Basic Math Examples

$(1 \frac{1}{2} - \frac{7}{8}) \div \frac{5}{13}$

Step 1

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

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Step 1.1

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

$(1 + \frac{1}{2} - \frac{7}{8}) \div \frac{5}{13}$

Step 1.2

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

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Step 1.2.1

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

$(\frac{2}{2} + \frac{1}{2} - \frac{7}{8}) \div \frac{5}{13}$

Step 1.2.2

Combine the numerators over the common denominator.

$(\frac{2 + 1}{2} - \frac{7}{8}) \div \frac{5}{13}$

Step 1.2.3

Add $2$ and $1$ .

$(\frac{3}{2} - \frac{7}{8}) \div \frac{5}{13}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$(\frac{3}{2} - \frac{7}{8}) \frac{13}{5}$

Step 3

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{3}{2} \cdot \frac{4}{4} - \frac{7}{8}) \frac{13}{5}$

Step 4

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

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Step 4.1

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

$(\frac{3 \cdot 4}{2 \cdot 4} - \frac{7}{8}) \frac{13}{5}$

Step 4.2

Multiply $2$ by $4$ .

$(\frac{3 \cdot 4}{8} - \frac{7}{8}) \frac{13}{5}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 - 7}{8} \cdot \frac{13}{5}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $4$ .

$\frac{12 - 7}{8} \cdot \frac{13}{5}$

Step 6.2

Subtract $7$ from $12$ .

$\frac{5}{8} \cdot \frac{13}{5}$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Cancel the common factor.

$\frac{5}{8} \cdot \frac{13}{5}$

Step 7.2

Rewrite the expression.

$\frac{1}{8} \cdot 13$

Step 8

Combine $\frac{1}{8}$ and $13$ .

$\frac{13}{8}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{8}$

Decimal Form:

$1.625$

Mixed Number Form:

$1 \frac{5}{8}$