Basic Math Examples

3.75 - (- \frac{3}{8} - \frac{1}{2} - (- \frac{5}{6}) + 4 \frac{2}{3}) - 0.125

$3.75 - (- \frac{3}{8} - \frac{1}{2} - (- \frac{5}{6}) + 4 \frac{2}{3}) - 0.125$

Step 1

Simplify each term.

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Step 1.1

Multiply

$- (- \frac{5}{6})$ .

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Step 1.1.1

Multiply

$- 1$ by

$- 1$ .

$3.75 - (- \frac{3}{8} - \frac{1}{2} + 1 (\frac{5}{6}) + 4 \frac{2}{3}) - 0.125$

Step 1.1.2

Multiply

$\frac{5}{6}$ by

$1$ .

$3.75 - (- \frac{3}{8} - \frac{1}{2} + \frac{5}{6} + 4 \frac{2}{3}) - 0.125$

Step 1.2

Convert

$4 \frac{2}{3}$ to an improper fraction.

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Step 1.2.1

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

$3.75 - (- \frac{3}{8} - \frac{1}{2} + \frac{5}{6} + 4 + \frac{2}{3}) - 0.125$

Step 1.2.2

Add

$4$ and

$\frac{2}{3}$ .

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Step 1.2.2.1

To write

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

$\frac{3}{3}$ .

$3.75 - (- \frac{3}{8} - \frac{1}{2} + \frac{5}{6} + 4 \cdot \frac{3}{3} + \frac{2}{3}) - 0.125$

Step 1.2.2.2

Combine

$4$ and

$\frac{3}{3}$ .

$3.75 - (- \frac{3}{8} - \frac{1}{2} + \frac{5}{6} + \frac{4 \cdot 3}{3} + \frac{2}{3}) - 0.125$

Step 1.2.2.3

Combine the numerators over the common denominator.

$3.75 - (- \frac{3}{8} - \frac{1}{2} + \frac{5}{6} + \frac{4 \cdot 3 + 2}{3}) - 0.125$

Step 1.2.2.4

Simplify the numerator.

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Step 1.2.2.4.1

Multiply

$4$ by

$3$ .

$3.75 - (- \frac{3}{8} - \frac{1}{2} + \frac{5}{6} + \frac{12 + 2}{3}) - 0.125$

Step 1.2.2.4.2

Add

$12$ and

$2$ .

$3.75 - (- \frac{3}{8} - \frac{1}{2} + \frac{5}{6} + \frac{14}{3}) - 0.125$

Step 2

Find the common denominator.

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Step 2.1

Multiply

$\frac{3}{8}$ by

$\frac{3}{3}$ .

$3.75 - (- (\frac{3}{8} \cdot \frac{3}{3}) - \frac{1}{2} + \frac{5}{6} + \frac{14}{3}) - 0.125$

Step 2.2

Multiply

$\frac{3}{8}$ by

$\frac{3}{3}$ .

$3.75 - (- \frac{3 \cdot 3}{8 \cdot 3} - \frac{1}{2} + \frac{5}{6} + \frac{14}{3}) - 0.125$

Step 2.3

Multiply

$\frac{1}{2}$ by

$\frac{12}{12}$ .

$3.75 - (- \frac{3 \cdot 3}{8 \cdot 3} - (\frac{1}{2} \cdot \frac{12}{12}) + \frac{5}{6} + \frac{14}{3}) - 0.125$

Step 2.4

Multiply

$\frac{1}{2}$ by

$\frac{12}{12}$ .

$3.75 - (- \frac{3 \cdot 3}{8 \cdot 3} - \frac{12}{2 \cdot 12} + \frac{5}{6} + \frac{14}{3}) - 0.125$

Step 2.5

Multiply

$\frac{5}{6}$ by

$\frac{4}{4}$ .

$3.75 - (- \frac{3 \cdot 3}{8 \cdot 3} - \frac{12}{2 \cdot 12} + \frac{5}{6} \cdot \frac{4}{4} + \frac{14}{3}) - 0.125$

Step 2.6

Multiply

$\frac{5}{6}$ by

$\frac{4}{4}$ .

$3.75 - (- \frac{3 \cdot 3}{8 \cdot 3} - \frac{12}{2 \cdot 12} + \frac{5 \cdot 4}{6 \cdot 4} + \frac{14}{3}) - 0.125$

Step 2.7

Multiply

$\frac{14}{3}$ by

$\frac{8}{8}$ .

$3.75 - (- \frac{3 \cdot 3}{8 \cdot 3} - \frac{12}{2 \cdot 12} + \frac{5 \cdot 4}{6 \cdot 4} + \frac{14}{3} \cdot \frac{8}{8}) - 0.125$

Step 2.8

Multiply

$\frac{14}{3}$ by

$\frac{8}{8}$ .

