Basic Math Examples

$\frac{7}{8} + (25 (0.25) - {(0.23 + \frac{1}{8})}^{2} - \frac{2}{3} \cdot 1 \frac{1}{3})$

Step 1

Remove parentheses.

$\frac{7}{8} + 25 (0.25) - {(0.23 + \frac{1}{8})}^{2} - \frac{2}{3} \cdot 1 \frac{1}{3}$

Step 2

Convert $1 \frac{1}{3}$ to an improper fraction.

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Step 2.1

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

$\frac{7}{8} + 25 (0.25) - {(0.23 + \frac{1}{8})}^{2} - \frac{2}{3} \cdot (1 + \frac{1}{3})$

Step 2.2

Add $1$ and $\frac{1}{3}$ .

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Step 2.2.1

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

$\frac{7}{8} + 25 (0.25) - {(0.23 + \frac{1}{8})}^{2} - \frac{2}{3} \cdot (\frac{3}{3} + \frac{1}{3})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{7}{8} + 25 (0.25) - {(0.23 + \frac{1}{8})}^{2} - \frac{2}{3} \cdot \frac{3 + 1}{3}$

Step 2.2.3

Add $3$ and $1$ .

$\frac{7}{8} + 25 (0.25) - {(0.23 + \frac{1}{8})}^{2} - \frac{2}{3} \cdot \frac{4}{3}$

Step 3

Simplify each term.

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Step 3.1

Multiply $25$ by $0.25$ .

$\frac{7}{8} + 6.25 - {(0.23 + \frac{1}{8})}^{2} - \frac{2}{3} \cdot \frac{4}{3}$

Step 3.2

To write $0.23$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{7}{8} + 6.25 - {(0.23 \cdot \frac{8}{8} + \frac{1}{8})}^{2} - \frac{2}{3} \cdot \frac{4}{3}$

Step 3.3

Combine $0.23$ and $\frac{8}{8}$ .

$\frac{7}{8} + 6.25 - {(\frac{0.23 \cdot 8}{8} + \frac{1}{8})}^{2} - \frac{2}{3} \cdot \frac{4}{3}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{7}{8} + 6.25 - {(\frac{0.23 \cdot 8 + 1}{8})}^{2} - \frac{2}{3} \cdot \frac{4}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $0.23$ by $8$ .

$\frac{7}{8} + 6.25 - {(\frac{1.84 + 1}{8})}^{2} - \frac{2}{3} \cdot \frac{4}{3}$

Step 3.5.2

Add $1.84$ and $1$ .

$\frac{7}{8} + 6.25 - {(\frac{2.84}{8})}^{2} - \frac{2}{3} \cdot \frac{4}{3}$

Step 3.6

Divide $2.84$ by $8$ .

$\frac{7}{8} + 6.25 - {0.355}^{2} - \frac{2}{3} \cdot \frac{4}{3}$

Step 3.7

Raise $0.355$ to the power of $2$ .

$\frac{7}{8} + 6.25 - 1 \cdot 0.126025 - \frac{2}{3} \cdot \frac{4}{3}$

Step 3.8

Multiply $- 1$ by $0.126025$ .

$\frac{7}{8} + 6.25 - 0.126025 - \frac{2}{3} \cdot \frac{4}{3}$

Step 3.9

Multiply $- \frac{2}{3} \cdot \frac{4}{3}$ .

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Step 3.9.1

Multiply $\frac{4}{3}$ by $\frac{2}{3}$ .

$\frac{7}{8} + 6.25 - 0.126025 - \frac{4 \cdot 2}{3 \cdot 3}$

Step 3.9.2

Multiply $4$ by $2$ .

$\frac{7}{8} + 6.25 - 0.126025 - \frac{8}{3 \cdot 3}$

Step 3.9.3

Multiply $3$ by $3$ .

$\frac{7}{8} + 6.25 - 0.126025 - \frac{8}{9}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{7}{8}$ by $\frac{9}{9}$ .

$\frac{7}{8} \cdot \frac{9}{9} + 6.25 - 0.126025 - \frac{8}{9}$

Step 4.2

Multiply $\frac{7}{8}$ by $\frac{9}{9}$ .

$\frac{7 \cdot 9}{8 \cdot 9} + 6.25 - 0.126025 - \frac{8}{9}$

Step 4.3

Write $6.25$ as a fraction with denominator $1$ .

