What is 1 6/18 /(5/6) ?

The solution to 1 6/18 /(5/6) is 2/45

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Popular >

Simplify 1 6/18÷(5/6)

Solution

1 \frac{6}{18} / (5/6)

Solution

\frac{2}{45}

Solution steps

1 \frac{6}{18} / (5/6)

Convert mixed numbers to improper fractions:

1 \frac{6}{18} = \frac{24}{18}

1 \frac{6}{18}

Convert mixed numbers to improper fraction:

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

1 \frac{6}{18} = \frac{1 \cdot 18 + 6}{18}

= \frac{24}{18}

= \frac{24}{18} / (5/6)

\frac{24}{18} = \frac{4}{3}

Cancel the common factor:

6

\frac{4}{3}

= \frac{4}{3} /5/6

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{4}{3} /5/6 : \frac{2}{45}

\frac{4}{3} /5/6

\frac{4}{3} /5 = \frac{4}{15}

\frac{4}{3} /5

Convert element to fraction:

5 = \frac{5}{1}

= \frac{4}{3} \div \frac{5}{1}

Apply the fraction rule:

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

= \frac{4}{3} \cdot \frac{1}{5}

Multiply fractions:

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

= \frac{4 \cdot 1}{3 \cdot 5}

Multiply the numbers:

4 \cdot 1 = 4

= \frac{4}{3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{4}{15}

= \frac{4}{15} /6

\frac{4}{15} /6 = \frac{2}{45}

\frac{4}{15} /6

Convert element to fraction:

6 = \frac{6}{1}

= \frac{4}{15} \div \frac{6}{1}

Apply the fraction rule:

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

= \frac{4}{15} \cdot \frac{1}{6}

Cross-cancel common factor:

2

4, 6

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

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

The prime factors common to

4, 6

are

= 2

= \frac{2}{15} \cdot \frac{1}{3}

Multiply fractions:

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

= \frac{2 \cdot 1}{15 \cdot 3}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{2}{15 \cdot 3}

Multiply the numbers:

15 \cdot 3 = 45

= \frac{2}{45}

= \frac{2}{45}

= \frac{2}{45}

Popular Examples

Simplify (21/1)÷1 3/4

(21/1) /1 \frac{3}{4}

22/3 long division

\frac{22}{3}

Convert to a Simplified Fraction 6.375 decimal to fraction

6.375

108/8 long division

\frac{108}{8}

Convert to a Simplified Fraction -0.625 decimal to fraction

- 0.625

Frequently Asked Questions (FAQ)

What is 1 6/18 /(5/6) ?
The solution to 1 6/18 /(5/6) is 2/45