What is (3/4+1/7)((-2)/5) ?

The solution to (3/4+1/7)((-2)/5) is -5/14

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Popular >

(3/4+1/7)((-2)/5)

Solution

(\frac{3}{4} + \frac{1}{7}) (\frac{- 2}{5})

Solution

- \frac{5}{14}

Solution steps

(\frac{3}{4} + \frac{1}{7}) (\frac{- 2}{5})

Apply the fraction rule

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

- \frac{2}{5}

= (\frac{3}{4} + \frac{1}{7}) (- \frac{2}{5})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{3}{4} + \frac{1}{7}) : \frac{25}{28}

\frac{3}{4} + \frac{1}{7}

\frac{3}{4} + \frac{1}{7} = \frac{25}{28}

\frac{3}{4} + \frac{1}{7}

Least Common Multiplier of

4, 7 : 28

4, 7

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

7 : 7

7

7

is a prime number, therefore no factorization is possible

= 7

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

4

7

= 2 \cdot 2 \cdot 7

Multiply the numbers:

2 \cdot 2 \cdot 7 = 28

= 28

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

28

For

\frac{3}{4} :

multiply the denominator and numerator by

7

\frac{3}{4} = \frac{3 \cdot 7}{4 \cdot 7} = \frac{21}{28}

For

\frac{1}{7} :

multiply the denominator and numerator by

4

\frac{1}{7} = \frac{1 \cdot 4}{7 \cdot 4} = \frac{4}{28}

= \frac{21}{28} + \frac{4}{28}

Since the denominators are equal, combine the fractions:

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

= \frac{21 + 4}{28}

Add the numbers:

21 + 4 = 25

= \frac{25}{28}

= \frac{25}{28}

= \frac{25}{28} (- \frac{2}{5})

Multiply and divide (left to right)

\frac{25}{28} (- \frac{2}{5}) : - \frac{5}{14}

\frac{25}{28} (- \frac{2}{5})

Apply rule

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

\frac{25}{28} (- \frac{2}{5}) = - \frac{25}{28} \cdot \frac{2}{5}

Apply the fraction rule:

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

\frac{25}{28} \cdot \frac{2}{5} = \frac{25 \cdot 2}{28 \cdot 5}

= - \frac{25 \cdot 2}{28 \cdot 5}

Cancel

\frac{25 \cdot 2}{28 \cdot 5} : \frac{5}{14}

\frac{25 \cdot 2}{28 \cdot 5}

Factor the number:

25 = 5 \cdot 5

= \frac{5 \cdot 5 \cdot 2}{28 \cdot 5}

Cancel the common factor:

5

= \frac{5 \cdot 2}{28}

Factor the number:

28 = 2 \cdot 14

= \frac{5 \cdot 2}{2 \cdot 14}

Cancel the common factor:

2

= \frac{5}{14}

= - \frac{5}{14}

= - \frac{5}{14}

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Frequently Asked Questions (FAQ)

What is (3/4+1/7)((-2)/5) ?
The solution to (3/4+1/7)((-2)/5) is -5/14