Evaluate 7 1/2÷(4 1/2-5 1/8)

$7 \frac{1}{2} \div (4 \frac{1}{2} - 5 \frac{1}{8})$

Step 1

Convert $7 \frac{1}{2}$ to an improper fraction.

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

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

Add $7$ and $\frac{1}{2}$ .

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $7$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $7$ by $2$ .

$\frac{14 + 1}{2} \div (4 \frac{1}{2} - 5 \frac{1}{8})$

Add $14$ and $1$ .

$\frac{15}{2} \div (4 \frac{1}{2} - 5 \frac{1}{8})$

Step 2

Convert $4 \frac{1}{2}$ to an improper fraction.

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

$\frac{15}{2} \div (4 + \frac{1}{2} - 5 \frac{1}{8})$

Add $4$ and $\frac{1}{2}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{15}{2} \div (4 \cdot \frac{2}{2} + \frac{1}{2} - 5 \frac{1}{8})$

Combine $4$ and $\frac{2}{2}$ .

$\frac{15}{2} \div (\frac{4 \cdot 2}{2} + \frac{1}{2} - 5 \frac{1}{8})$

Combine the numerators over the common denominator.

$\frac{15}{2} \div (\frac{4 \cdot 2 + 1}{2} - 5 \frac{1}{8})$

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{15}{2} \div (\frac{8 + 1}{2} - 5 \frac{1}{8})$

Add $8$ and $1$ .

$\frac{15}{2} \div (\frac{9}{2} - 5 \frac{1}{8})$

Step 3

Convert $5 \frac{1}{8}$ to an improper fraction.

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

$\frac{15}{2} \div (\frac{9}{2} - (5 + \frac{1}{8}))$

Add $5$ and $\frac{1}{8}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{15}{2} \div (\frac{9}{2} - (5 \cdot \frac{8}{8} + \frac{1}{8}))$

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

$\frac{15}{2} \div (\frac{9}{2} - (\frac{5 \cdot 8}{8} + \frac{1}{8}))$

Combine the numerators over the common denominator.

$\frac{15}{2} \div (\frac{9}{2} - \frac{5 \cdot 8 + 1}{8})$

Simplify the numerator.

Multiply $5$ by $8$ .

$\frac{15}{2} \div (\frac{9}{2} - \frac{40 + 1}{8})$

Add $40$ and $1$ .

$\frac{15}{2} \div (\frac{9}{2} - \frac{41}{8})$

Step 4

Rewrite the division as a fraction.

$\frac{\frac{15}{2}}{\frac{9}{2} - \frac{41}{8}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{2} \cdot \frac{1}{\frac{9}{2} - \frac{41}{8}}$

Step 6

Simplify the denominator.

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{15}{2} \cdot \frac{1}{\frac{9}{2} \cdot \frac{4}{4} - \frac{41}{8}}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9}{2}$ by $\frac{4}{4}$ .

$\frac{15}{2} \cdot \frac{1}{\frac{9 \cdot 4}{2 \cdot 4} - \frac{41}{8}}$

Multiply $2$ by $4$ .

$\frac{15}{2} \cdot \frac{1}{\frac{9 \cdot 4}{8} - \frac{41}{8}}$

Combine the numerators over the common denominator.

$\frac{15}{2} \cdot \frac{1}{\frac{9 \cdot 4 - 41}{8}}$

Simplify the numerator.

Multiply $9$ by $4$ .

$\frac{15}{2} \cdot \frac{1}{\frac{36 - 41}{8}}$

Subtract $41$ from $36$ .

$\frac{15}{2} \cdot \frac{1}{\frac{- 5}{8}}$

Move the negative in front of the fraction.

$\frac{15}{2} \cdot \frac{1}{- \frac{5}{8}}$

Step 7

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{15}{2} \cdot \frac{- 1 (- 1)}{- \frac{5}{8}}$

Move the negative in front of the fraction.

$\frac{15}{2} (- \frac{1}{\frac{5}{8}})$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{2} (- (1 (\frac{8}{5})))$

Step 9

Multiply $\frac{8}{5}$ by $1$ .

$\frac{15}{2} (- \frac{8}{5})$

Step 10

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{8}{5}$ into the numerator.

$\frac{15}{2} \cdot \frac{- 8}{5}$

Factor $5$ out of $15$ .

$\frac{5 (3)}{2} \cdot \frac{- 8}{5}$

Cancel the common factor.

$\frac{5 \cdot 3}{2} \cdot \frac{- 8}{5}$

Rewrite the expression.

$\frac{3}{2} \cdot - 8$

Step 11

Cancel the common factor of $2$ .

Factor $2$ out of $- 8$ .

$\frac{3}{2} \cdot (2 (- 4))$

Cancel the common factor.

$\frac{3}{2} \cdot (2 \cdot - 4)$

Rewrite the expression.

$3 \cdot - 4$

Step 12

Multiply $3$ by $- 4$ .

$- 12$

Evaluate 7 1/2÷(4 1/2-5 1/8)

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