What is (5/6)/(10/11) ?

The solution to (5/6)/(10/11) is 11/12

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Simplify (5/6)÷(10/11)

(5/6) / (10/11)

\frac{11}{12}

Solution steps

(5/6) / (10/11)

Follow the PEMDAS order of operations

Calculate within parentheses

(5/6) : \frac{5}{6}

5/6

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

= \frac{5}{6}

= \frac{5}{6} / (10/11)

Calculate within parentheses

(10/11) : \frac{10}{11}

10/11

10/11 = \frac{10}{11}

= \frac{10}{11}

= \frac{5}{6} / \frac{10}{11}

Multiply and divide (left to right)

\frac{5}{6} / \frac{10}{11} : \frac{11}{12}

\frac{5}{6} / \frac{10}{11}

Apply the fraction rule:

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

= \frac{5}{6} \cdot \frac{11}{10}

Cross-cancel common factor:

5

5, 10

Greatest Common Divisor (GCD)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5

The prime factors common to

5, 10

are

= 5

= \frac{1}{6} \cdot \frac{11}{2}

Multiply fractions:

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

= \frac{1 \cdot 11}{6 \cdot 2}

Multiply the numbers:

1 \cdot 11 = 11

= \frac{11}{6 \cdot 2}

Multiply the numbers:

6 \cdot 2 = 12

= \frac{11}{12}

= \frac{11}{12}

4.95

t h e \frac{15}{60}

\frac{144}{18}

180 - 36

12 \cdot 60