Basic Math Examples

- \frac{5}{8} + 1 \frac{1}{2}

$- \frac{5}{8} + 1 \frac{1}{2}$

Step 1

Convert

1 \frac{1}{2}

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

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Step 1.1

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

- \frac{5}{8} + 1 + \frac{1}{2}

$- \frac{5}{8} + 1 + \frac{1}{2}$

Step 1.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

- \frac{5}{8} + \frac{2}{2} + \frac{1}{2}

$- \frac{5}{8} + \frac{2}{2} + \frac{1}{2}$

Step 1.2.2

Combine the numerators over the common denominator.

- \frac{5}{8} + \frac{2 + 1}{2}

$- \frac{5}{8} + \frac{2 + 1}{2}$

Step 1.2.3

Add

2

$2$ and

1

$1$ .

- \frac{5}{8} + \frac{3}{2}

$- \frac{5}{8} + \frac{3}{2}$

- \frac{5}{8} + \frac{3}{2}

$- \frac{5}{8} + \frac{3}{2}$

- \frac{5}{8} + \frac{3}{2}

$- \frac{5}{8} + \frac{3}{2}$

Step 2

To write

\frac{3}{2}

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

\frac{4}{4}

$\frac{4}{4}$ .

- \frac{5}{8} + \frac{3}{2} \cdot \frac{4}{4}

$- \frac{5}{8} + \frac{3}{2} \cdot \frac{4}{4}$

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{3}{2}

$\frac{3}{2}$ by

\frac{4}{4}

$\frac{4}{4}$ .

- \frac{5}{8} + \frac{3 \cdot 4}{2 \cdot 4}

$- \frac{5}{8} + \frac{3 \cdot 4}{2 \cdot 4}$

Step 3.2

Multiply

2

$2$ by

4

$4$ .

- \frac{5}{8} + \frac{3 \cdot 4}{8}

$- \frac{5}{8} + \frac{3 \cdot 4}{8}$

- \frac{5}{8} + \frac{3 \cdot 4}{8}

$- \frac{5}{8} + \frac{3 \cdot 4}{8}$

Step 4

Combine the numerators over the common denominator.

\frac{- 5 + 3 \cdot 4}{8}

$\frac{- 5 + 3 \cdot 4}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

3

$3$ by

4

$4$ .

\frac{- 5 + 12}{8}

$\frac{- 5 + 12}{8}$

Step 5.2

Add

- 5

$- 5$ and

12

$12$ .

\frac{7}{8}

$\frac{7}{8}$

\frac{7}{8}

$\frac{7}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{7}{8}

$\frac{7}{8}$

Decimal Form:

0.875

$0.875$