Basic Math Examples

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

Step 1

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $2$ and $\frac{1}{2}$ .

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $2$ .

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

Step 1.2.4.2

Add $4$ and $1$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Combine the numerators over the common denominator.

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

Step 2.2.3

Add $5$ and $1$ .

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

Step 3

Convert $3 \frac{5}{8}$ to an improper fraction.

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Step 3.1

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

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

Step 3.2

Add $3$ and $\frac{5}{8}$ .

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Step 3.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Step 3.2.2

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

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

Step 3.2.3

Combine the numerators over the common denominator.

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

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $3$ by $8$ .

$\frac{1}{5} \cdot \frac{5}{2} \div \frac{6}{5} - \frac{1}{4} + \frac{24 + 5}{8}$

Step 3.2.4.2

Add $24$ and $5$ .

$\frac{1}{5} \cdot \frac{5}{2} \div \frac{6}{5} - \frac{1}{4} + \frac{29}{8}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{1}{5} \cdot \frac{5}{2} \div \frac{6}{5}$ by $\frac{8}{8}$ .

$\frac{1}{5} \cdot \frac{5}{2} \div \frac{6}{5} \cdot \frac{8}{8} - \frac{1}{4} + \frac{29}{8}$

Step 4.2

Multiply $\frac{1}{5} \cdot \frac{5}{2} \div \frac{6}{5}$ by $\frac{8}{8}$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{\frac{6}{5} \cdot 8} - \frac{1}{4} + \frac{29}{8}$

Step 4.3

Multiply $\frac{1}{4}$ by $\frac{\frac{6 \cdot 2}{5}}{\frac{6 \cdot 2}{5}}$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{\frac{6}{5} \cdot 8} - (\frac{1}{4} \cdot \frac{\frac{6 \cdot 2}{5}}{\frac{6 \cdot 2}{5}}) + \frac{29}{8}$

Step 4.4

Multiply $\frac{1}{4}$ by $\frac{\frac{6 \cdot 2}{5}}{\frac{6 \cdot 2}{5}}$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{\frac{6}{5} \cdot 8} - \frac{\frac{6 \cdot 2}{5}}{4 \frac{6 \cdot 2}{5}} + \frac{29}{8}$

Step 4.5

Multiply $\frac{29}{8}$ by $\frac{\frac{6}{5}}{\frac{6}{5}}$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{\frac{6}{5} \cdot 8} - \frac{\frac{6 \cdot 2}{5}}{4 \frac{6 \cdot 2}{5}} + \frac{29}{8} \cdot \frac{\frac{6}{5}}{\frac{6}{5}}$

Step 4.6

Multiply $\frac{29}{8}$ by $\frac{\frac{6}{5}}{\frac{6}{5}}$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{\frac{6}{5} \cdot 8} - \frac{\frac{6 \cdot 2}{5}}{4 \frac{6 \cdot 2}{5}} + \frac{29 (\frac{6}{5})}{8 (\frac{6}{5})}$

Step 4.7

Multiply $6$ by $2$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{\frac{6}{5} \cdot 8} - \frac{\frac{6 \cdot 2}{5}}{4 (\frac{12}{5})} + \frac{29 (\frac{6}{5})}{8 (\frac{6}{5})}$

Step 4.8

Combine $4$ and $\frac{12}{5}$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{\frac{6}{5} \cdot 8} - \frac{\frac{6 \cdot 2}{5}}{\frac{4 \cdot 12}{5}} + \frac{29 (\frac{6}{5})}{8 (\frac{6}{5})}$

Step 4.9

Multiply $4$ by $12$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{\frac{6}{5} \cdot 8} - \frac{\frac{6 \cdot 2}{5}}{\frac{48}{5}} + \frac{29 (\frac{6}{5})}{8 (\frac{6}{5})}$

Step 4.10

Combine $8$ and $\frac{6}{5}$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{\frac{6}{5} \cdot 8} - \frac{\frac{6 \cdot 2}{5}}{\frac{48}{5}} + \frac{29 (\frac{6}{5})}{\frac{8 \cdot 6}{5}}$

Step 4.11

Multiply $8$ by $6$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{\frac{6}{5} \cdot 8} - \frac{\frac{6 \cdot 2}{5}}{\frac{48}{5}} + \frac{29 (\frac{6}{5})}{\frac{48}{5}}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{8 (\frac{6}{5})} + \frac{- \frac{6 \cdot 2}{5} + 29 (\frac{6}{5})}{\frac{48}{5}}$

Step 6

Simplify each term.

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Step 6.1

Multiply $6$ by $2$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{8 (\frac{6}{5})} + \frac{- \frac{12}{5} + 29 (\frac{6}{5})}{\frac{48}{5}}$

Step 6.2

Multiply $29 (\frac{6}{5})$ .

