Basic Math Examples

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

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

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.

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

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

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.

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

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

Step 1.2.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

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

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

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

$0$ and

0.5

$0.5$ is

0.5

$0.5$ .

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

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

Step 2.2

- \frac{3}{2}

$- \frac{3}{2}$ is approximately

- 1.5

$- 1.5$ which is negative so negate

- \frac{3}{2}

$- \frac{3}{2}$ 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}

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

Step 2.2.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 2.2.2.2

Combine the numerators over the common denominator.

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

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

Step 2.2.2.3

Add

2

$2$ and

1

$1$ .

0.5 + \frac{3}{2}

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

0.5 + \frac{3}{2}

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

0.5 + \frac{3}{2}

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

0.5 + \frac{3}{2}

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

Step 3

To write

0.5

$0.5$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 4

Combine

0.5

$0.5$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply

0.5

$0.5$ by

2

$2$ .

\frac{1 + 3}{2}

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

Step 6.2

Add

1

$1$ and

3

$3$ .

\frac{4}{2}

$\frac{4}{2}$

\frac{4}{2}

$\frac{4}{2}$

Step 7

Divide

4

$4$ by

2

$2$ .

2

$2$