Basic Math Examples

- \frac{1}{2} + 2 \frac{3}{8}

$- \frac{1}{2} + 2 \frac{3}{8}$

Step 1

Convert

2 \frac{3}{8}

$2 \frac{3}{8}$ to an improper fraction.

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Step 1.1

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

- \frac{1}{2} + 2 + \frac{3}{8}

$- \frac{1}{2} + 2 + \frac{3}{8}$

Step 1.2

Add

2

$2$ and

\frac{3}{8}

$\frac{3}{8}$ .

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Step 1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

- \frac{1}{2} + 2 \cdot \frac{8}{8} + \frac{3}{8}

$- \frac{1}{2} + 2 \cdot \frac{8}{8} + \frac{3}{8}$

Step 1.2.2

Combine

2

$2$ and

\frac{8}{8}

$\frac{8}{8}$ .

- \frac{1}{2} + \frac{2 \cdot 8}{8} + \frac{3}{8}

$- \frac{1}{2} + \frac{2 \cdot 8}{8} + \frac{3}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

- \frac{1}{2} + \frac{2 \cdot 8 + 3}{8}

$- \frac{1}{2} + \frac{2 \cdot 8 + 3}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

8

$8$ .

- \frac{1}{2} + \frac{16 + 3}{8}

$- \frac{1}{2} + \frac{16 + 3}{8}$

Step 1.2.4.2

Add

16

$16$ and

3

$3$ .

- \frac{1}{2} + \frac{19}{8}

$- \frac{1}{2} + \frac{19}{8}$

- \frac{1}{2} + \frac{19}{8}

$- \frac{1}{2} + \frac{19}{8}$

- \frac{1}{2} + \frac{19}{8}

$- \frac{1}{2} + \frac{19}{8}$

- \frac{1}{2} + \frac{19}{8}

$- \frac{1}{2} + \frac{19}{8}$

Step 2

To write

- \frac{1}{2}

$- \frac{1}{2}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

- \frac{1}{2} \cdot \frac{4}{4} + \frac{19}{8}

$- \frac{1}{2} \cdot \frac{4}{4} + \frac{19}{8}$

Step 3

Write each expression with a common denominator of

8

$8$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{4}{4}

$\frac{4}{4}$ .

- \frac{4}{2 \cdot 4} + \frac{19}{8}

$- \frac{4}{2 \cdot 4} + \frac{19}{8}$

Step 3.2

Multiply

2

$2$ by

4

$4$ .

- \frac{4}{8} + \frac{19}{8}

$- \frac{4}{8} + \frac{19}{8}$

- \frac{4}{8} + \frac{19}{8}

$- \frac{4}{8} + \frac{19}{8}$

Step 4

Combine the numerators over the common denominator.

\frac{- 4 + 19}{8}

$\frac{- 4 + 19}{8}$

Step 5

Add

- 4

$- 4$ and

19

$19$ .

\frac{15}{8}

$\frac{15}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{15}{8}

$\frac{15}{8}$

Decimal Form:

1.875

$1.875$

Mixed Number Form:

1 \frac{7}{8}

$1 \frac{7}{8}$