What is 2/3 (4 1/6-7/6) ?

The solution to 2/3 (4 1/6-7/6) is 2

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2/3 (4 1/6-7/6)

\frac{2}{3} (4 \frac{1}{6} - \frac{7}{6})

2

Solution steps

\frac{2}{3} (4 \frac{1}{6} - \frac{7}{6})

Convert mixed numbers to improper fractions:

4 \frac{1}{6} = \frac{25}{6}

4 \frac{1}{6}

Convert mixed numbers to improper fraction:

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

4 \frac{1}{6} = \frac{4 \cdot 6 + 1}{6}

= \frac{25}{6}

= \frac{2}{3} (\frac{25}{6} - \frac{7}{6})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{25}{6} - \frac{7}{6}) : 3

\frac{25}{6} - \frac{7}{6}

\frac{25}{6} - \frac{7}{6} = 3

\frac{25}{6} - \frac{7}{6}

Apply rule

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

= \frac{25 - 7}{6}

Subtract the numbers:

25 - 7 = 18

= \frac{18}{6}

Divide the numbers:

\frac{18}{6} = 3

= 3

= 3

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

Multiply and divide (left to right)

\frac{2}{3} \cdot 3 : 2

\frac{2}{3} \cdot 3

Convert element to fraction:

3 = \frac{3}{1}

= \frac{2}{3} \cdot \frac{3}{1}

Cross-cancel common factor:

3

= \frac{2}{1}

Divide the numbers:

\frac{2}{1} = 2

= 2

= 2

3 + 2 - 5

500 - (31 - 6) \div 5 - 3 \div (4 - 1)

- 2 \times (5 + 2)

7^{2} - 4 (3) (3)

- (- 9) (2) + [(6) + (- 4) + (- 2)]