Basic Math Examples

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

Step 1

Remove parentheses.

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Subtract $3$ from $- 5$ .

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

Step 4

Find the common denominator.

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Step 4.1

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

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

Step 4.2

Multiply $\frac{4}{1}$ by $\frac{8}{8}$ .

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

Step 4.3

Multiply $\frac{4}{1}$ by $\frac{8}{8}$ .

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

Step 4.4

Write $- (5 - \frac{3}{4})$ as a fraction with denominator $1$ .

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

Step 4.5

Multiply $\frac{- (5 - \frac{3}{4})}{1}$ by $\frac{8}{8}$ .

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

Step 4.6

Multiply $\frac{- (5 - \frac{3}{4})}{1}$ by $\frac{8}{8}$ .

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

Step 4.7

Write $3$ as a fraction with denominator $1$ .

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

Step 4.8

Multiply $\frac{3}{1}$ by $\frac{8}{8}$ .

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

Step 4.9

Multiply $\frac{3}{1}$ by $\frac{8}{8}$ .

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

Step 4.10

Multiply $\frac{- 1}{2}$ by $\frac{4}{4}$ .

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

Step 4.11

Multiply $\frac{- 1}{2}$ by $\frac{4}{4}$ .

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

Step 4.12

Multiply $2$ by $4$ .

$\frac{4 \cdot 8}{8} + \frac{- (5 - \frac{3}{4}) \cdot 8}{8} + \frac{3 \cdot 8}{8} + \frac{- 8}{8} + \frac{- 1 \cdot 4}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 \cdot 8 - (5 - \frac{3}{4}) \cdot 8 + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6

Simplify each term.

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Step 6.1

Multiply $4$ by $8$ .

$\frac{32 - (5 - \frac{3}{4}) \cdot 8 + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6.2

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

$\frac{32 - (5 \cdot \frac{4}{4} - \frac{3}{4}) \cdot 8 + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6.3

Combine $5$ and $\frac{4}{4}$ .

$\frac{32 - (\frac{5 \cdot 4}{4} - \frac{3}{4}) \cdot 8 + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6.4

Combine the numerators over the common denominator.

$\frac{32 - \frac{5 \cdot 4 - 3}{4} \cdot 8 + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $5$ by $4$ .

$\frac{32 - \frac{20 - 3}{4} \cdot 8 + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6.5.2

Subtract $3$ from $20$ .

$\frac{32 - \frac{17}{4} \cdot 8 + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6.6

Cancel the common factor of $4$ .

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Step 6.6.1

Move the leading negative in $- \frac{17}{4}$ into the numerator.

$\frac{32 + \frac{- 17}{4} \cdot 8 + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6.6.2

Factor $4$ out of $8$ .

$\frac{32 + \frac{- 17}{4} \cdot (4 (2)) + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6.6.3

Cancel the common factor.

$\frac{32 + \frac{- 17}{4} \cdot (4 \cdot 2) + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6.6.4

Rewrite the expression.

$\frac{32 - 17 \cdot 2 + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6.7

Multiply $- 17$ by $2$ .

$\frac{32 - 34 + 3 \cdot 8 - 8 - 1 \cdot 4}{8}$

Step 6.8

Multiply $3$ by $8$ .

$\frac{32 - 34 + 24 - 8 - 1 \cdot 4}{8}$

Step 6.9

Multiply $- 1$ by $4$ .

$\frac{32 - 34 + 24 - 8 - 4}{8}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Subtract $34$ from $32$ .

$\frac{- 2 + 24 - 8 - 4}{8}$

Step 7.2

Simplify by adding and subtracting.

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Step 7.2.1

Add $- 2$ and $24$ .

$\frac{22 - 8 - 4}{8}$

Step 7.2.2

Subtract $8$ from $22$ .

$\frac{14 - 4}{8}$

Step 7.2.3

Subtract $4$ from $14$ .

$\frac{10}{8}$

Step 7.3

Cancel the common factor of $10$ and $8$ .

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Step 7.3.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{8}$

Step 7.3.2

Cancel the common factors.

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Step 7.3.2.1

Factor $2$ out of $8$ .

$\frac{2 \cdot 5}{2 \cdot 4}$

Step 7.3.2.2

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot 4}$

Step 7.3.2.3

Rewrite the expression.

$\frac{5}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$