What is -5/6+4/8-9/10+1/2 ?

The solution to -5/6+4/8-9/10+1/2 is -11/15

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Popular Pre Algebra >

-5/6+4/8-9/10+1/2

Solution

- 5/6 + 4/8 - 9/10 + 1/2

Solution

- \frac{11}{15}

Decimal

- 0.73333 \dots

Solution steps

- 5/6 + 4/8 - 9/10 + 1/2

Follow the PEMDAS order of operations

Multiply and divide (left to right)

- 5/6 : \frac{- 5}{6}

- 5/6

- 5/6 = \frac{- 5}{6}

= \frac{- 5}{6}

= \frac{- 5}{6} + 4/8 - 9/10 + 1/2

Multiply and divide (left to right)

4/8 : \frac{4}{8}

4/8

4/8 = \frac{4}{8}

= \frac{4}{8}

= \frac{- 5}{6} + \frac{4}{8} - 9/10 + 1/2

Multiply and divide (left to right)

9/10 : \frac{9}{10}

9/10

9/10 = \frac{9}{10}

= \frac{9}{10}

= \frac{- 5}{6} + \frac{4}{8} - \frac{9}{10} + 1/2

Multiply and divide (left to right)

1/2 : \frac{1}{2}

1/2

1/2 = \frac{1}{2}

= \frac{1}{2}

= \frac{- 5}{6} + \frac{4}{8} - \frac{9}{10} + \frac{1}{2}

Add and subtract (left to right)

\frac{- 5}{6} + \frac{4}{8} - \frac{9}{10} + \frac{1}{2} : - \frac{11}{15}

\frac{- 5}{6} + \frac{4}{8} - \frac{9}{10} + \frac{1}{2}

\frac{- 5}{6} + \frac{4}{8} = - \frac{1}{3}

\frac{- 5}{6} + \frac{4}{8}

Apply the fraction rule:

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

= - \frac{5}{6} + \frac{4}{8}

Cancel

\frac{4}{8} : \frac{1}{2}

\frac{4}{8}

Cancel the common factor:

4

= \frac{1}{2}

= - \frac{5}{6} + \frac{1}{2}

Least Common Multiplier of

6, 2 : 6

6, 2

Least Common Multiplier (LCM)

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

6

2

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

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

6

For

\frac{1}{2} :

multiply the denominator and numerator by

3

\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}

= - \frac{5}{6} + \frac{3}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{- 5 + 3}{6}

Add/Subtract the numbers:

- 5 + 3 = - 2

= \frac{- 2}{6}

Apply the fraction rule:

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

= - \frac{2}{6}

Cancel the common factor:

2

= - \frac{1}{3}

= - \frac{1}{3} - \frac{9}{10} + \frac{1}{2}

- \frac{1}{3} - \frac{9}{10} = - \frac{37}{30}

- \frac{1}{3} - \frac{9}{10}

Least Common Multiplier of

3, 10 : 30

3, 10

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5

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

3

10

= 3 \cdot 2 \cdot 5

Multiply the numbers:

3 \cdot 2 \cdot 5 = 30

= 30

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

30

For

\frac{1}{3} :

multiply the denominator and numerator by

10

\frac{1}{3} = \frac{1 \cdot 10}{3 \cdot 10} = \frac{10}{30}

For

\frac{9}{10} :

multiply the denominator and numerator by

3

\frac{9}{10} = \frac{9 \cdot 3}{10 \cdot 3} = \frac{27}{30}

= - \frac{10}{30} - \frac{27}{30}

Since the denominators are equal, combine the fractions:

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

= \frac{- 10 - 27}{30}

Subtract the numbers:

- 10 - 27 = - 37

= \frac{- 37}{30}

Apply the fraction rule:

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

= - \frac{37}{30}

= - \frac{37}{30} + \frac{1}{2}

- \frac{37}{30} + \frac{1}{2} = - \frac{11}{15}

- \frac{37}{30} + \frac{1}{2}

Least Common Multiplier of

30, 2 : 30

30, 2

Least Common Multiplier (LCM)

Prime factorization of

30 : 2 \cdot 3 \cdot 5

30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 5

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

30

2

= 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 3 \cdot 5 = 30

= 30

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

30

For

\frac{1}{2} :

multiply the denominator and numerator by

15

\frac{1}{2} = \frac{1 \cdot 15}{2 \cdot 15} = \frac{15}{30}

= - \frac{37}{30} + \frac{15}{30}

Since the denominators are equal, combine the fractions:

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

= \frac{- 37 + 15}{30}

Add/Subtract the numbers:

- 37 + 15 = - 22

= \frac{- 22}{30}

Apply the fraction rule:

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

= - \frac{22}{30}

Cancel the common factor:

2

= - \frac{11}{15}

= - \frac{11}{15}

= - \frac{11}{15}

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What is -5/6+4/8-9/10+1/2 ?
The solution to -5/6+4/8-9/10+1/2 is -11/15

-5/6+4/8-9/10+1/2

Solution

Solution

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What is -5/6+4/8-9/10+1/2 ?

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