Algebra Examples

37 \frac{1}{2} %

$37 \frac{1}{2} %$

Step 1

Convert the percentage to a fraction by placing the expression over

100

$100$ . Percentage means 'out of

100

$100$ '.

\frac{37 \frac{1}{2}}{100}

$\frac{37 \frac{1}{2}}{100}$

Step 2

Reduce the fraction.

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Step 2.1

Convert

37 \frac{1}{2}

$37 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1

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

\frac{37 + \frac{1}{2}}{100}

$\frac{37 + \frac{1}{2}}{100}$

Step 2.1.2

Add

37

$37$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.1.2.1

To write

37

$37$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{37 \cdot \frac{2}{2} + \frac{1}{2}}{100}

$\frac{37 \cdot \frac{2}{2} + \frac{1}{2}}{100}$

Step 2.1.2.2

Combine

37

$37$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{\frac{37 \cdot 2}{2} + \frac{1}{2}}{100}

$\frac{\frac{37 \cdot 2}{2} + \frac{1}{2}}{100}$

Step 2.1.2.3

Combine the numerators over the common denominator.

\frac{\frac{37 \cdot 2 + 1}{2}}{100}

$\frac{\frac{37 \cdot 2 + 1}{2}}{100}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply

37

$37$ by

2

$2$ .

\frac{\frac{74 + 1}{2}}{100}

$\frac{\frac{74 + 1}{2}}{100}$

Step 2.1.2.4.2

Add

74

$74$ and

1

$1$ .

\frac{\frac{75}{2}}{100}

$\frac{\frac{75}{2}}{100}$

\frac{\frac{75}{2}}{100}

$\frac{\frac{75}{2}}{100}$

\frac{\frac{75}{2}}{100}

$\frac{\frac{75}{2}}{100}$

\frac{\frac{75}{2}}{100}

$\frac{\frac{75}{2}}{100}$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

\frac{75}{2} \cdot \frac{1}{100}

$\frac{75}{2} \cdot \frac{1}{100}$

Step 2.3

Cancel the common factor of

25

$25$ .

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Step 2.3.1

Factor

25

$25$ out of

75

$75$ .

\frac{25 (3)}{2} \cdot \frac{1}{100}

$\frac{25 (3)}{2} \cdot \frac{1}{100}$

Step 2.3.2

Factor

25

$25$ out of

100

$100$ .

\frac{25 \cdot 3}{2} \cdot \frac{1}{25 \cdot 4}

$\frac{25 \cdot 3}{2} \cdot \frac{1}{25 \cdot 4}$

Step 2.3.3

Cancel the common factor.

$\frac{25 \cdot 3}{2} \cdot \frac{1}{25 \cdot 4}$

Step 2.3.4

Rewrite the expression.

$\frac{3}{2} \cdot \frac{1}{4}$

Step 2.4

Multiply

$\frac{3}{2}$ by

$\frac{1}{4}$ .

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

Step 2.5

Multiply

$2$ by

$4$ .

$\frac{3}{8}$