What is 3/5+(1/2+7/8) ?

The solution to 3/5+(1/2+7/8) is 1 39/40

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Popular Pre Algebra >

3/5+(1/2+7/8)

Solution

\frac{3}{5} + (\frac{1}{2} + \frac{7}{8})

Solution

1 \frac{39}{40}

Decimal

1.975

Solution steps

\frac{3}{5} + (\frac{1}{2} + \frac{7}{8})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{2} + \frac{7}{8}) : \frac{11}{8}

\frac{1}{2} + \frac{7}{8}

\frac{1}{2} + \frac{7}{8} = \frac{11}{8}

\frac{1}{2} + \frac{7}{8}

Least Common Multiplier of

2, 8 : 8

2, 8

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

2

8

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

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

8

For

\frac{1}{2} :

multiply the denominator and numerator by

4

\frac{1}{2} = \frac{1 \cdot 4}{2 \cdot 4} = \frac{4}{8}

= \frac{4}{8} + \frac{7}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{4 + 7}{8}

Add the numbers:

4 + 7 = 11

= \frac{11}{8}

= \frac{11}{8}

= \frac{3}{5} + \frac{11}{8}

Add and subtract (left to right)

\frac{3}{5} + \frac{11}{8} : \frac{79}{40}

\frac{3}{5} + \frac{11}{8}

\frac{3}{5} + \frac{11}{8} = \frac{79}{40}

\frac{3}{5} + \frac{11}{8}

Least Common Multiplier of

5, 8 : 40

5, 8

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

5

8

= 5 \cdot 2 \cdot 2 \cdot 2

Multiply the numbers:

5 \cdot 2 \cdot 2 \cdot 2 = 40

= 40

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

40

For

\frac{3}{5} :

multiply the denominator and numerator by

8

\frac{3}{5} = \frac{3 \cdot 8}{5 \cdot 8} = \frac{24}{40}

For

\frac{11}{8} :

multiply the denominator and numerator by

5

\frac{11}{8} = \frac{11 \cdot 5}{8 \cdot 5} = \frac{55}{40}

= \frac{24}{40} + \frac{55}{40}

Since the denominators are equal, combine the fractions:

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

= \frac{24 + 55}{40}

Add the numbers:

24 + 55 = 79

= \frac{79}{40}

= \frac{79}{40}

= \frac{79}{40}

Convert improper fractions to mixed numbers:

\frac{79}{40} = 1 \frac{39}{40}

\frac{79}{40} = 1

Remainder

39

\frac{79}{40}

Write the problem in long division format

40 \overline{∣ 79}

Divide

79

40

to get

1

Divide

79

40

to get

1

1 40 \overline{∣ 79}

Multiply the quotient digit

(1)

by the divisor

40

1 40 \overline{∣ 79} \underline{40}

Subtract

40

from

79

1 40 \overline{∣ 79} \underline{40} 39

1 40 \overline{∣ 79} \underline{40} 39

The solution for Long Division of

\frac{79}{40}

1

with remainder of

39

1 Remainder 39

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{79}{40} = 1 \frac{39}{40}

= 1 \frac{39}{40}

= 1 \frac{39}{40}

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Frequently Asked Questions (FAQ)

What is 3/5+(1/2+7/8) ?
The solution to 3/5+(1/2+7/8) is 1 39/40

3/5+(1/2+7/8)

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 3/5+(1/2+7/8) ?

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