What is 3/2-(1/8)/(8/5) ?

The solution to 3/2-(1/8)/(8/5) is 1 27/64

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Popular Pre Algebra >

3/2-(1/8)/(8/5)

Solution

3/2 - (1/8) / (8/5)

Solution

1 \frac{27}{64}

Decimal

1.421875

Solution steps

3/2 - (1/8) / (8/5)

Follow the PEMDAS order of operations

Calculate within parentheses

(1/8) : \frac{1}{8}

1/8

1/8 = \frac{1}{8}

= \frac{1}{8}

= 3/2 - \frac{1}{8} / (8/5)

Calculate within parentheses

(8/5) : \frac{8}{5}

8/5

8/5 = \frac{8}{5}

= \frac{8}{5}

= 3/2 - \frac{1}{8} / \frac{8}{5}

Multiply and divide (left to right)

3/2 : \frac{3}{2}

3/2

3/2 = \frac{3}{2}

= \frac{3}{2}

= \frac{3}{2} - \frac{1}{8} / \frac{8}{5}

Multiply and divide (left to right)

\frac{1}{8} / \frac{8}{5} : \frac{5}{64}

\frac{1}{8} / \frac{8}{5}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{1}{8} \cdot \frac{5}{8}

Multiply fractions:

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

= \frac{1 \cdot 5}{8 \cdot 8}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5}{8 \cdot 8}

Multiply the numbers:

8 \cdot 8 = 64

= \frac{5}{64}

= \frac{3}{2} - \frac{5}{64}

Add and subtract (left to right)

\frac{3}{2} - \frac{5}{64} : \frac{91}{64}

\frac{3}{2} - \frac{5}{64}

\frac{3}{2} - \frac{5}{64} = \frac{91}{64}

\frac{3}{2} - \frac{5}{64}

Least Common Multiplier of

2, 64 : 64

2, 64

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

64 : 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2

64

64

divides by

264 = 32 \cdot 2

= 2 \cdot 32

32

divides by

232 = 16 \cdot 2

= 2 \cdot 2 \cdot 16

16

divides by

216 = 8 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2

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

2

64

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 64

= 64

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

64

For

\frac{3}{2} :

multiply the denominator and numerator by

32

\frac{3}{2} = \frac{3 \cdot 32}{2 \cdot 32} = \frac{96}{64}

= \frac{96}{64} - \frac{5}{64}

Since the denominators are equal, combine the fractions:

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

= \frac{96 - 5}{64}

Subtract the numbers:

96 - 5 = 91

= \frac{91}{64}

= \frac{91}{64}

= \frac{91}{64}

Convert improper fractions to mixed numbers:

\frac{91}{64} = 1 \frac{27}{64}

\frac{91}{64} = 1

Remainder

27

\frac{91}{64}

Write the problem in long division format

64 \overline{∣ 91}

Divide

91

64

to get

1

Divide

91

64

to get

1

1 64 \overline{∣ 91}

Multiply the quotient digit

(1)

by the divisor

64

1 64 \overline{∣ 91} \underline{64}

Subtract

64

from

91

1 64 \overline{∣ 91} \underline{64} 27

1 64 \overline{∣ 91} \underline{64} 27

The solution for Long Division of

\frac{91}{64}

1

with remainder of

27

1 Remainder 27

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{91}{64} = 1 \frac{27}{64}

= 1 \frac{27}{64}

= 1 \frac{27}{64}

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What is 3/2-(1/8)/(8/5) ?
The solution to 3/2-(1/8)/(8/5) is 1 27/64

3/2-(1/8)/(8/5)

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 3/2-(1/8)/(8/5) ?

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