What is 8/5 \div (-2)-3*((-1)/4) ?

The solution to 8/5 \div (-2)-3*((-1)/4) is -1/20

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8/5 \div (-2)-3*((-1)/4)

Solution

\frac{8}{5} \div (- 2) - 3 \cdot (\frac{- 1}{4})

Solution

- \frac{1}{20}

Solution steps

\frac{8}{5} \div (- 2) - 3 (\frac{- 1}{4})

Apply the fraction rule

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

- \frac{1}{4}

= \frac{8}{5} \div (- 2) - 3 (- \frac{1}{4})

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{8}{5} \div (- 2) : - \frac{4}{5}

\frac{8}{5} \div (- 2)

Apply rule

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

\frac{8}{5} \div (- 2) = - \frac{8}{5} \div 2

Convert element to fraction:

2 = \frac{2}{1}

= - \frac{8}{5} \div \frac{2}{1}

Apply the fraction rule:

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

= - \frac{8}{5} \cdot \frac{1}{2}

Cross-cancel common factor:

2

= - \frac{4}{5}

= - \frac{4}{5} - 3 (- \frac{1}{4})

Multiply and divide (left to right)

3 (- \frac{1}{4}) : - \frac{3}{4}

3 (- \frac{1}{4})

Apply rule

a \cdot (- b) = - a \cdot b

3 (- \frac{1}{4}) = - 3 \cdot \frac{1}{4}

Convert element to fraction:

3 = \frac{3}{1}

= - \frac{3}{1} \cdot \frac{1}{4}

Apply the fraction rule:

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

\frac{3}{1} \cdot \frac{1}{4} = \frac{3 \cdot 1}{1 \cdot 4}

= - \frac{3 \cdot 1}{1 \cdot 4}

Multiply the numbers:

3 \cdot 1 = 3

= - \frac{3}{1 \cdot 4}

Multiply the numbers:

1 \cdot 4 = 4

= - \frac{3}{4}

= - \frac{4}{5} - (- \frac{3}{4})

Add and subtract (left to right)

- \frac{4}{5} - (- \frac{3}{4}) : - \frac{1}{20}

- \frac{4}{5} - (- \frac{3}{4})

Apply rule

- (- a) = + a

- (- \frac{3}{4}) = + \frac{3}{4}

= - \frac{4}{5} + \frac{3}{4}

- \frac{4}{5} + \frac{3}{4} = - \frac{1}{20}

- \frac{4}{5} + \frac{3}{4}

Least Common Multiplier of

5, 4 : 20

5, 4

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

5

4

= 5 \cdot 2 \cdot 2

Multiply the numbers:

5 \cdot 2 \cdot 2 = 20

= 20

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

20

For

\frac{4}{5} :

multiply the denominator and numerator by

4

\frac{4}{5} = \frac{4 \cdot 4}{5 \cdot 4} = \frac{16}{20}

For

\frac{3}{4} :

multiply the denominator and numerator by

5

\frac{3}{4} = \frac{3 \cdot 5}{4 \cdot 5} = \frac{15}{20}

= - \frac{16}{20} + \frac{15}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{- 16 + 15}{20}

Add/Subtract the numbers:

- 16 + 15 = - 1

= \frac{- 1}{20}

Apply the fraction rule:

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

= - \frac{1}{20}

= - \frac{1}{20}

= - \frac{1}{20}

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Frequently Asked Questions (FAQ)

What is 8/5 \div (-2)-3*((-1)/4) ?
The solution to 8/5 \div (-2)-3*((-1)/4) is -1/20