Basic Math Examples

$(\frac{2}{3} - \frac{4}{5}) \cdot \frac{8}{10} + (\frac{5}{6} + \frac{4}{5}) \div \frac{2}{9}$

Step 1

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{2}{3} - \frac{4}{5}) \cdot \frac{8}{10} + (\frac{5}{6} \cdot \frac{5}{5} + \frac{4}{5}) \div \frac{2}{9}$

Step 2

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(\frac{2}{3} - \frac{4}{5}) \cdot \frac{8}{10} + (\frac{5}{6} \cdot \frac{5}{5} + \frac{4}{5} \cdot \frac{6}{6}) \div \frac{2}{9}$

Step 3

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{5}{6}$ by $\frac{5}{5}$ .

$(\frac{2}{3} - \frac{4}{5}) \cdot \frac{8}{10} + (\frac{5 \cdot 5}{6 \cdot 5} + \frac{4}{5} \cdot \frac{6}{6}) \div \frac{2}{9}$

Step 3.2

Multiply $6$ by $5$ .

$(\frac{2}{3} - \frac{4}{5}) \cdot \frac{8}{10} + (\frac{5 \cdot 5}{30} + \frac{4}{5} \cdot \frac{6}{6}) \div \frac{2}{9}$

Step 3.3

Multiply $\frac{4}{5}$ by $\frac{6}{6}$ .

$(\frac{2}{3} - \frac{4}{5}) \cdot \frac{8}{10} + (\frac{5 \cdot 5}{30} + \frac{4 \cdot 6}{5 \cdot 6}) \div \frac{2}{9}$

Step 3.4

Multiply $5$ by $6$ .

$(\frac{2}{3} - \frac{4}{5}) \cdot \frac{8}{10} + (\frac{5 \cdot 5}{30} + \frac{4 \cdot 6}{30}) \div \frac{2}{9}$

Step 4

Combine the numerators over the common denominator.

$(\frac{2}{3} - \frac{4}{5}) \cdot \frac{8}{10} + \frac{5 \cdot 5 + 4 \cdot 6}{30} \div \frac{2}{9}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $5$ by $5$ .

$(\frac{2}{3} - \frac{4}{5}) \cdot \frac{8}{10} + \frac{25 + 4 \cdot 6}{30} \div \frac{2}{9}$

Step 5.2

Multiply $4$ by $6$ .

$(\frac{2}{3} - \frac{4}{5}) \cdot \frac{8}{10} + \frac{25 + 24}{30} \div \frac{2}{9}$

Step 5.3

Add $25$ and $24$ .

$(\frac{2}{3} - \frac{4}{5}) \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{2}{3} \cdot \frac{5}{5} - \frac{4}{5}) \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6.2

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{2}{3} \cdot \frac{5}{5} - \frac{4}{5} \cdot \frac{3}{3}) \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 6.3.1

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$(\frac{2 \cdot 5}{3 \cdot 5} - \frac{4}{5} \cdot \frac{3}{3}) \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6.3.2

Multiply $3$ by $5$ .

$(\frac{2 \cdot 5}{15} - \frac{4}{5} \cdot \frac{3}{3}) \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6.3.3

Multiply $\frac{4}{5}$ by $\frac{3}{3}$ .

$(\frac{2 \cdot 5}{15} - \frac{4 \cdot 3}{5 \cdot 3}) \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6.3.4

Multiply $5$ by $3$ .

$(\frac{2 \cdot 5}{15} - \frac{4 \cdot 3}{15}) \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6.4

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 - 4 \cdot 3}{15} \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6.5

Simplify the numerator.

Tap for more steps...

Step 6.5.1

Multiply $2$ by $5$ .

$\frac{10 - 4 \cdot 3}{15} \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6.5.2

Multiply $- 4$ by $3$ .

$\frac{10 - 12}{15} \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6.5.3

Subtract $12$ from $10$ .

$\frac{- 2}{15} \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6.6

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.6.1

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{15} \cdot \frac{8}{10} + \frac{49}{30} \div \frac{2}{9}$

Step 6.6.2

Factor $2$ out of $10$ .

