Basic Math Examples

$38 \frac{2}{3} - 25 \frac{13}{16}$

Step 1

Convert

$38 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$38 + \frac{2}{3} - 25 \frac{13}{16}$

Step 1.2

Add

$38$ and

$\frac{2}{3}$ .

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Step 1.2.1

To write

$38$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$38 \cdot \frac{3}{3} + \frac{2}{3} - 25 \frac{13}{16}$

Step 1.2.2

Combine

$38$ and

$\frac{3}{3}$ .

$\frac{38 \cdot 3}{3} + \frac{2}{3} - 25 \frac{13}{16}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{38 \cdot 3 + 2}{3} - 25 \frac{13}{16}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$38$ by

$3$ .

$\frac{114 + 2}{3} - 25 \frac{13}{16}$

Step 1.2.4.2

Add

$114$ and

$2$ .

$\frac{116}{3} - 25 \frac{13}{16}$

Step 2

Convert

$25 \frac{13}{16}$ to an improper fraction.

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Step 2.1

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

$\frac{116}{3} - (25 + \frac{13}{16})$

Step 2.2

Add

$25$ and

$\frac{13}{16}$ .

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Step 2.2.1

To write

$25$ as a fraction with a common denominator, multiply by

$\frac{16}{16}$ .

$\frac{116}{3} - (25 \cdot \frac{16}{16} + \frac{13}{16})$

Step 2.2.2

Combine

$25$ and

$\frac{16}{16}$ .

$\frac{116}{3} - (\frac{25 \cdot 16}{16} + \frac{13}{16})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{116}{3} - \frac{25 \cdot 16 + 13}{16}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$25$ by

$16$ .

$\frac{116}{3} - \frac{400 + 13}{16}$

Step 2.2.4.2

Add

$400$ and

$13$ .

$\frac{116}{3} - \frac{413}{16}$

Step 3

To write

$\frac{116}{3}$ as a fraction with a common denominator, multiply by

$\frac{16}{16}$ .

$\frac{116}{3} \cdot \frac{16}{16} - \frac{413}{16}$

Step 4

To write

$- \frac{413}{16}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{116}{3} \cdot \frac{16}{16} - \frac{413}{16} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of

$48$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{116}{3}$ by

$\frac{16}{16}$ .

$\frac{116 \cdot 16}{3 \cdot 16} - \frac{413}{16} \cdot \frac{3}{3}$

Step 5.2

Multiply

$3$ by

$16$ .

$\frac{116 \cdot 16}{48} - \frac{413}{16} \cdot \frac{3}{3}$

Step 5.3

Multiply

$\frac{413}{16}$ by

$\frac{3}{3}$ .

$\frac{116 \cdot 16}{48} - \frac{413 \cdot 3}{16 \cdot 3}$

Step 5.4

Multiply

$16$ by

$3$ .

$\frac{116 \cdot 16}{48} - \frac{413 \cdot 3}{48}$

Step 6

Combine the numerators over the common denominator.

$\frac{116 \cdot 16 - 413 \cdot 3}{48}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$116$ by

$16$ .

$\frac{1856 - 413 \cdot 3}{48}$

Step 7.2

Multiply

$- 413$ by

$3$ .

$\frac{1856 - 1239}{48}$

Step 7.3

Subtract

$1239$ from

$1856$ .

$\frac{617}{48}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{617}{48}$

Decimal Form:

$12.8541\overline{6}$

Mixed Number Form:

$12 \frac{41}{48}$