Algebra Examples

$\frac{5}{8} + \frac{3}{4} \div \frac{- 2}{3} - \frac{5}{6}$

Step 1

Find the common denominator.

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Step 1.1

Move the negative in front of the fraction.

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

Step 1.2

Multiply $\frac{5}{8}$ by $\frac{\frac{3 \cdot 2}{3}}{\frac{3 \cdot 2}{3}}$ .

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

Step 1.3

Multiply $\frac{5}{8}$ by $\frac{\frac{3 \cdot 2}{3}}{\frac{3 \cdot 2}{3}}$ .

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

Step 1.4

Multiply $\frac{3}{4} \div (- \frac{2}{3})$ by $\frac{- 24}{- 24}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{8 \frac{3 \cdot 2}{3}} + \frac{3}{4} \div (- \frac{2}{3}) \cdot \frac{- 24}{- 24} - \frac{5}{6}$

Step 1.5

Multiply $\frac{3}{4} \div (- \frac{2}{3})$ by $\frac{- 24}{- 24}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{8 \frac{3 \cdot 2}{3}} + \frac{\frac{3}{4} \cdot - 24}{- \frac{2}{3} \cdot - 24} - \frac{5}{6}$

Step 1.6

Multiply $\frac{5}{6}$ by $\frac{\frac{4 \cdot 2}{3}}{\frac{4 \cdot 2}{3}}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{8 \frac{3 \cdot 2}{3}} + \frac{\frac{3}{4} \cdot - 24}{- \frac{2}{3} \cdot - 24} - (\frac{5}{6} \cdot \frac{\frac{4 \cdot 2}{3}}{\frac{4 \cdot 2}{3}})$

Step 1.7

Multiply $\frac{5}{6}$ by $\frac{\frac{4 \cdot 2}{3}}{\frac{4 \cdot 2}{3}}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{8 \frac{3 \cdot 2}{3}} + \frac{\frac{3}{4} \cdot - 24}{- \frac{2}{3} \cdot - 24} - \frac{5 \frac{4 \cdot 2}{3}}{6 \frac{4 \cdot 2}{3}}$

Step 1.8

Multiply $3$ by $2$ .

$\frac{5 \frac{3 \cdot 2}{3}}{8 (\frac{6}{3})} + \frac{\frac{3}{4} \cdot - 24}{- \frac{2}{3} \cdot - 24} - \frac{5 \frac{4 \cdot 2}{3}}{6 \frac{4 \cdot 2}{3}}$

Step 1.9

Combine $8$ and $\frac{6}{3}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{8 \cdot 6}{3}} + \frac{\frac{3}{4} \cdot - 24}{- \frac{2}{3} \cdot - 24} - \frac{5 \frac{4 \cdot 2}{3}}{6 \frac{4 \cdot 2}{3}}$

Step 1.10

Multiply $8$ by $6$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{48}{3}} + \frac{\frac{3}{4} \cdot - 24}{- \frac{2}{3} \cdot - 24} - \frac{5 \frac{4 \cdot 2}{3}}{6 \frac{4 \cdot 2}{3}}$

Step 1.11

Reorder the factors of $- \frac{2}{3} \cdot - 24$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{48}{3}} + \frac{\frac{3}{4} \cdot - 24}{- 24 \cdot - 1 \frac{2}{3}} - \frac{5 \frac{4 \cdot 2}{3}}{6 \frac{4 \cdot 2}{3}}$

Step 1.12

Multiply $- 24$ by $- 1$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{48}{3}} + \frac{\frac{3}{4} \cdot - 24}{24 (\frac{2}{3})} - \frac{5 \frac{4 \cdot 2}{3}}{6 \frac{4 \cdot 2}{3}}$

Step 1.13

Combine $24$ and $\frac{2}{3}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{48}{3}} + \frac{\frac{3}{4} \cdot - 24}{\frac{24 \cdot 2}{3}} - \frac{5 \frac{4 \cdot 2}{3}}{6 \frac{4 \cdot 2}{3}}$

Step 1.14

Multiply $24$ by $2$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{48}{3}} + \frac{\frac{3}{4} \cdot - 24}{\frac{48}{3}} - \frac{5 \frac{4 \cdot 2}{3}}{6 \frac{4 \cdot 2}{3}}$

Step 1.15

Multiply $4$ by $2$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{48}{3}} + \frac{\frac{3}{4} \cdot - 24}{\frac{48}{3}} - \frac{5 \frac{4 \cdot 2}{3}}{6 (\frac{8}{3})}$

Step 1.16

Combine $6$ and $\frac{8}{3}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{48}{3}} + \frac{\frac{3}{4} \cdot - 24}{\frac{48}{3}} - \frac{5 \frac{4 \cdot 2}{3}}{\frac{6 \cdot 8}{3}}$

Step 1.17

Multiply $6$ by $8$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{48}{3}} + \frac{\frac{3}{4} \cdot - 24}{\frac{48}{3}} - \frac{5 \frac{4 \cdot 2}{3}}{\frac{48}{3}}$

Step 2

Combine the numerators over the common denominator.

$\frac{5 \frac{3 \cdot 2}{3} + \frac{3}{4} \cdot - 24 - 5 \frac{4 \cdot 2}{3}}{\frac{48}{3}}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Cancel the common factor.

$\frac{5 \frac{3 \cdot 2}{3} + \frac{3}{4} \cdot - 24 - 5 \frac{4 \cdot 2}{3}}{\frac{48}{3}}$

Step 3.1.2

Divide $2$ by $1$ .