$\frac{2 \cdot - 1}{15} \cdot \frac{8}{2 \cdot 5} + \frac{49}{30} \div \frac{2}{9}$

Step 6.6.3

Cancel the common factor.

$\frac{2 \cdot - 1}{15} \cdot \frac{8}{2 \cdot 5} + \frac{49}{30} \div \frac{2}{9}$

Step 6.6.4

Rewrite the expression.

$\frac{- 1}{15} \cdot \frac{8}{5} + \frac{49}{30} \div \frac{2}{9}$

Step 6.7

Multiply $\frac{- 1}{15}$ by $\frac{8}{5}$ .

$\frac{- 1 \cdot 8}{15 \cdot 5} + \frac{49}{30} \div \frac{2}{9}$

Step 6.8

Multiply $- 1$ by $8$ .

$\frac{- 8}{15 \cdot 5} + \frac{49}{30} \div \frac{2}{9}$

Step 6.9

Multiply $15$ by $5$ .

$\frac{- 8}{75} + \frac{49}{30} \div \frac{2}{9}$

Step 6.10

Move the negative in front of the fraction.

$- \frac{8}{75} + \frac{49}{30} \div \frac{2}{9}$

Step 6.11

To divide by a fraction, multiply by its reciprocal.

$- \frac{8}{75} + \frac{49}{30} \cdot \frac{9}{2}$

Step 6.12

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.12.1

Factor $3$ out of $30$ .

$- \frac{8}{75} + \frac{49}{3 (10)} \cdot \frac{9}{2}$

Step 6.12.2

Factor $3$ out of $9$ .

$- \frac{8}{75} + \frac{49}{3 \cdot 10} \cdot \frac{3 \cdot 3}{2}$

Step 6.12.3

Cancel the common factor.

$- \frac{8}{75} + \frac{49}{3 \cdot 10} \cdot \frac{3 \cdot 3}{2}$

Step 6.12.4

Rewrite the expression.

$- \frac{8}{75} + \frac{49}{10} \cdot \frac{3}{2}$

Step 6.13

Multiply $\frac{49}{10}$ by $\frac{3}{2}$ .

$- \frac{8}{75} + \frac{49 \cdot 3}{10 \cdot 2}$

Step 6.14

Multiply $49$ by $3$ .

$- \frac{8}{75} + \frac{147}{10 \cdot 2}$

Step 6.15

Multiply $10$ by $2$ .

$- \frac{8}{75} + \frac{147}{20}$

Step 7

To write $- \frac{8}{75}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{8}{75} \cdot \frac{4}{4} + \frac{147}{20}$

Step 8

To write $\frac{147}{20}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$- \frac{8}{75} \cdot \frac{4}{4} + \frac{147}{20} \cdot \frac{15}{15}$

Step 9

Write each expression with a common denominator of $300$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 9.1

Multiply $\frac{8}{75}$ by $\frac{4}{4}$ .

$- \frac{8 \cdot 4}{75 \cdot 4} + \frac{147}{20} \cdot \frac{15}{15}$

Step 9.2

Multiply $75$ by $4$ .

$- \frac{8 \cdot 4}{300} + \frac{147}{20} \cdot \frac{15}{15}$

Step 9.3

Multiply $\frac{147}{20}$ by $\frac{15}{15}$ .

$- \frac{8 \cdot 4}{300} + \frac{147 \cdot 15}{20 \cdot 15}$

Step 9.4

Multiply $20$ by $15$ .

$- \frac{8 \cdot 4}{300} + \frac{147 \cdot 15}{300}$

Step 10

Combine the numerators over the common denominator.

$\frac{- 8 \cdot 4 + 147 \cdot 15}{300}$

Step 11

Simplify the numerator.

Tap for more steps...

Step 11.1

Multiply $- 8$ by $4$ .

$\frac{- 32 + 147 \cdot 15}{300}$

Step 11.2

Multiply $147$ by $15$ .

$\frac{- 32 + 2205}{300}$

Step 11.3

Add $- 32$ and $2205$ .

$\frac{2173}{300}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{2173}{300}$

Decimal Form:

$7.24\overline{3}$

Mixed Number Form:

$7 \frac{73}{300}$