$3.75 - (- \frac{3 \cdot 3}{8 \cdot 3} - \frac{12}{2 \cdot 12} + \frac{5 \cdot 4}{6 \cdot 4} + \frac{14 \cdot 8}{3 \cdot 8}) - 0.125$

Step 2.9

Reorder the factors of

$8 \cdot 3$ .

$3.75 - (- \frac{3 \cdot 3}{3 \cdot 8} - \frac{12}{2 \cdot 12} + \frac{5 \cdot 4}{6 \cdot 4} + \frac{14 \cdot 8}{3 \cdot 8}) - 0.125$

Step 2.10

Multiply

$3$ by

$8$ .

$3.75 - (- \frac{3 \cdot 3}{24} - \frac{12}{2 \cdot 12} + \frac{5 \cdot 4}{6 \cdot 4} + \frac{14 \cdot 8}{3 \cdot 8}) - 0.125$

Step 2.11

Multiply

$2$ by

$12$ .

$3.75 - (- \frac{3 \cdot 3}{24} - \frac{12}{24} + \frac{5 \cdot 4}{6 \cdot 4} + \frac{14 \cdot 8}{3 \cdot 8}) - 0.125$

Step 2.12

Reorder the factors of

$6 \cdot 4$ .

$3.75 - (- \frac{3 \cdot 3}{24} - \frac{12}{24} + \frac{5 \cdot 4}{4 \cdot 6} + \frac{14 \cdot 8}{3 \cdot 8}) - 0.125$

Step 2.13

Multiply

$4$ by

$6$ .

$3.75 - (- \frac{3 \cdot 3}{24} - \frac{12}{24} + \frac{5 \cdot 4}{24} + \frac{14 \cdot 8}{3 \cdot 8}) - 0.125$

Step 2.14

Multiply

$3$ by

$8$ .

$3.75 - (- \frac{3 \cdot 3}{24} - \frac{12}{24} + \frac{5 \cdot 4}{24} + \frac{14 \cdot 8}{24}) - 0.125$

Step 3

Combine the numerators over the common denominator.

$3.75 - \frac{- 3 \cdot 3 - 12 + 5 \cdot 4 + 14 \cdot 8}{24} - 0.125$

Step 4

Simplify each term.

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Step 4.1

Multiply

$- 3$ by

$3$ .

$3.75 - \frac{- 9 - 12 + 5 \cdot 4 + 14 \cdot 8}{24} - 0.125$

Step 4.2

Multiply

$5$ by

$4$ .

$3.75 - \frac{- 9 - 12 + 20 + 14 \cdot 8}{24} - 0.125$

Step 4.3

Multiply

$14$ by

$8$ .

$3.75 - \frac{- 9 - 12 + 20 + 112}{24} - 0.125$

Step 5

Subtract

$12$ from

$- 9$ .

$3.75 - \frac{- 21 + 20 + 112}{24} - 0.125$

Step 6

Add

$- 21$ and

$20$ .

$3.75 - \frac{- 1 + 112}{24} - 0.125$

Step 7

Add

$- 1$ and

$112$ .

$3.75 - \frac{111}{24} - 0.125$

Step 8

Cancel the common factor of

$111$ and

$24$ .

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Step 8.1

Factor

$3$ out of

$111$ .

$3.75 - \frac{3 (37)}{24} - 0.125$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor

$3$ out of

$24$ .

$3.75 - \frac{3 \cdot 37}{3 \cdot 8} - 0.125$

Step 8.2.2

Cancel the common factor.

$3.75 - \frac{3 \cdot 37}{3 \cdot 8} - 0.125$

Step 8.2.3

Rewrite the expression.

$3.75 - \frac{37}{8} - 0.125$

Step 9

To write

$3.75$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$3.75 \cdot \frac{8}{8} - \frac{37}{8} - 0.125$

Step 10

Combine

$3.75$ and

$\frac{8}{8}$ .

$\frac{3.75 \cdot 8}{8} - \frac{37}{8} - 0.125$

Step 11

Combine the numerators over the common denominator.

$\frac{3.75 \cdot 8 - 37}{8} - 0.125$

Step 12

Simplify the numerator.

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Step 12.1

Multiply

$3.75$ by

$8$ .

$\frac{30 - 37}{8} - 0.125$

Step 12.2

Subtract

$37$ from

$30$ .

$\frac{- 7}{8} - 0.125$

Step 13

To write

$- 0.125$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$\frac{- 7}{8} - 0.125 \cdot \frac{8}{8}$

Step 14

Combine

$- 0.125$ and

$\frac{8}{8}$ .

$\frac{- 7}{8} + \frac{- 0.125 \cdot 8}{8}$

Step 15

Combine the numerators over the common denominator.

$\frac{- 7 - 0.125 \cdot 8}{8}$

Step 16

Simplify the numerator.

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Step 16.1

Multiply

$- 0.125$ by

$8$ .

$\frac{- 7 - 1}{8}$

Step 16.2

Subtract

$1$ from

$- 7$ .

$\frac{- 8}{8}$

Step 17

Divide

$- 8$ by

$8$ .

$- 1$