$\frac{5 \cdot 2 + \frac{3}{4} \cdot - 24 - 5 \frac{4 \cdot 2}{3}}{\frac{48}{3}}$

Step 3.2

Multiply $5$ by $2$ .

$\frac{10 + \frac{3}{4} \cdot - 24 - 5 \frac{4 \cdot 2}{3}}{\frac{48}{3}}$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Factor $4$ out of $- 24$ .

$\frac{10 + \frac{3}{4} \cdot (4 (- 6)) - 5 \frac{4 \cdot 2}{3}}{\frac{48}{3}}$

Step 3.3.2

Cancel the common factor.

$\frac{10 + \frac{3}{4} \cdot (4 \cdot - 6) - 5 \frac{4 \cdot 2}{3}}{\frac{48}{3}}$

Step 3.3.3

Rewrite the expression.

$\frac{10 + 3 \cdot - 6 - 5 \frac{4 \cdot 2}{3}}{\frac{48}{3}}$

Step 3.4

Multiply $3$ by $- 6$ .

$\frac{10 - 18 - 5 \frac{4 \cdot 2}{3}}{\frac{48}{3}}$

Step 3.5

Multiply $4$ by $2$ .

$\frac{10 - 18 - 5 (\frac{8}{3})}{\frac{48}{3}}$

Step 3.6

Multiply $- 5 (\frac{8}{3})$ .

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Step 3.6.1

Combine $- 5$ and $\frac{8}{3}$ .

$\frac{10 - 18 + \frac{- 5 \cdot 8}{3}}{\frac{48}{3}}$

Step 3.6.2

Multiply $- 5$ by $8$ .

$\frac{10 - 18 + \frac{- 40}{3}}{\frac{48}{3}}$

Step 3.7

Move the negative in front of the fraction.

$\frac{10 - 18 - \frac{40}{3}}{\frac{48}{3}}$

Step 4

Find the common denominator.

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Step 4.1

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

$\frac{\frac{10}{1} - 18 - \frac{40}{3}}{\frac{48}{3}}$

Step 4.2

Multiply $\frac{10}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{10}{1} \cdot \frac{3}{3} - 18 - \frac{40}{3}}{\frac{48}{3}}$

Step 4.3

Multiply $\frac{10}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{10 \cdot 3}{3} - 18 - \frac{40}{3}}{\frac{48}{3}}$

Step 4.4

Write $- 18$ as a fraction with denominator $1$ .

$\frac{\frac{10 \cdot 3}{3} + \frac{- 18}{1} - \frac{40}{3}}{\frac{48}{3}}$

Step 4.5

Multiply $\frac{- 18}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{10 \cdot 3}{3} + \frac{- 18}{1} \cdot \frac{3}{3} - \frac{40}{3}}{\frac{48}{3}}$

Step 4.6

Multiply $\frac{- 18}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{10 \cdot 3}{3} + \frac{- 18 \cdot 3}{3} - \frac{40}{3}}{\frac{48}{3}}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{10 \cdot 3 - 18 \cdot 3 - 40}{3}}{\frac{48}{3}}$

Step 6

Simplify each term.

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Step 6.1

Multiply $10$ by $3$ .

$\frac{\frac{30 - 18 \cdot 3 - 40}{3}}{\frac{48}{3}}$

Step 6.2

Multiply $- 18$ by $3$ .

$\frac{\frac{30 - 54 - 40}{3}}{\frac{48}{3}}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Subtract $54$ from $30$ .

$\frac{\frac{- 24 - 40}{3}}{\frac{48}{3}}$

Step 7.2

Simplify the expression.

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Step 7.2.1

Subtract $40$ from $- 24$ .

$\frac{\frac{- 64}{3}}{\frac{48}{3}}$

Step 7.2.2

Move the negative in front of the fraction.

$\frac{- \frac{64}{3}}{\frac{48}{3}}$

Step 7.3

Cancel the common factor of $48$ and $3$ .

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Step 7.3.1

Factor $3$ out of $48$ .

$\frac{- \frac{64}{3}}{\frac{3 \cdot 16}{3}}$

Step 7.3.2

Cancel the common factors.

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Step 7.3.2.1

Factor $3$ out of $3$ .

$\frac{- \frac{64}{3}}{\frac{3 \cdot 16}{3 (1)}}$

Step 7.3.2.2

Cancel the common factor.

$\frac{- \frac{64}{3}}{\frac{3 \cdot 16}{3 \cdot 1}}$

Step 7.3.2.3

Rewrite the expression.

$\frac{- \frac{64}{3}}{\frac{16}{1}}$

Step 7.3.2.4

Divide $16$ by $1$ .

$\frac{- \frac{64}{3}}{16}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$- \frac{64}{3} \cdot \frac{1}{16}$

Step 9

Cancel the common factor of $16$ .

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Step 9.1

Move the leading negative in $- \frac{64}{3}$ into the numerator.

$\frac{- 64}{3} \cdot \frac{1}{16}$

Step 9.2

Factor $16$ out of $- 64$ .

$\frac{16 (- 4)}{3} \cdot \frac{1}{16}$

Step 9.3

Cancel the common factor.

$\frac{16 \cdot - 4}{3} \cdot \frac{1}{16}$

Step 9.4

Rewrite the expression.

$\frac{- 4}{3}$

Step 10

Move the negative in front of the fraction.

$- \frac{4}{3}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{4}{3}$

Decimal Form:

$- 1.\overline{3}$

Mixed Number Form:

$- 1 \frac{1}{3}$