Basic Math Examples

$| 0.5 | + | - 1 \frac{1}{2} |$

Step 1

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

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Step 1.1

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

$| 0.5 | + | - (1 + \frac{1}{2}) |$

Step 1.2

Add $1$ and $\frac{1}{2}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$| 0.5 | + | - (\frac{2}{2} + \frac{1}{2}) |$

Step 1.2.2

Combine the numerators over the common denominator.

$| 0.5 | + | - \frac{2 + 1}{2} |$

Step 1.2.3

Add $2$ and $1$ .

$| 0.5 | + | - \frac{3}{2} |$

Step 2

Simplify each term.

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Step 2.1

The absolute value is the distance between a number and zero. The distance between $0$ and $0.5$ is $0.5$ .

$0.5 + | - \frac{3}{2} |$

Step 2.2

$- \frac{3}{2}$ is approximately $- 1.5$ which is negative so negate $- \frac{3}{2}$ and remove the absolute value

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Step 2.2.1

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

$0.5 + 1 + \frac{1}{2}$

Step 2.2.2

Add $1$ and $\frac{1}{2}$ .

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Step 2.2.2.1

Write $1$ as a fraction with a common denominator.

$0.5 + \frac{2}{2} + \frac{1}{2}$

Step 2.2.2.2

Combine the numerators over the common denominator.

$0.5 + \frac{2 + 1}{2}$

Step 2.2.2.3

Add $2$ and $1$ .

$0.5 + \frac{3}{2}$

Step 3

To write $0.5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$0.5 \cdot \frac{2}{2} + \frac{3}{2}$

Step 4

Combine $0.5$ and $\frac{2}{2}$ .

$\frac{0.5 \cdot 2}{2} + \frac{3}{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{0.5 \cdot 2 + 3}{2}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $0.5$ by $2$ .

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

Step 6.2

Add $1$ and $3$ .

$\frac{4}{2}$

Step 7

Divide $4$ by $2$ .

$2$