What is 1 1/8 /(1/4) ?

The solution to 1 1/8 /(1/4) is 4 1/2

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Popular >

Simplify 1 1/8÷(1/4)

Solution

1 \frac{1}{8} / (1/4)

Solution

4 \frac{1}{2}

Solution steps

1 \frac{1}{8} / (1/4)

Convert mixed numbers to improper fractions:

1 \frac{1}{8} = \frac{9}{8}

1 \frac{1}{8}

Convert mixed numbers to improper fraction:

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

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

= \frac{9}{8}

= \frac{9}{8} / (1/4)

Follow the PEMDAS order of operations

Calculate within parentheses

(1/4) : \frac{1}{4}

1/4

1/4 = \frac{1}{4}

= \frac{1}{4}

= \frac{9}{8} / \frac{1}{4}

Multiply and divide (left to right)

\frac{9}{8} / \frac{1}{4} : \frac{9}{2}

\frac{9}{8} / \frac{1}{4}

Apply the fraction rule:

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

= \frac{9}{8} \cdot \frac{4}{1}

Cross-cancel common factor:

4

4, 8

Greatest Common Divisor (GCD)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 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

The prime factors common to

4, 8

are

= 2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4

= \frac{9}{2}

= \frac{9}{2}

Convert improper fractions to mixed numbers:

\frac{9}{2} = 4 \frac{1}{2}

\frac{9}{2} = 4

Remainder

1

\frac{9}{2}

Write the problem in long division format

2 \overline{∣ 9}

Divide

9

2

to get

4

Divide

9

2

to get

4

4 2 \overline{∣ 9}

Multiply the quotient digit

(4)

by the divisor

2

4 2 \overline{∣ 9} \underline{8}

Subtract

8

from

9

4 2 \overline{∣ 9} \underline{8} 1

4 2 \overline{∣ 9} \underline{8} 1

The solution for Long Division of

\frac{9}{2}

4

with remainder of

1

4 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{9}{2} = 4 \frac{1}{2}

= 4 \frac{1}{2}

= 4 \frac{1}{2}

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171

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Frequently Asked Questions (FAQ)

What is 1 1/8 /(1/4) ?
The solution to 1 1/8 /(1/4) is 4 1/2