What is 20 3/4 /(1/6) ?

The solution to 20 3/4 /(1/6) is 124 1/2

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Popular Pre Algebra >

Simplify 20 3/4÷(1/6)

Solution

20 \frac{3}{4} / (1/6)

Solution

124 \frac{1}{2}

Decimal

124.5

Solution steps

20 \frac{3}{4} / (1/6)

Convert mixed numbers to improper fractions:

20 \frac{3}{4} = \frac{83}{4}

20 \frac{3}{4}

Convert mixed numbers to improper fraction:

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

20 \frac{3}{4} = \frac{20 \cdot 4 + 3}{4}

= \frac{83}{4}

= \frac{83}{4} / (1/6)

Follow the PEMDAS order of operations

Calculate within parentheses

(1/6) : \frac{1}{6}

1/6

1/6 = \frac{1}{6}

= \frac{1}{6}

= \frac{83}{4} / \frac{1}{6}

Multiply and divide (left to right)

\frac{83}{4} / \frac{1}{6} : \frac{249}{2}

\frac{83}{4} / \frac{1}{6}

Apply the fraction rule:

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

= \frac{83}{4} \cdot \frac{6}{1}

Cross-cancel common factor:

2

6, 4

Greatest Common Divisor (GCD)

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

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

The prime factors common to

6, 4

are

= 2

= \frac{83}{2} \cdot \frac{3}{1}

Multiply fractions:

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

= \frac{83 \cdot 3}{2 \cdot 1}

Multiply the numbers:

83 \cdot 3 = 249

= \frac{249}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{249}{2}

= \frac{249}{2}

Convert improper fractions to mixed numbers:

\frac{249}{2} = 124 \frac{1}{2}

\frac{249}{2} = 124

Remainder

1

\frac{249}{2}

Write the problem in long division format

2 \overline{∣ 249}

Divide

2

2

to get

1

Divide

2

2

to get

1

1 2 \overline{∣ 249}

Multiply the quotient digit

(1)

by the divisor

2

1 2 \overline{∣ 249} \underline{2}

Subtract

2

from

2

1 2 \overline{∣ 249} \underline{2} 0

Bring down the next number of the dividend

1 2 \overline{∣ 249} \underline{2} 04

1 2 \overline{∣ 249} \underline{2} 04

Divide

4

2

to get

2

Divide

4

2

to get

2

12 2 \overline{∣ 249} \underline{2} 04

Multiply the quotient digit

(2)

by the divisor

2

12 2 \overline{∣ 249} \underline{2} 04 \underline{4}

Subtract

4

from

4

12 2 \overline{∣ 249} \underline{2} 04 \underline{4} 0

Bring down the next number of the dividend

12 2 \overline{∣ 249} \underline{2} 04 \underline{4} 09

12 2 \overline{∣ 249} \underline{2} 04 \underline{4} 09

Divide

9

2

to get

4

Divide

9

2

to get

4

124 2 \overline{∣ 249} \underline{2} 04 \underline{4} 09

Multiply the quotient digit

(4)

by the divisor

2

124 2 \overline{∣ 249} \underline{2} 04 \underline{4} 09 \underline{8}

Subtract

8

from

9

124 2 \overline{∣ 249} \underline{2} 04 \underline{4} 09 \underline{8} 1

124 2 \overline{∣ 249} \underline{2} 04 \underline{4} 09 \underline{8} 1

The solution for Long Division of

\frac{249}{2}

124

with remainder of

1

124 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{249}{2} = 124 \frac{1}{2}

= 124 \frac{1}{2}

= 124 \frac{1}{2}

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Frequently Asked Questions (FAQ)

What is 20 3/4 /(1/6) ?
The solution to 20 3/4 /(1/6) is 124 1/2

Simplify 20 3/4÷(1/6)

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 20 3/4 /(1/6) ?

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