Basic Math Examples

∣ ∣ ∣ \frac{1}{3} - 2 ∣ ∣ ∣ \div \frac{5}{6} - 1

$| \frac{1}{3} - 2 | \div \frac{5}{6} - 1$

Step 1

To write

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

$\frac{3}{3}$ .

$| \frac{1}{3} - 2 \cdot \frac{3}{3} | \div \frac{5}{6} - 1$

Step 2

Combine

$- 2$ and

$\frac{3}{3}$ .

$| \frac{1}{3} + \frac{- 2 \cdot 3}{3} | \div \frac{5}{6} - 1$

Step 3

Combine the numerators over the common denominator.

$| \frac{1 - 2 \cdot 3}{3} | \div \frac{5}{6} - 1$

Step 4

Simplify the numerator.

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Step 4.1

Multiply

$- 2$ by

$3$ .

$| \frac{1 - 6}{3} | \div \frac{5}{6} - 1$

Step 4.2

Subtract

$6$ from

$1$ .

$| \frac{- 5}{3} | \div \frac{5}{6} - 1$

Step 5

Simplify each term.

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Step 5.1

To divide by a fraction, multiply by its reciprocal.

$| \frac{- 5}{3} | \frac{6}{5} - 1$

Step 5.2

Move the negative in front of the fraction.

$| - \frac{5}{3} | \frac{6}{5} - 1$

Step 5.3

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

$- 1.\overline{6}$ which is negative so negate

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

$\frac{5}{3} \cdot \frac{6}{5} - 1$

Step 5.4

Cancel the common factor of

$5$ .

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Step 5.4.1

Cancel the common factor.

$\frac{5}{3} \cdot \frac{6}{5} - 1$

Step 5.4.2

Rewrite the expression.

$\frac{1}{3} \cdot 6 - 1$

Step 5.5

Cancel the common factor of

$3$ .

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Step 5.5.1

Factor

$3$ out of

$6$ .

$\frac{1}{3} \cdot (3 (2)) - 1$

Step 5.5.2

Cancel the common factor.

$\frac{1}{3} \cdot (3 \cdot 2) - 1$

Step 5.5.3

Rewrite the expression.

$2 - 1$

Step 6

Subtract

$1$ from

$2$ .

$1$