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

The solution to 2/3-(1+1/2) is -5/6

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Popular >

2/3-(1+1/2)

Solution

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

Solution

- \frac{5}{6}

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

(1 + \frac{1}{2}) : \frac{3}{2}

1 + \frac{1}{2}

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

1 + \frac{1}{2}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

1 \cdot 2 + 1 = 3

1 \cdot 2 + 1

Multiply the numbers:

1 \cdot 2 = 2

= 2 + 1

Add the numbers:

2 + 1 = 3

= 3

= \frac{3}{2}

= \frac{3}{2}

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

Add and subtract (left to right)

\frac{2}{3} - \frac{3}{2} : - \frac{5}{6}

\frac{2}{3} - \frac{3}{2}

\frac{2}{3} - \frac{3}{2} = - \frac{5}{6}

\frac{2}{3} - \frac{3}{2}

Least Common Multiplier of

3, 2 : 6

3, 2

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Multiply each factor the greatest number of times it occurs in either

3

2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= 6

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

6

For

\frac{2}{3} :

multiply the denominator and numerator by

2

\frac{2}{3} = \frac{2 \cdot 2}{3 \cdot 2} = \frac{4}{6}

For

\frac{3}{2} :

multiply the denominator and numerator by

3

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

= \frac{4}{6} - \frac{9}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{4 - 9}{6}

Subtract the numbers:

4 - 9 = - 5

= \frac{- 5}{6}

Apply the fraction rule:

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

= - \frac{5}{6}

= - \frac{5}{6}

= - \frac{5}{6}

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Frequently Asked Questions (FAQ)

What is 2/3-(1+1/2) ?
The solution to 2/3-(1+1/2) is -5/6