$\frac{7 \cdot 9}{8 \cdot 9} + \frac{6.25}{1} - 0.126025 - \frac{8}{9}$

Step 4.4

Multiply $\frac{6.25}{1}$ by $\frac{72}{72}$ .

$\frac{7 \cdot 9}{8 \cdot 9} + \frac{6.25}{1} \cdot \frac{72}{72} - 0.126025 - \frac{8}{9}$

Step 4.5

Multiply $\frac{6.25}{1}$ by $\frac{72}{72}$ .

$\frac{7 \cdot 9}{8 \cdot 9} + \frac{6.25 \cdot 72}{72} - 0.126025 - \frac{8}{9}$

Step 4.6

Write $- 0.126025$ as a fraction with denominator $1$ .

$\frac{7 \cdot 9}{8 \cdot 9} + \frac{6.25 \cdot 72}{72} + \frac{- 0.126025}{1} - \frac{8}{9}$

Step 4.7

Multiply $\frac{- 0.126025}{1}$ by $\frac{72}{72}$ .

$\frac{7 \cdot 9}{8 \cdot 9} + \frac{6.25 \cdot 72}{72} + \frac{- 0.126025}{1} \cdot \frac{72}{72} - \frac{8}{9}$

Step 4.8

Multiply $\frac{- 0.126025}{1}$ by $\frac{72}{72}$ .

$\frac{7 \cdot 9}{8 \cdot 9} + \frac{6.25 \cdot 72}{72} + \frac{- 0.126025 \cdot 72}{72} - \frac{8}{9}$

Step 4.9

Multiply $\frac{8}{9}$ by $\frac{8}{8}$ .

$\frac{7 \cdot 9}{8 \cdot 9} + \frac{6.25 \cdot 72}{72} + \frac{- 0.126025 \cdot 72}{72} - (\frac{8}{9} \cdot \frac{8}{8})$

Step 4.10

Multiply $\frac{8}{9}$ by $\frac{8}{8}$ .

$\frac{7 \cdot 9}{8 \cdot 9} + \frac{6.25 \cdot 72}{72} + \frac{- 0.126025 \cdot 72}{72} - \frac{8 \cdot 8}{9 \cdot 8}$

Step 4.11

Multiply $8$ by $9$ .

$\frac{7 \cdot 9}{72} + \frac{6.25 \cdot 72}{72} + \frac{- 0.126025 \cdot 72}{72} - \frac{8 \cdot 8}{9 \cdot 8}$

Step 4.12

Reorder the factors of $9 \cdot 8$ .

$\frac{7 \cdot 9}{72} + \frac{6.25 \cdot 72}{72} + \frac{- 0.126025 \cdot 72}{72} - \frac{8 \cdot 8}{8 \cdot 9}$

Step 4.13

Multiply $8$ by $9$ .

$\frac{7 \cdot 9}{72} + \frac{6.25 \cdot 72}{72} + \frac{- 0.126025 \cdot 72}{72} - \frac{8 \cdot 8}{72}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 \cdot 9 + 6.25 \cdot 72 - 0.126025 \cdot 72 - 8 \cdot 8}{72}$

Step 6

Simplify each term.

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Step 6.1

Multiply $7$ by $9$ .

$\frac{63 + 6.25 \cdot 72 - 0.126025 \cdot 72 - 8 \cdot 8}{72}$

Step 6.2

Multiply $6.25$ by $72$ .

$\frac{63 + 450 - 0.126025 \cdot 72 - 8 \cdot 8}{72}$

Step 6.3

Multiply $- 0.126025$ by $72$ .

$\frac{63 + 450 - 9.0738 - 8 \cdot 8}{72}$

Step 6.4

Multiply $- 8$ by $8$ .

$\frac{63 + 450 - 9.0738 - 64}{72}$

Step 7

Simplify the expression.

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Step 7.1

Add $63$ and $450$ .

$\frac{513 - 9.0738 - 64}{72}$

Step 7.2

Subtract $9.0738$ from $513$ .

$\frac{503.9262 - 64}{72}$

Step 7.3

Subtract $64$ from $503.9262$ .

$\frac{439.9262}{72}$

Step 7.4

Divide $439.9262$ by $72$ .

$6.110086\overline{1}$