Combine 15 1/4-8 6/20

$15 \frac{1}{4} - 8 \frac{6}{20}$

Step 1

Convert $15 \frac{1}{4}$ to an improper fraction.

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

$15 + \frac{1}{4} - 8 \frac{6}{20}$

Add $15$ and $\frac{1}{4}$ .

To write $15$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$15 \cdot \frac{4}{4} + \frac{1}{4} - 8 \frac{6}{20}$

Combine $15$ and $\frac{4}{4}$ .

$\frac{15 \cdot 4}{4} + \frac{1}{4} - 8 \frac{6}{20}$

Combine the numerators over the common denominator.

$\frac{15 \cdot 4 + 1}{4} - 8 \frac{6}{20}$

Simplify the numerator.

Multiply $15$ by $4$ .

$\frac{60 + 1}{4} - 8 \frac{6}{20}$

Add $60$ and $1$ .

$\frac{61}{4} - 8 \frac{6}{20}$

Step 2

Convert $8 \frac{6}{20}$ to an improper fraction.

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

$\frac{61}{4} - (8 + \frac{6}{20})$

Add $8$ and $\frac{6}{20}$ .

To write $8$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{61}{4} - (8 \cdot \frac{20}{20} + \frac{6}{20})$

Combine $8$ and $\frac{20}{20}$ .

$\frac{61}{4} - (\frac{8 \cdot 20}{20} + \frac{6}{20})$

Combine the numerators over the common denominator.

$\frac{61}{4} - \frac{8 \cdot 20 + 6}{20}$

Simplify the numerator.

Multiply $8$ by $20$ .

$\frac{61}{4} - \frac{160 + 6}{20}$

Add $160$ and $6$ .

$\frac{61}{4} - \frac{166}{20}$

Step 3

Cancel the common factor of $166$ and $20$ .

Factor $2$ out of $166$ .

$\frac{61}{4} - \frac{2 (83)}{20}$

Cancel the common factors.

Factor $2$ out of $20$ .

$\frac{61}{4} - \frac{2 \cdot 83}{2 \cdot 10}$

Cancel the common factor.

$\frac{61}{4} - \frac{2 \cdot 83}{2 \cdot 10}$

Rewrite the expression.

$\frac{61}{4} - \frac{83}{10}$

Step 4

To write $\frac{61}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{61}{4} \cdot \frac{5}{5} - \frac{83}{10}$

Step 5

To write $- \frac{83}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{61}{4} \cdot \frac{5}{5} - \frac{83}{10} \cdot \frac{2}{2}$

Step 6

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{61}{4}$ by $\frac{5}{5}$ .

$\frac{61 \cdot 5}{4 \cdot 5} - \frac{83}{10} \cdot \frac{2}{2}$

Multiply $4$ by $5$ .

$\frac{61 \cdot 5}{20} - \frac{83}{10} \cdot \frac{2}{2}$

Multiply $\frac{83}{10}$ by $\frac{2}{2}$ .

$\frac{61 \cdot 5}{20} - \frac{83 \cdot 2}{10 \cdot 2}$

Multiply $10$ by $2$ .

$\frac{61 \cdot 5}{20} - \frac{83 \cdot 2}{20}$

Step 7

Combine the numerators over the common denominator.

$\frac{61 \cdot 5 - 83 \cdot 2}{20}$

Step 8

Simplify the numerator.

Multiply $61$ by $5$ .

$\frac{305 - 83 \cdot 2}{20}$

Multiply $- 83$ by $2$ .

$\frac{305 - 166}{20}$

Subtract $166$ from $305$ .

$\frac{139}{20}$

Combine 15 1/4-8 6/20

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