What is 12/18 \div ((-1)/2+3/8) ?

The solution to 12/18 \div ((-1)/2+3/8) is -16/3

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12/18 \div ((-1)/2+3/8)

Solution

\frac{12}{18} \div (\frac{- 1}{2} + \frac{3}{8})

Solution

- \frac{16}{3}

Solution steps

\frac{12}{18} \div (\frac{- 1}{2} + \frac{3}{8})

\frac{12}{18} = \frac{2}{3}

Cancel the common factor:

6

\frac{2}{3}

= \frac{2}{3} \div (\frac{- 1}{2} + \frac{3}{8})

Apply the fraction rule

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

- \frac{1}{2}

= \frac{2}{3} \div (- \frac{1}{2} + \frac{3}{8})

Follow the PEMDAS order of operations

Calculate within parentheses

(- \frac{1}{2} + \frac{3}{8}) : - \frac{1}{8}

- \frac{1}{2} + \frac{3}{8}

- \frac{1}{2} + \frac{3}{8} = - \frac{1}{8}

- \frac{1}{2} + \frac{3}{8}

Least Common Multiplier of

2, 8 : 8

2, 8

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

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

2

8

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

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

8

For

\frac{1}{2} :

multiply the denominator and numerator by

4

\frac{1}{2} = \frac{1 \cdot 4}{2 \cdot 4} = \frac{4}{8}

= - \frac{4}{8} + \frac{3}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{- 4 + 3}{8}

Add/Subtract the numbers:

- 4 + 3 = - 1

= \frac{- 1}{8}

Apply the fraction rule:

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

= - \frac{1}{8}

= - \frac{1}{8}

= \frac{2}{3} \div (- \frac{1}{8})

Multiply and divide (left to right)

\frac{2}{3} \div (- \frac{1}{8}) : - \frac{16}{3}

\frac{2}{3} \div (- \frac{1}{8})

Apply rule

a \div (- b) = - a \div b

\frac{2}{3} \div (- \frac{1}{8}) = - \frac{2}{3} \div \frac{1}{8}

Apply the fraction rule:

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

= - \frac{2}{3} \cdot \frac{8}{1}

Apply rule

\frac{a}{1} = a

= - 8 \cdot \frac{2}{3}

Convert element to fraction:

8 = \frac{8}{1}

= \frac{2}{3} \cdot \frac{8}{1}

Multiply fractions:

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

= - \frac{2 \cdot 8}{3 \cdot 1}

Multiply the numbers:

2 \cdot 8 = 16

= - \frac{16}{3 \cdot 1}

Multiply the numbers:

3 \cdot 1 = 3

= - \frac{16}{3}

= - \frac{16}{3}

Popular Examples

3(2/3+5/6)-1/2

3 (\frac{2}{3} + \frac{5}{6}) - \frac{1}{2}

20-8+2^2*3

20 - 8 + 2^{2} \cdot 3

9[5-2(1+4)]

9 [5 - 2 (1 + 4)]

1-0-0

1 - 0 - 0

1+3/2 (3/7)

1 + \frac{3}{2} (\frac{3}{7})

Frequently Asked Questions (FAQ)

What is 12/18 \div ((-1)/2+3/8) ?
The solution to 12/18 \div ((-1)/2+3/8) is -16/3