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Step 6.2.1

Combine $29$ and $\frac{6}{5}$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{8 (\frac{6}{5})} + \frac{- \frac{12}{5} + \frac{29 \cdot 6}{5}}{\frac{48}{5}}$

Step 6.2.2

Multiply $29$ by $6$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{8 (\frac{6}{5})} + \frac{- \frac{12}{5} + \frac{174}{5}}{\frac{48}{5}}$

Step 7

Combine fractions.

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Step 7.1

Combine the numerators over the common denominator.

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{8 (\frac{6}{5})} + \frac{\frac{- 12 + 174}{5}}{\frac{48}{5}}$

Step 7.2

Add $- 12$ and $174$ .

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{8 (\frac{6}{5})} + \frac{\frac{162}{5}}{\frac{48}{5}}$

Step 8

Simplify each term.

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Step 8.1

Cancel the common factor of $8$ .

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Step 8.1.1

Cancel the common factor.

$\frac{\frac{1}{5} \cdot \frac{5}{2} \cdot 8}{8 (\frac{6}{5})} + \frac{\frac{162}{5}}{\frac{48}{5}}$

Step 8.1.2

Rewrite the expression.

$\frac{\frac{1}{5} \cdot \frac{5}{2}}{\frac{6}{5}} + \frac{\frac{162}{5}}{\frac{48}{5}}$

Step 8.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{5} \cdot \frac{5}{2} \frac{5}{6} + \frac{\frac{162}{5}}{\frac{48}{5}}$

Step 8.3

Cancel the common factor of $5$ .

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Step 8.3.1

Cancel the common factor.

$\frac{1}{5} \cdot \frac{5}{2} \frac{5}{6} + \frac{\frac{162}{5}}{\frac{48}{5}}$

Step 8.3.2

Rewrite the expression.

$\frac{1}{2} \cdot \frac{5}{6} + \frac{\frac{162}{5}}{\frac{48}{5}}$

Step 8.4

Multiply $\frac{1}{2} \cdot \frac{5}{6}$ .

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Step 8.4.1

Multiply $\frac{1}{2}$ by $\frac{5}{6}$ .

$\frac{5}{2 \cdot 6} + \frac{\frac{162}{5}}{\frac{48}{5}}$

Step 8.4.2

Multiply $2$ by $6$ .

$\frac{5}{12} + \frac{\frac{162}{5}}{\frac{48}{5}}$

Step 8.5

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{12} + \frac{162}{5} \cdot \frac{5}{48}$

Step 8.6

Cancel the common factor of $6$ .

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Step 8.6.1

Factor $6$ out of $162$ .

$\frac{5}{12} + \frac{6 (27)}{5} \cdot \frac{5}{48}$

Step 8.6.2

Factor $6$ out of $48$ .

$\frac{5}{12} + \frac{6 \cdot 27}{5} \cdot \frac{5}{6 \cdot 8}$

Step 8.6.3

Cancel the common factor.

$\frac{5}{12} + \frac{6 \cdot 27}{5} \cdot \frac{5}{6 \cdot 8}$

Step 8.6.4

Rewrite the expression.

$\frac{5}{12} + \frac{27}{5} \cdot \frac{5}{8}$

Step 8.7

Cancel the common factor of $5$ .

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Step 8.7.1

Cancel the common factor.

$\frac{5}{12} + \frac{27}{5} \cdot \frac{5}{8}$

Step 8.7.2

Rewrite the expression.

$\frac{5}{12} + 27 (\frac{1}{8})$

Step 8.8

Combine $27$ and $\frac{1}{8}$ .

$\frac{5}{12} + \frac{27}{8}$

Step 9

To write $\frac{5}{12}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{12} \cdot \frac{2}{2} + \frac{27}{8}$

Step 10

To write $\frac{27}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{12} \cdot \frac{2}{2} + \frac{27}{8} \cdot \frac{3}{3}$

Step 11

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 11.1

Multiply $\frac{5}{12}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 2}{12 \cdot 2} + \frac{27}{8} \cdot \frac{3}{3}$

Step 11.2

Multiply $12$ by $2$ .

$\frac{5 \cdot 2}{24} + \frac{27}{8} \cdot \frac{3}{3}$

Step 11.3

Multiply $\frac{27}{8}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 2}{24} + \frac{27 \cdot 3}{8 \cdot 3}$

Step 11.4

Multiply $8$ by $3$ .

$\frac{5 \cdot 2}{24} + \frac{27 \cdot 3}{24}$

Step 12

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 + 27 \cdot 3}{24}$

Step 13

Simplify the numerator.

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Step 13.1

Multiply $5$ by $2$ .

$\frac{10 + 27 \cdot 3}{24}$

Step 13.2

Multiply $27$ by $3$ .

$\frac{10 + 81}{24}$

Step 13.3

Add $10$ and $81$ .

$\frac{91}{24}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{91}{24}$

Decimal Form:

$3.791\overline{6}$

Mixed Number Form:

$3 \frac{19}{24}$