiply by its reciprocal.

$\frac{4}{3} - (\frac{7}{10} \cdot \frac{20}{7})$

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{4}{3} - (\frac{7}{10} \cdot \frac{20}{7})$

Rewrite the expression.

$\frac{4}{3} - (\frac{1}{10} \cdot 20)$

Cancel the common factor of $10$ .

Factor $10$ out of $20$ .

$\frac{4}{3} - (\frac{1}{10} \cdot (10 (2)))$

Cancel the common factor.

$\frac{4}{3} - (\frac{1}{10} \cdot (10 \cdot 2))$

Rewrite the expression.

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

Multiply $- 1$ by $2$ .

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

Step 2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4}{3} - 2 \cdot \frac{3}{3}$

Step 3

Combine $- 2$ and $\frac{3}{3}$ .

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

Step 4

Combine the numerators over the common denominator.

$\frac{4 - 2 \cdot 3}{3}$

Step 5

Simplify the numerator.

Multiply $- 2$ by $3$ .

$\frac{4 - 6}{3}$

Subtract $6$ from $4$ .

$\frac{- 2}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{3}$

Decimal Form:

$- 0.\overline{6}$

Evaluate 3/4*16/9-(7/10)÷(7/20)

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