Basic Math Examples

\frac{- 2}{5} - ∣ ∣ ∣ \frac{- 1}{10} + \frac{1}{- 2} ∣ ∣ ∣

$\frac{- 2}{5} - | \frac{- 1}{10} + \frac{1}{- 2} |$

Step 1

Simplify each term.

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Step 1.1

Move the negative in front of the fraction.

- \frac{2}{5} - ∣ ∣ ∣ \frac{- 1}{10} + \frac{1}{- 2} ∣ ∣ ∣

$- \frac{2}{5} - | \frac{- 1}{10} + \frac{1}{- 2} |$

Step 1.2

Simplify each term.

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Step 1.2.1

Move the negative in front of the fraction.

- \frac{2}{5} - ∣ ∣ ∣ - \frac{1}{10} + \frac{1}{- 2} ∣ ∣ ∣

$- \frac{2}{5} - | - \frac{1}{10} + \frac{1}{- 2} |$

Step 1.2.2

Move the negative in front of the fraction.

- \frac{2}{5} - ∣ ∣ ∣ - \frac{1}{10} - \frac{1}{2} ∣ ∣ ∣

$- \frac{2}{5} - | - \frac{1}{10} - \frac{1}{2} |$

- \frac{2}{5} - ∣ ∣ ∣ - \frac{1}{10} - \frac{1}{2} ∣ ∣ ∣

$- \frac{2}{5} - | - \frac{1}{10} - \frac{1}{2} |$

Step 1.3

To write

- \frac{1}{2}

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

\frac{5}{5}

$\frac{5}{5}$ .

- \frac{2}{5} - ∣ ∣ ∣ - \frac{1}{10} - \frac{1}{2} \cdot \frac{5}{5} ∣ ∣ ∣

$- \frac{2}{5} - | - \frac{1}{10} - \frac{1}{2} \cdot \frac{5}{5} |$

Step 1.4

Write each expression with a common denominator of

10

$10$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 1.4.1

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{5}{5}

$\frac{5}{5}$ .

- \frac{2}{5} - ∣ ∣ ∣ - \frac{1}{10} - \frac{5}{2 \cdot 5} ∣ ∣ ∣

$- \frac{2}{5} - | - \frac{1}{10} - \frac{5}{2 \cdot 5} |$

Step 1.4.2

Multiply

2

$2$ by

5

$5$ .

- \frac{2}{5} - ∣ ∣ ∣ - \frac{1}{10} - \frac{5}{10} ∣ ∣ ∣

$- \frac{2}{5} - | - \frac{1}{10} - \frac{5}{10} |$

- \frac{2}{5} - ∣ ∣ ∣ - \frac{1}{10} - \frac{5}{10} ∣ ∣ ∣

$- \frac{2}{5} - | - \frac{1}{10} - \frac{5}{10} |$

Step 1.5

Combine the numerators over the common denominator.

- \frac{2}{5} - ∣ ∣ ∣ \frac{- 1 - 5}{10} ∣ ∣ ∣

$- \frac{2}{5} - | \frac{- 1 - 5}{10} |$

Step 1.6

Subtract

5

$5$ from

- 1

$- 1$ .

- \frac{2}{5} - ∣ ∣ ∣ \frac{- 6}{10} ∣ ∣ ∣

$- \frac{2}{5} - | \frac{- 6}{10} |$

Step 1.7

Cancel the common factor of

- 6

$- 6$ and

10

$10$ .

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Step 1.7.1

Factor

2

$2$ out of

- 6

$- 6$ .

- \frac{2}{5} - ∣ ∣ ∣ \frac{2 (- 3)}{10} ∣ ∣ ∣

$- \frac{2}{5} - | \frac{2 (- 3)}{10} |$

Step 1.7.2

Cancel the common factors.

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Step 1.7.2.1

Factor

2

$2$ out of

10

$10$ .

- \frac{2}{5} - ∣ ∣ ∣ \frac{2 \cdot - 3}{2 \cdot 5} ∣ ∣ ∣

$- \frac{2}{5} - | \frac{2 \cdot - 3}{2 \cdot 5} |$

Step 1.7.2.2

Cancel the common factor.

$- \frac{2}{5} - | \frac{2 \cdot - 3}{2 \cdot 5} |$

Step 1.7.2.3

Rewrite the expression.

$- \frac{2}{5} - | \frac{- 3}{5} |$

Step 1.8

Move the negative in front of the fraction.

$- \frac{2}{5} - | - \frac{3}{5} |$

Step 1.9

$- \frac{3}{5}$ is approximately

$- 0.6$ which is negative so negate

$- \frac{3}{5}$ and remove the absolute value

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

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract

$3$ from

$- 2$ .

$\frac{- 5}{5}$

Step 2.2.2

Divide

$- 5$ by

$5$ .

$- 1$