Basic Math Examples

$(\frac{5}{2} + \frac{1}{4} - \frac{7}{8}) \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 1

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

$(\frac{5}{2} \cdot \frac{2}{2} + \frac{1}{4} - \frac{7}{8}) \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

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

$(\frac{5 \cdot 2}{2 \cdot 2} + \frac{1}{4} - \frac{7}{8}) \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 2.2

Multiply $2$ by $2$ .

$(\frac{5 \cdot 2}{4} + \frac{1}{4} - \frac{7}{8}) \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 3

Combine the numerators over the common denominator.

$(\frac{5 \cdot 2 + 1}{4} - \frac{7}{8}) \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $5$ by $2$ .

$(\frac{10 + 1}{4} - \frac{7}{8}) \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 4.2

Add $10$ and $1$ .

$(\frac{11}{4} - \frac{7}{8}) \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 5

To write $\frac{11}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{11}{4} \cdot \frac{2}{2} - \frac{7}{8}) \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 6

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{11}{4}$ by $\frac{2}{2}$ .

$(\frac{11 \cdot 2}{4 \cdot 2} - \frac{7}{8}) \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 6.2

Multiply $4$ by $2$ .

$(\frac{11 \cdot 2}{8} - \frac{7}{8}) \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 7

Combine the numerators over the common denominator.

$\frac{11 \cdot 2 - 7}{8} \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $11$ by $2$ .

$\frac{22 - 7}{8} \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 8.2

Subtract $7$ from $22$ .

$\frac{15}{8} \div (- \frac{3}{16}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9

Simplify each term.

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Step 9.1

To divide by a fraction, multiply by its reciprocal.

$\frac{15}{8} (- \frac{16}{3}) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.2

Cancel the common factor of $3$ .

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Step 9.2.1

Move the leading negative in $- \frac{16}{3}$ into the numerator.

$\frac{15}{8} \cdot \frac{- 16}{3} - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.2.2

Factor $3$ out of $15$ .

$\frac{3 (5)}{8} \cdot \frac{- 16}{3} - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.2.3

Cancel the common factor.

$\frac{3 \cdot 5}{8} \cdot \frac{- 16}{3} - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.2.4

Rewrite the expression.

$\frac{5}{8} \cdot - 16 - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.3

Cancel the common factor of $8$ .

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Step 9.3.1

Factor $8$ out of $- 16$ .

$\frac{5}{8} \cdot (8 (- 2)) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.3.2

Cancel the common factor.

$\frac{5}{8} \cdot (8 \cdot - 2) - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.3.3

Rewrite the expression.

$5 \cdot - 2 - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.4

Multiply $5$ by $- 2$ .

$- 10 - \frac{5}{3} \cdot (- \frac{2}{7}) + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.5

Multiply $- \frac{5}{3} (- \frac{2}{7})$ .

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Step 9.5.1

Multiply $- 1$ by $- 1$ .

$- 10 + 1 (\frac{5}{3}) \frac{2}{7} + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.5.2

Multiply $\frac{5}{3}$ by $1$ .

$- 10 + \frac{5}{3} \cdot \frac{2}{7} + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.5.3

Multiply $\frac{5}{3}$ by $\frac{2}{7}$ .

$- 10 + \frac{5 \cdot 2}{3 \cdot 7} + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.5.4

Multiply $5$ by $2$ .

$- 10 + \frac{10}{3 \cdot 7} + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.5.5

Multiply $3$ by $7$ .

$- 10 + \frac{10}{21} + (- \frac{1}{2}) {(- 2)}^{3} - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.6

Raise $- 2$ to the power of $3$ .

$- 10 + \frac{10}{21} - \frac{1}{2} \cdot - 8 - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.7

Cancel the common factor of $2$ .

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Step 9.7.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 10 + \frac{10}{21} + \frac{- 1}{2} \cdot - 8 - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.7.2

Factor $2$ out of $- 8$ .

$- 10 + \frac{10}{21} + \frac{- 1}{2} \cdot (2 (- 4)) - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.7.3

Cancel the common factor.

$- 10 + \frac{10}{21} + \frac{- 1}{2} \cdot (2 \cdot - 4) - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.7.4

Rewrite the expression.

$- 10 + \frac{10}{21} - 1 \cdot - 4 - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.8

Multiply $- 1$ by $- 4$ .

$- 10 + \frac{10}{21} + 4 - (3 - \frac{9}{5}) \div (- \frac{1}{5})$

Step 9.9

To divide by a fraction, multiply by its reciprocal.

