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

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

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

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

3

Solution steps

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

\frac{6}{1} = 6

Apply rule

\frac{a}{1} = a

6

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

Follow the PEMDAS order of operations

Calculate within parentheses

(6 - \frac{3}{2}) : \frac{9}{2}

6 - \frac{3}{2}

6 - \frac{3}{2} = \frac{9}{2}

6 - \frac{3}{2}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

6 \cdot 2 - 3 = 9

6 \cdot 2 - 3

Multiply the numbers:

6 \cdot 2 = 12

= 12 - 3

Subtract the numbers:

12 - 3 = 9

= 9

= \frac{9}{2}

= \frac{9}{2}

= \frac{2}{3} \cdot \frac{9}{2}

Multiply and divide (left to right)

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

\frac{2}{3} \cdot \frac{9}{2}

Cross-cancel common factor:

2

= \frac{9}{3}

Divide the numbers:

\frac{9}{3} = 3

= 3

= 3

3 (2 - 4) + 30 \div 6 - 2

2 \times \frac{22}{7} \times 7^{2}

6 + 5^{2}

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

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