What is 2/3+((-1)/8+3/4) ?

The solution to 2/3+((-1)/8+3/4) is 1 7/24

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Popular Pre Algebra >

2/3+((-1)/8+3/4)

Solution

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

Solution

1 \frac{7}{24}

Decimal

1.29166 \dots

Solution steps

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

Apply the fraction rule

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

- \frac{1}{8}

= \frac{2}{3} - \frac{1}{8} + \frac{3}{4}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{2}{3} - \frac{1}{8} + \frac{3}{4} : \frac{31}{24}

\frac{2}{3} - \frac{1}{8} + \frac{3}{4}

\frac{2}{3} - \frac{1}{8} = \frac{13}{24}

\frac{2}{3} - \frac{1}{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{2}{3} :

multiply the denominator and numerator by

8

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

For

\frac{1}{8} :

multiply the denominator and numerator by

3

\frac{1}{8} = \frac{1 \cdot 3}{8 \cdot 3} = \frac{3}{24}

= \frac{16}{24} - \frac{3}{24}

Since the denominators are equal, combine the fractions:

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

= \frac{16 - 3}{24}

Subtract the numbers:

16 - 3 = 13

= \frac{13}{24}

= \frac{13}{24} + \frac{3}{4}

\frac{13}{24} + \frac{3}{4} = \frac{31}{24}

\frac{13}{24} + \frac{3}{4}

Least Common Multiplier of

24, 4 : 24

24, 4

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

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

24

4

= 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}{4} :

multiply the denominator and numerator by

6

\frac{3}{4} = \frac{3 \cdot 6}{4 \cdot 6} = \frac{18}{24}

= \frac{13}{24} + \frac{18}{24}

Since the denominators are equal, combine the fractions:

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

= \frac{13 + 18}{24}

Add the numbers:

13 + 18 = 31

= \frac{31}{24}

= \frac{31}{24}

= \frac{31}{24}

Convert improper fractions to mixed numbers:

\frac{31}{24} = 1 \frac{7}{24}

\frac{31}{24} = 1

Remainder

7

\frac{31}{24}

Write the problem in long division format

24 \overline{∣ 31}

Divide

31

24

to get

1

Divide

31

24

to get

1

1 24 \overline{∣ 31}

Multiply the quotient digit

(1)

by the divisor

24

1 24 \overline{∣ 31} \underline{24}

Subtract

24

from

31

1 24 \overline{∣ 31} \underline{24} 7

1 24 \overline{∣ 31} \underline{24} 7

The solution for Long Division of

\frac{31}{24}

1

with remainder of

7

1 Remainder 7

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{31}{24} = 1 \frac{7}{24}

= 1 \frac{7}{24}

= 1 \frac{7}{24}

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Frequently Asked Questions (FAQ)

What is 2/3+((-1)/8+3/4) ?
The solution to 2/3+((-1)/8+3/4) is 1 7/24

2/3+((-1)/8+3/4)

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 2/3+((-1)/8+3/4) ?

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