$- 10 + \frac{10}{21} + 4 - ((3 - \frac{9}{5}) (- 5))$

Step 9.10

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

$- 10 + \frac{10}{21} + 4 - ((3 \cdot \frac{5}{5} - \frac{9}{5}) \cdot - 5)$

Step 9.11

Combine $3$ and $\frac{5}{5}$ .

$- 10 + \frac{10}{21} + 4 - ((\frac{3 \cdot 5}{5} - \frac{9}{5}) \cdot - 5)$

Step 9.12

Combine the numerators over the common denominator.

$- 10 + \frac{10}{21} + 4 - (\frac{3 \cdot 5 - 9}{5} \cdot - 5)$

Step 9.13

Simplify the numerator.

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Step 9.13.1

Multiply $3$ by $5$ .

$- 10 + \frac{10}{21} + 4 - (\frac{15 - 9}{5} \cdot - 5)$

Step 9.13.2

Subtract $9$ from $15$ .

$- 10 + \frac{10}{21} + 4 - (\frac{6}{5} \cdot - 5)$

Step 9.14

Cancel the common factor of $5$ .

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Step 9.14.1

Factor $5$ out of $- 5$ .

$- 10 + \frac{10}{21} + 4 - (\frac{6}{5} \cdot (5 (- 1)))$

Step 9.14.2

Cancel the common factor.

$- 10 + \frac{10}{21} + 4 - (\frac{6}{5} \cdot (5 \cdot - 1))$

Step 9.14.3

Rewrite the expression.

$- 10 + \frac{10}{21} + 4 - (6 \cdot - 1)$

Step 9.15

Multiply $6$ by $- 1$ .

$- 10 + \frac{10}{21} + 4 - - 6$

Step 9.16

Multiply $- 1$ by $- 6$ .

$- 10 + \frac{10}{21} + 4 + 6$

Step 10

Find the common denominator.

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Step 10.1

Write $- 10$ as a fraction with denominator $1$ .

$\frac{- 10}{1} + \frac{10}{21} + 4 + 6$

Step 10.2

Multiply $\frac{- 10}{1}$ by $\frac{21}{21}$ .

$\frac{- 10}{1} \cdot \frac{21}{21} + \frac{10}{21} + 4 + 6$

Step 10.3

Multiply $\frac{- 10}{1}$ by $\frac{21}{21}$ .

$\frac{- 10 \cdot 21}{21} + \frac{10}{21} + 4 + 6$

Step 10.4

Write $4$ as a fraction with denominator $1$ .

$\frac{- 10 \cdot 21}{21} + \frac{10}{21} + \frac{4}{1} + 6$

Step 10.5

Multiply $\frac{4}{1}$ by $\frac{21}{21}$ .

$\frac{- 10 \cdot 21}{21} + \frac{10}{21} + \frac{4}{1} \cdot \frac{21}{21} + 6$

Step 10.6

Multiply $\frac{4}{1}$ by $\frac{21}{21}$ .

$\frac{- 10 \cdot 21}{21} + \frac{10}{21} + \frac{4 \cdot 21}{21} + 6$

Step 10.7

Write $6$ as a fraction with denominator $1$ .

$\frac{- 10 \cdot 21}{21} + \frac{10}{21} + \frac{4 \cdot 21}{21} + \frac{6}{1}$

Step 10.8

Multiply $\frac{6}{1}$ by $\frac{21}{21}$ .

$\frac{- 10 \cdot 21}{21} + \frac{10}{21} + \frac{4 \cdot 21}{21} + \frac{6}{1} \cdot \frac{21}{21}$

Step 10.9

Multiply $\frac{6}{1}$ by $\frac{21}{21}$ .

$\frac{- 10 \cdot 21}{21} + \frac{10}{21} + \frac{4 \cdot 21}{21} + \frac{6 \cdot 21}{21}$

Step 11

Combine the numerators over the common denominator.

$\frac{- 10 \cdot 21 + 10 + 4 \cdot 21 + 6 \cdot 21}{21}$

Step 12

Simplify each term.

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Step 12.1

Multiply $- 10$ by $21$ .

$\frac{- 210 + 10 + 4 \cdot 21 + 6 \cdot 21}{21}$

Step 12.2

Multiply $4$ by $21$ .

$\frac{- 210 + 10 + 84 + 6 \cdot 21}{21}$

Step 12.3

Multiply $6$ by $21$ .

$\frac{- 210 + 10 + 84 + 126}{21}$

Step 13

Simplify by adding numbers.

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Step 13.1

Add $- 210$ and $10$ .

$\frac{- 200 + 84 + 126}{21}$

Step 13.2

Add $- 200$ and $84$ .

$\frac{- 116 + 126}{21}$

Step 13.3

Add $- 116$ and $126$ .

$\frac{10}{21}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{21}$

Decimal Form:

$0.\overline{476190}$