Basic Math Examples

$(- \frac{64}{18} + 8) - (- \frac{1}{16} + 1)$

Step 1

Find the common denominator.

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Step 1.1

Write $8$ as a fraction with denominator $1$ .

$- \frac{64}{18} + \frac{8}{1} - (- \frac{1}{16} + 1)$

Step 1.2

Multiply $\frac{8}{1}$ by $\frac{18}{18}$ .

$- \frac{64}{18} + \frac{8}{1} \cdot \frac{18}{18} - (- \frac{1}{16} + 1)$

Step 1.3

Multiply $\frac{8}{1}$ by $\frac{18}{18}$ .

$- \frac{64}{18} + \frac{8 \cdot 18}{18} - (- \frac{1}{16} + 1)$

Step 1.4

Write $- (- \frac{1}{16} + 1)$ as a fraction with denominator $1$ .

$- \frac{64}{18} + \frac{8 \cdot 18}{18} + \frac{- (- \frac{1}{16} + 1)}{1}$

Step 1.5

Multiply $\frac{- (- \frac{1}{16} + 1)}{1}$ by $\frac{18}{18}$ .

$- \frac{64}{18} + \frac{8 \cdot 18}{18} + \frac{- (- \frac{1}{16} + 1)}{1} \cdot \frac{18}{18}$

Step 1.6

Multiply $\frac{- (- \frac{1}{16} + 1)}{1}$ by $\frac{18}{18}$ .

$- \frac{64}{18} + \frac{8 \cdot 18}{18} + \frac{- (- \frac{1}{16} + 1) \cdot 18}{18}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 64 + 8 \cdot 18 - (- \frac{1}{16} + 1) \cdot 18}{18}$

Step 3

Simplify each term.

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Step 3.1

Multiply $8$ by $18$ .

$\frac{- 64 + 144 - (- \frac{1}{16} + 1) \cdot 18}{18}$

Step 3.2

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

$\frac{- 64 + 144 - (- \frac{1}{16} + \frac{16}{16}) \cdot 18}{18}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{- 64 + 144 - \frac{- 1 + 16}{16} \cdot 18}{18}$

Step 3.4

Add $- 1$ and $16$ .

$\frac{- 64 + 144 - \frac{15}{16} \cdot 18}{18}$

Step 3.5

Cancel the common factor of $2$ .

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Step 3.5.1

Move the leading negative in $- \frac{15}{16}$ into the numerator.

$\frac{- 64 + 144 + \frac{- 15}{16} \cdot 18}{18}$

Step 3.5.2

Factor $2$ out of $16$ .

$\frac{- 64 + 144 + \frac{- 15}{2 (8)} \cdot 18}{18}$

Step 3.5.3

Factor $2$ out of $18$ .

$\frac{- 64 + 144 + \frac{- 15}{2 \cdot 8} \cdot (2 \cdot 9)}{18}$

Step 3.5.4

Cancel the common factor.

$\frac{- 64 + 144 + \frac{- 15}{2 \cdot 8} \cdot (2 \cdot 9)}{18}$

Step 3.5.5

Rewrite the expression.

$\frac{- 64 + 144 + \frac{- 15}{8} \cdot 9}{18}$

Step 3.6

Combine $\frac{- 15}{8}$ and $9$ .

$\frac{- 64 + 144 + \frac{- 15 \cdot 9}{8}}{18}$

Step 3.7

Multiply $- 15$ by $9$ .

$\frac{- 64 + 144 + \frac{- 135}{8}}{18}$

Step 3.8

Move the negative in front of the fraction.

$\frac{- 64 + 144 - \frac{135}{8}}{18}$

Step 4

Find the common denominator.

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Step 4.1

Write $- 64$ as a fraction with denominator $1$ .

$\frac{\frac{- 64}{1} + 144 - \frac{135}{8}}{18}$

Step 4.2

Multiply $\frac{- 64}{1}$ by $\frac{8}{8}$ .

$\frac{\frac{- 64}{1} \cdot \frac{8}{8} + 144 - \frac{135}{8}}{18}$

Step 4.3

Multiply $\frac{- 64}{1}$ by $\frac{8}{8}$ .

$\frac{\frac{- 64 \cdot 8}{8} + 144 - \frac{135}{8}}{18}$

Step 4.4

Write $144$ as a fraction with denominator $1$ .

$\frac{\frac{- 64 \cdot 8}{8} + \frac{144}{1} - \frac{135}{8}}{18}$

Step 4.5

Multiply $\frac{144}{1}$ by $\frac{8}{8}$ .

$\frac{\frac{- 64 \cdot 8}{8} + \frac{144}{1} \cdot \frac{8}{8} - \frac{135}{8}}{18}$

Step 4.6

Multiply $\frac{144}{1}$ by $\frac{8}{8}$ .

$\frac{\frac{- 64 \cdot 8}{8} + \frac{144 \cdot 8}{8} - \frac{135}{8}}{18}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{- 64 \cdot 8 + 144 \cdot 8 - 135}{8}}{18}$

Step 6

Simplify each term.

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Step 6.1

Multiply $- 64$ by $8$ .

$\frac{\frac{- 512 + 144 \cdot 8 - 135}{8}}{18}$

Step 6.2

Multiply $144$ by $8$ .

$\frac{\frac{- 512 + 1152 - 135}{8}}{18}$

Step 7

Simplify by adding and subtracting.

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Step 7.1

Add $- 512$ and $1152$ .

$\frac{\frac{640 - 135}{8}}{18}$

Step 7.2

Subtract $135$ from $640$ .

$\frac{\frac{505}{8}}{18}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{505}{8} \cdot \frac{1}{18}$

Step 9

Multiply $\frac{505}{8} \cdot \frac{1}{18}$ .

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Step 9.1

Multiply $\frac{505}{8}$ by $\frac{1}{18}$ .

$\frac{505}{8 \cdot 18}$

Step 9.2

Multiply $8$ by $18$ .

$\frac{505}{144}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{505}{144}$

Decimal Form:

$3.5069\overline{4}$

Mixed Number Form:

$3 \frac{73}{144}$