Basic Math Examples

$7 \frac{1}{2} \div 1 \frac{1}{4}$

Step 1

Convert

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

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Step 1.1

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

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

Step 1.2

Add

$7$ and

$\frac{1}{2}$ .

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Step 1.2.1

To write

$7$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

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

Step 1.2.2

Combine

$7$ and

$\frac{2}{2}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 + 1}{2} \div 1 \frac{1}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$7$ by

$2$ .

$\frac{14 + 1}{2} \div 1 \frac{1}{4}$

Step 1.2.4.2

Add

$14$ and

$1$ .

$\frac{15}{2} \div 1 \frac{1}{4}$

Step 2

Convert

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

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Step 2.1

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

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

Step 2.2

Add

$1$ and

$\frac{1}{4}$ .

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Step 2.2.1

Write

$1$ as a fraction with a common denominator.

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

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{15}{2} \div \frac{4 + 1}{4}$

Step 2.2.3

Add

$4$ and

$1$ .

$\frac{15}{2} \div \frac{5}{4}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{15}{2} \cdot \frac{4}{5}$

Step 4

Cancel the common factor of

$5$ .

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Step 4.1

Factor

$5$ out of

$15$ .

$\frac{5 (3)}{2} \cdot \frac{4}{5}$

Step 4.2

Cancel the common factor.

$\frac{5 \cdot 3}{2} \cdot \frac{4}{5}$

Step 4.3

Rewrite the expression.

$\frac{3}{2} \cdot 4$

Step 5

Cancel the common factor of

$2$ .

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Step 5.1

Factor

$2$ out of

$4$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$3 \cdot 2$

Step 6

Multiply

$3$ by

$2$ .

$6$