Basic Math Examples

$\frac{\frac{5}{25}}{3} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div 1 \frac{5}{6}$

Step 1

Convert $1 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

$\frac{\frac{5}{25}}{3} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div (1 + \frac{5}{6})$

Step 1.2

Add $1$ and $\frac{5}{6}$ .

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Step 1.2.1

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

$\frac{\frac{5}{25}}{3} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div (\frac{6}{6} + \frac{5}{6})$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{\frac{5}{25}}{3} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div \frac{6 + 5}{6}$

Step 1.2.3

Add $6$ and $5$ .

$\frac{\frac{5}{25}}{3} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div \frac{11}{6}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $5$ and $25$ .

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Step 2.1.1

Factor $5$ out of $5$ .

$\frac{\frac{5 (1)}{25}}{3} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div \frac{11}{6}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $5$ out of $25$ .

$\frac{\frac{5 \cdot 1}{5 \cdot 5}}{3} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div \frac{11}{6}$

Step 2.1.2.2

Cancel the common factor.

$\frac{\frac{5 \cdot 1}{5 \cdot 5}}{3} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div \frac{11}{6}$

Step 2.1.2.3

Rewrite the expression.

$\frac{\frac{1}{5}}{3} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div \frac{11}{6}$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{5} \cdot \frac{1}{3} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div \frac{11}{6}$

Step 2.3

Multiply $\frac{1}{5} \cdot \frac{1}{3}$ .

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Step 2.3.1

Multiply $\frac{1}{5}$ by $\frac{1}{3}$ .

$\frac{1}{5 \cdot 3} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div \frac{11}{6}$

Step 2.3.2

Multiply $5$ by $3$ .

$\frac{1}{15} + 3 (2 - \frac{7}{8}) - \frac{3}{4} \div \frac{11}{6}$

Step 2.4

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{15} + 3 (2 \cdot \frac{8}{8} - \frac{7}{8}) - \frac{3}{4} \div \frac{11}{6}$

Step 2.5

Combine $2$ and $\frac{8}{8}$ .

$\frac{1}{15} + 3 (\frac{2 \cdot 8}{8} - \frac{7}{8}) - \frac{3}{4} \div \frac{11}{6}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{1}{15} + 3 \frac{2 \cdot 8 - 7}{8} - \frac{3}{4} \div \frac{11}{6}$

Step 2.7

Simplify the numerator.

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Step 2.7.1

Multiply $2$ by $8$ .

$\frac{1}{15} + 3 \frac{16 - 7}{8} - \frac{3}{4} \div \frac{11}{6}$

Step 2.7.2

Subtract $7$ from $16$ .

$\frac{1}{15} + 3 (\frac{9}{8}) - \frac{3}{4} \div \frac{11}{6}$

Step 2.8

Multiply $3 (\frac{9}{8})$ .

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Step 2.8.1

Combine $3$ and $\frac{9}{8}$ .

$\frac{1}{15} + \frac{3 \cdot 9}{8} - \frac{3}{4} \div \frac{11}{6}$

Step 2.8.2

Multiply $3$ by $9$ .

$\frac{1}{15} + \frac{27}{8} - \frac{3}{4} \div \frac{11}{6}$

Step 2.9

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{15} + \frac{27}{8} - (\frac{3}{4} \cdot \frac{6}{11})$

Step 2.10

Cancel the common factor of $2$ .

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Step 2.10.1

Factor $2$ out of $4$ .

$\frac{1}{15} + \frac{27}{8} - (\frac{3}{2 (2)} \cdot \frac{6}{11})$

Step 2.10.2

Factor $2$ out of $6$ .

$\frac{1}{15} + \frac{27}{8} - (\frac{3}{2 \cdot 2} \cdot \frac{2 \cdot 3}{11})$

Step 2.10.3

Cancel the common factor.

$\frac{1}{15} + \frac{27}{8} - (\frac{3}{2 \cdot 2} \cdot \frac{2 \cdot 3}{11})$

Step 2.10.4

Rewrite the expression.

$\frac{1}{15} + \frac{27}{8} - (\frac{3}{2} \cdot \frac{3}{11})$

Step 2.11

Multiply $\frac{3}{2}$ by $\frac{3}{11}$ .

$\frac{1}{15} + \frac{27}{8} - \frac{3 \cdot 3}{2 \cdot 11}$

Step 2.12

Multiply $3$ by $3$ .

$\frac{1}{15} + \frac{27}{8} - \frac{9}{2 \cdot 11}$

Step 2.13

Multiply $2$ by $11$ .

$\frac{1}{15} + \frac{27}{8} - \frac{9}{22}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{1}{15}$ by $\frac{88}{88}$ .

$\frac{1}{15} \cdot \frac{88}{88} + \frac{27}{8} - \frac{9}{22}$

Step 3.2

Multiply $\frac{1}{15}$ by $\frac{88}{88}$ .

$\frac{88}{15 \cdot 88} + \frac{27}{8} - \frac{9}{22}$

Step 3.3

Multiply $\frac{27}{8}$ by $\frac{165}{165}$ .

$\frac{88}{15 \cdot 88} + \frac{27}{8} \cdot \frac{165}{165} - \frac{9}{22}$

Step 3.4

Multiply $\frac{27}{8}$ by $\frac{165}{165}$ .

$\frac{88}{15 \cdot 88} + \frac{27 \cdot 165}{8 \cdot 165} - \frac{9}{22}$

Step 3.5

Multiply $\frac{9}{22}$ by $\frac{60}{60}$ .

$\frac{88}{15 \cdot 88} + \frac{27 \cdot 165}{8 \cdot 165} - (\frac{9}{22} \cdot \frac{60}{60})$

Step 3.6

Multiply $\frac{9}{22}$ by $\frac{60}{60}$ .

$\frac{88}{15 \cdot 88} + \frac{27 \cdot 165}{8 \cdot 165} - \frac{9 \cdot 60}{22 \cdot 60}$

Step 3.7

Multiply $15$ by $88$ .

$\frac{88}{1320} + \frac{27 \cdot 165}{8 \cdot 165} - \frac{9 \cdot 60}{22 \cdot 60}$

Step 3.8

Multiply $8$ by $165$ .

$\frac{88}{1320} + \frac{27 \cdot 165}{1320} - \frac{9 \cdot 60}{22 \cdot 60}$

Step 3.9

Multiply $22$ by $60$ .

$\frac{88}{1320} + \frac{27 \cdot 165}{1320} - \frac{9 \cdot 60}{1320}$

Step 4

Combine the numerators over the common denominator.

$\frac{88 + 27 \cdot 165 - 9 \cdot 60}{1320}$

Step 5

Simplify each term.

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Step 5.1

Multiply $27$ by $165$ .

$\frac{88 + 4455 - 9 \cdot 60}{1320}$

Step 5.2

Multiply $- 9$ by $60$ .

$\frac{88 + 4455 - 540}{1320}$

Step 6

Simplify by adding and subtracting.

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Step 6.1

Add $88$ and $4455$ .

$\frac{4543 - 540}{1320}$

Step 6.2

Subtract $540$ from $4543$ .

$\frac{4003}{1320}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{4003}{1320}$

Decimal Form:

$3.032\overline{57}$

Mixed Number Form:

$3 \frac{43}{1320}$