What is 2/3-(2\div 4/5+1/2) ?

The solution to 2/3-(2\div 4/5+1/2) is -7/3

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Popular >

2/3-(2\div 4/5+1/2)

Solution

\frac{2}{3} - (2 \div \frac{4}{5} + \frac{1}{2})

Solution

- \frac{7}{3}

Solution steps

\frac{2}{3} - (2 \div \frac{4}{5} + \frac{1}{2})

Follow the PEMDAS order of operations

Calculate within parentheses

(2 \div \frac{4}{5} + \frac{1}{2}) : 3

2 \div \frac{4}{5} + \frac{1}{2}

Multiply and divide (left to right)

2 \div \frac{4}{5} : \frac{5}{2}

2 \div \frac{4}{5}

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} \div \frac{4}{5}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{2}{1} \cdot \frac{5}{4}

Cross-cancel common factor:

2

2, 4

Greatest Common Divisor (GCD)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

The prime factors common to

2, 4

are

= 2

= \frac{5}{2}

= \frac{5}{2} + \frac{1}{2}

Add and subtract (left to right)

\frac{5}{2} + \frac{1}{2} : 3

\frac{5}{2} + \frac{1}{2}

\frac{5}{2} + \frac{1}{2} = 3

\frac{5}{2} + \frac{1}{2}

Apply rule

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

= \frac{5 + 1}{2}

Add the numbers:

5 + 1 = 6

= \frac{6}{2}

Divide the numbers:

\frac{6}{2} = 3

= 3

= 3

= 3

= \frac{2}{3} - 3

Add and subtract (left to right)

\frac{2}{3} - 3 : - \frac{7}{3}

\frac{2}{3} - 3

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

\frac{2}{3} - 3

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

- 3 \cdot 3 + 2 = - 7

- 3 \cdot 3 + 2

Multiply the numbers:

3 \cdot 3 = 9

= - 9 + 2

Add/Subtract the numbers:

- 9 + 2 = - 7

= - 7

= \frac{- 7}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{7}{3}

= - \frac{7}{3}

= - \frac{7}{3}

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Frequently Asked Questions (FAQ)

What is 2/3-(2\div 4/5+1/2) ?
The solution to 2/3-(2\div 4/5+1/2) is -7/3