What is (2/9)/(5/12) ?

The solution to (2/9)/(5/12) is 8/15

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Write the Fraction in Simplest Form (2/9)÷(5/12)

(2/9) / (5/12)

\frac{8}{15}

Solution steps

(2/9) / (5/12)

Follow the PEMDAS order of operations

Calculate within parentheses

(2/9) : \frac{2}{9}

2/9

2/9 = \frac{2}{9}

= \frac{2}{9}

= \frac{2}{9} / (5/12)

Calculate within parentheses

(5/12) : \frac{5}{12}

5/12

5/12 = \frac{5}{12}

= \frac{5}{12}

= \frac{2}{9} / \frac{5}{12}

Multiply and divide (left to right)

\frac{2}{9} / \frac{5}{12} : \frac{8}{15}

\frac{2}{9} / \frac{5}{12}

Apply the fraction rule:

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

= \frac{2}{9} \cdot \frac{12}{5}

Cross-cancel common factor:

3

12, 9

Greatest Common Divisor (GCD)

Prime factorization of

12 : 2 \cdot 2 \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

The prime factors common to

12, 9

are

= 3

= \frac{2}{3} \cdot \frac{4}{5}

Multiply fractions:

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

= \frac{2 \cdot 4}{3 \cdot 5}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{8}{3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{8}{15}

= \frac{8}{15}

1 \frac{2}{4}

\frac{170}{20}

\frac{36}{16}

t h e \frac{50}{80}

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