What is (-1 1/3+7/8)+2/3 ?

The solution to (-1 1/3+7/8)+2/3 is 5/24

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Popular >

(-1 1/3+7/8)+2/3

Solution

(- 1 \frac{1}{3} + \frac{7}{8}) + \frac{2}{3}

Solution

\frac{5}{24}

Solution steps

(- 1 \frac{1}{3} + \frac{7}{8}) + \frac{2}{3}

Convert mixed numbers to improper fractions:

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

1 \frac{1}{3}

Convert mixed numbers to improper fraction:

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

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

= \frac{4}{3}

= (- \frac{4}{3} + \frac{7}{8}) + \frac{2}{3}

Follow the PEMDAS order of operations

Calculate within parentheses

(- \frac{4}{3} + \frac{7}{8}) : - \frac{11}{24}

- \frac{4}{3} + \frac{7}{8}

- \frac{4}{3} + \frac{7}{8} = - \frac{11}{24}

- \frac{4}{3} + \frac{7}{8}

Least Common Multiplier of

3, 8 : 24

3, 8

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

3

8

= 3 \cdot 2 \cdot 2 \cdot 2

Multiply the numbers:

3 \cdot 2 \cdot 2 \cdot 2 = 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{4}{3} :

multiply the denominator and numerator by

8

\frac{4}{3} = \frac{4 \cdot 8}{3 \cdot 8} = \frac{32}{24}

For

\frac{7}{8} :

multiply the denominator and numerator by

3

\frac{7}{8} = \frac{7 \cdot 3}{8 \cdot 3} = \frac{21}{24}

= - \frac{32}{24} + \frac{21}{24}

Since the denominators are equal, combine the fractions:

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

= \frac{- 32 + 21}{24}

Add/Subtract the numbers:

- 32 + 21 = - 11

= \frac{- 11}{24}

Apply the fraction rule:

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

= - \frac{11}{24}

= - \frac{11}{24}

= - \frac{11}{24} + \frac{2}{3}

Add and subtract (left to right)

- \frac{11}{24} + \frac{2}{3} : \frac{5}{24}

- \frac{11}{24} + \frac{2}{3}

- \frac{11}{24} + \frac{2}{3} = \frac{5}{24}

- \frac{11}{24} + \frac{2}{3}

Least Common Multiplier of

24, 3 : 24

24, 3

Least Common Multiplier (LCM)

Prime factorization of

24 : 2 \cdot 2 \cdot 2 \cdot 3

24

24

divides by

224 = 12 \cdot 2

= 2 \cdot 12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 3

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

24

3

= 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{2}{3} :

multiply the denominator and numerator by

8

\frac{2}{3} = \frac{2 \cdot 8}{3 \cdot 8} = \frac{16}{24}

= - \frac{11}{24} + \frac{16}{24}

Since the denominators are equal, combine the fractions:

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

= \frac{- 11 + 16}{24}

Add/Subtract the numbers:

- 11 + 16 = 5

= \frac{5}{24}

= \frac{5}{24}

= \frac{5}{24}

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Frequently Asked Questions (FAQ)

What is (-1 1/3+7/8)+2/3 ?
The solution to (-1 1/3+7/8)+2/3 is 5/24