Basic Math Examples

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

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 $8$ .

$- 1$