Basic Math Examples

$4 \frac{3}{8} - 1 \frac{5}{22} \div 3 \frac{3}{11} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 1

Convert $4 \frac{3}{8}$ to an improper fraction.

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Step 1.1

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

$4 + \frac{3}{8} - 1 \frac{5}{22} \div 3 \frac{3}{11} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 1.2

Add $4$ and $\frac{3}{8}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$4 \cdot \frac{8}{8} + \frac{3}{8} - 1 \frac{5}{22} \div 3 \frac{3}{11} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 1.2.2

Combine $4$ and $\frac{8}{8}$ .

$\frac{4 \cdot 8}{8} + \frac{3}{8} - 1 \frac{5}{22} \div 3 \frac{3}{11} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 8 + 3}{8} - 1 \frac{5}{22} \div 3 \frac{3}{11} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $8$ .

$\frac{32 + 3}{8} - 1 \frac{5}{22} \div 3 \frac{3}{11} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 1.2.4.2

Add $32$ and $3$ .

$\frac{35}{8} - 1 \frac{5}{22} \div 3 \frac{3}{11} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 2

Rewrite the division as a fraction.

$\frac{35}{8} - \frac{1 \frac{5}{22}}{3 \frac{3}{11}} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 3

Convert $1 \frac{5}{22}$ to an improper fraction.

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Step 3.1

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

$\frac{35}{8} - \frac{1 + \frac{5}{22}}{3 \frac{3}{11}} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 3.2

Add $1$ and $\frac{5}{22}$ .

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Step 3.2.1

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

$\frac{35}{8} - \frac{\frac{22}{22} + \frac{5}{22}}{3 \frac{3}{11}} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{35}{8} - \frac{\frac{22 + 5}{22}}{3 \frac{3}{11}} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 3.2.3

Add $22$ and $5$ .

$\frac{35}{8} - \frac{\frac{27}{22}}{3 \frac{3}{11}} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 4

Convert $3 \frac{3}{11}$ to an improper fraction.

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Step 4.1

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

$\frac{35}{8} - \frac{\frac{27}{22}}{3 + \frac{3}{11}} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 4.2

Add $3$ and $\frac{3}{11}$ .

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Step 4.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{35}{8} - \frac{\frac{27}{22}}{3 \cdot \frac{11}{11} + \frac{3}{11}} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 4.2.2

Combine $3$ and $\frac{11}{11}$ .

$\frac{35}{8} - \frac{\frac{27}{22}}{\frac{3 \cdot 11}{11} + \frac{3}{11}} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{35}{8} - \frac{\frac{27}{22}}{\frac{3 \cdot 11 + 3}{11}} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $3$ by $11$ .

$\frac{35}{8} - \frac{\frac{27}{22}}{\frac{33 + 3}{11}} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 4.2.4.2

Add $33$ and $3$ .

$\frac{35}{8} - \frac{\frac{27}{22}}{\frac{36}{11}} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{35}{8} - (\frac{27}{22} \cdot \frac{11}{36}) + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 6

Cancel the common factor of $9$ .

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Step 6.1

Factor $9$ out of $27$ .

$\frac{35}{8} - (\frac{9 (3)}{22} \cdot \frac{11}{36}) + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 6.2

Factor $9$ out of $36$ .

$\frac{35}{8} - (\frac{9 \cdot 3}{22} \cdot \frac{11}{9 \cdot 4}) + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 6.3

Cancel the common factor.

$\frac{35}{8} - (\frac{9 \cdot 3}{22} \cdot \frac{11}{9 \cdot 4}) + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 6.4

Rewrite the expression.

$\frac{35}{8} - (\frac{3}{22} \cdot \frac{11}{4}) + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 7

Cancel the common factor of $11$ .

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Step 7.1

Factor $11$ out of $22$ .

$\frac{35}{8} - (\frac{3}{11 (2)} \cdot \frac{11}{4}) + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 7.2

Cancel the common factor.

$\frac{35}{8} - (\frac{3}{11 \cdot 2} \cdot \frac{11}{4}) + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 7.3

Rewrite the expression.

$\frac{35}{8} - (\frac{3}{2} \cdot \frac{1}{4}) + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 8

Multiply $\frac{3}{2}$ by $\frac{1}{4}$ .

$\frac{35}{8} - \frac{3}{2 \cdot 4} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 9

Multiply $2$ by $4$ .

$\frac{35}{8} - \frac{3}{8} + 2 \frac{1}{2} \cdot \frac{7}{12}$

Step 10

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

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Step 10.1

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

$\frac{35}{8} - \frac{3}{8} + (2 + \frac{1}{2}) \cdot \frac{7}{12}$

Step 10.2

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

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Step 10.2.1

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

$\frac{35}{8} - \frac{3}{8} + (2 \cdot \frac{2}{2} + \frac{1}{2}) \cdot \frac{7}{12}$

Step 10.2.2

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

$\frac{35}{8} - \frac{3}{8} + (\frac{2 \cdot 2}{2} + \frac{1}{2}) \cdot \frac{7}{12}$

Step 10.2.3

Combine the numerators over the common denominator.

$\frac{35}{8} - \frac{3}{8} + \frac{2 \cdot 2 + 1}{2} \cdot \frac{7}{12}$

Step 10.2.4

Simplify the numerator.

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Step 10.2.4.1

Multiply $2$ by $2$ .

$\frac{35}{8} - \frac{3}{8} + \frac{4 + 1}{2} \cdot \frac{7}{12}$

Step 10.2.4.2

Add $4$ and $1$ .

$\frac{35}{8} - \frac{3}{8} + \frac{5}{2} \cdot \frac{7}{12}$

Step 11

Multiply $\frac{5}{2} \cdot \frac{7}{12}$ .

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Step 11.1

Multiply $\frac{5}{2}$ by $\frac{7}{12}$ .

$\frac{35}{8} - \frac{3}{8} + \frac{5 \cdot 7}{2 \cdot 12}$

Step 11.2

Multiply $5$ by $7$ .

$\frac{35}{8} - \frac{3}{8} + \frac{35}{2 \cdot 12}$

Step 11.3

Multiply $2$ by $12$ .

$\frac{35}{8} - \frac{3}{8} + \frac{35}{24}$

Step 12

Combine the numerators over the common denominator.

$\frac{35 - 3}{8} + \frac{35}{24}$

Step 13

Subtract $3$ from $35$ .

$\frac{32}{8} + \frac{35}{24}$

Step 14

To write $\frac{32}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{32}{8} \cdot \frac{3}{3} + \frac{35}{24}$

Step 15

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

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Step 15.1

Multiply $\frac{32}{8}$ by $\frac{3}{3}$ .

$\frac{32 \cdot 3}{8 \cdot 3} + \frac{35}{24}$

Step 15.2

Multiply $8$ by $3$ .

$\frac{32 \cdot 3}{24} + \frac{35}{24}$

Step 16

Combine the numerators over the common denominator.

$\frac{32 \cdot 3 + 35}{24}$

Step 17

Simplify the numerator.

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Step 17.1

Multiply $32$ by $3$ .

$\frac{96 + 35}{24}$

Step 17.2

Add $96$ and $35$ .

$\frac{131}{24}$