Basic Math Examples

$33 \frac{11}{20} - 15 \frac{19}{30}$

Step 1

Convert $33 \frac{11}{20}$ to an improper fraction.

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Step 1.1

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

$33 + \frac{11}{20} - 15 \frac{19}{30}$

Step 1.2

Add $33$ and $\frac{11}{20}$ .

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Step 1.2.1

To write $33$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$33 \cdot \frac{20}{20} + \frac{11}{20} - 15 \frac{19}{30}$

Step 1.2.2

Combine $33$ and $\frac{20}{20}$ .

$\frac{33 \cdot 20}{20} + \frac{11}{20} - 15 \frac{19}{30}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{33 \cdot 20 + 11}{20} - 15 \frac{19}{30}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $33$ by $20$ .

$\frac{660 + 11}{20} - 15 \frac{19}{30}$

Step 1.2.4.2

Add $660$ and $11$ .

$\frac{671}{20} - 15 \frac{19}{30}$

Step 2

Convert $15 \frac{19}{30}$ to an improper fraction.

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Step 2.1

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

$\frac{671}{20} - (15 + \frac{19}{30})$

Step 2.2

Add $15$ and $\frac{19}{30}$ .

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Step 2.2.1

To write $15$ as a fraction with a common denominator, multiply by $\frac{30}{30}$ .

$\frac{671}{20} - (15 \cdot \frac{30}{30} + \frac{19}{30})$

Step 2.2.2

Combine $15$ and $\frac{30}{30}$ .

$\frac{671}{20} - (\frac{15 \cdot 30}{30} + \frac{19}{30})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{671}{20} - \frac{15 \cdot 30 + 19}{30}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $15$ by $30$ .

$\frac{671}{20} - \frac{450 + 19}{30}$

Step 2.2.4.2

Add $450$ and $19$ .

$\frac{671}{20} - \frac{469}{30}$

Step 3

To write $\frac{671}{20}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{671}{20} \cdot \frac{3}{3} - \frac{469}{30}$

Step 4

To write $- \frac{469}{30}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{671}{20} \cdot \frac{3}{3} - \frac{469}{30} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{671}{20}$ by $\frac{3}{3}$ .

$\frac{671 \cdot 3}{20 \cdot 3} - \frac{469}{30} \cdot \frac{2}{2}$

Step 5.2

Multiply $20$ by $3$ .

$\frac{671 \cdot 3}{60} - \frac{469}{30} \cdot \frac{2}{2}$

Step 5.3

Multiply $\frac{469}{30}$ by $\frac{2}{2}$ .

$\frac{671 \cdot 3}{60} - \frac{469 \cdot 2}{30 \cdot 2}$

Step 5.4

Multiply $30$ by $2$ .

$\frac{671 \cdot 3}{60} - \frac{469 \cdot 2}{60}$

Step 6

Combine the numerators over the common denominator.

$\frac{671 \cdot 3 - 469 \cdot 2}{60}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $671$ by $3$ .

$\frac{2013 - 469 \cdot 2}{60}$

Step 7.2

Multiply $- 469$ by $2$ .

$\frac{2013 - 938}{60}$

Step 7.3

Subtract $938$ from $2013$ .

$\frac{1075}{60}$

Step 8

Cancel the common factor of $1075$ and $60$ .

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Step 8.1

Factor $5$ out of $1075$ .

$\frac{5 (215)}{60}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $5$ out of $60$ .

$\frac{5 \cdot 215}{5 \cdot 12}$

Step 8.2.2

Cancel the common factor.

$\frac{5 \cdot 215}{5 \cdot 12}$

Step 8.2.3

Rewrite the expression.

$\frac{215}{12}$