What is 2/3 \times (2-5/6) ?

The solution to 2/3 \times (2-5/6) is 7/9

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2/3 \times (2-5/6)

\frac{2}{3} \cdot (2 - \frac{5}{6})

\frac{7}{9}

Solution steps

\frac{2}{3} (2 - \frac{5}{6})

Follow the PEMDAS order of operations

Calculate within parentheses

(2 - \frac{5}{6}) : \frac{7}{6}

2 - \frac{5}{6}

2 - \frac{5}{6} = \frac{7}{6}

2 - \frac{5}{6}

Convert element to fraction:

2 = \frac{2 \cdot 6}{6}

= \frac{2 \cdot 6}{6} - \frac{5}{6}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 \cdot 6 - 5}{6}

2 \cdot 6 - 5 = 7

2 \cdot 6 - 5

Multiply the numbers:

2 \cdot 6 = 12

= 12 - 5

Subtract the numbers:

12 - 5 = 7

= 7

= \frac{7}{6}

= \frac{7}{6}

= \frac{2}{3} \cdot \frac{7}{6}

Multiply and divide (left to right)

\frac{2}{3} \cdot \frac{7}{6} : \frac{7}{9}

\frac{2}{3} \cdot \frac{7}{6}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{2 \cdot 7}{3 \cdot 6}

Cancel

\frac{2 \cdot 7}{3 \cdot 6} : \frac{7}{9}

\frac{2 \cdot 7}{3 \cdot 6}

Factor the number:

6 = 2 \cdot 3

= \frac{2 \cdot 7}{3 \cdot 2 \cdot 3}

Cancel the common factor:

2

= \frac{7}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{7}{9}

= \frac{7}{9}

= \frac{7}{9}

- 3 (- 2)^{2} + 1

- 4 (1) + 3

- 4^{2} + 5 (- 4) - 9

10 (2) + 6 (9)

- 4 (2) - 3