What is (-3/8+5/12)\times (-24) ?

The solution to (-3/8+5/12)\times (-24) is -1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(-3/8+5/12)\times (-24)

Solution

(- \frac{3}{8} + \frac{5}{12}) \cdot (- 24)

Solution

- 1

Solution steps

(- \frac{3}{8} + \frac{5}{12}) (- 24)

Follow the PEMDAS order of operations

Calculate within parentheses

(- \frac{3}{8} + \frac{5}{12}) : \frac{1}{24}

- \frac{3}{8} + \frac{5}{12}

- \frac{3}{8} + \frac{5}{12} = \frac{1}{24}

- \frac{3}{8} + \frac{5}{12}

Least Common Multiplier of

8, 12 : 24

8, 12

Least Common Multiplier (LCM)

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

Prime factorization of

12 : 2 \cdot 2 \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

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

8

12

= 2 \cdot 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 3 = 24

= 24

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

24

For

\frac{3}{8} :

multiply the denominator and numerator by

3

\frac{3}{8} = \frac{3 \cdot 3}{8 \cdot 3} = \frac{9}{24}

For

\frac{5}{12} :

multiply the denominator and numerator by

2

\frac{5}{12} = \frac{5 \cdot 2}{12 \cdot 2} = \frac{10}{24}

= - \frac{9}{24} + \frac{10}{24}

Since the denominators are equal, combine the fractions:

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

= \frac{- 9 + 10}{24}

Add/Subtract the numbers:

- 9 + 10 = 1

= \frac{1}{24}

= \frac{1}{24}

= \frac{1}{24} (- 24)

Multiply and divide (left to right)

\frac{1}{24} (- 24) : - 1

\frac{1}{24} (- 24)

Apply rule

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

\frac{1}{24} (- 24) = - \frac{1}{24} \cdot 24

Convert element to fraction:

24 = \frac{24}{1}

= - \frac{1}{24} \cdot \frac{24}{1}

Cross-cancel common factor:

24

= - 1

= - 1

Popular Examples

10+9/2-9/4

10 + \frac{9}{2} - \frac{9}{4}

4(1)^3-36(1)

4 (1)^{3} - 36 (1)

5/8-(15/7+3/8)

\frac{5}{8} - (\frac{15}{7} + \frac{3}{8})

((-3))/(3^2-10(-3)+25)

\frac{( - 3 )}{3 ^{2} - 10 ( - 3 ) + 25}

-1/3000+242+6/125

- \frac{1}{3000} + 242 + \frac{6}{125}

Frequently Asked Questions (FAQ)

What is (-3/8+5/12)\times (-24) ?
The solution to (-3/8+5/12)\times (-24) is -1