What is (4/5)/(6/7) ?

The solution to (4/5)/(6/7) is 14/15

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Write the Fraction in Simplest Form (4/5)÷(6/7)

(4/5) / (6/7)

\frac{14}{15}

Solution steps

(4/5) / (6/7)

Follow the PEMDAS order of operations

Calculate within parentheses

(4/5) : \frac{4}{5}

4/5

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

= \frac{4}{5}

= \frac{4}{5} / (6/7)

Calculate within parentheses

(6/7) : \frac{6}{7}

6/7

6/7 = \frac{6}{7}

= \frac{6}{7}

= \frac{4}{5} / \frac{6}{7}

Multiply and divide (left to right)

\frac{4}{5} / \frac{6}{7} : \frac{14}{15}

\frac{4}{5} / \frac{6}{7}

Apply the fraction rule:

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

= \frac{4}{5} \cdot \frac{7}{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}{5} \cdot \frac{7}{3}

Multiply fractions:

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

= \frac{2 \cdot 7}{5 \cdot 3}

Multiply the numbers:

2 \cdot 7 = 14

= \frac{14}{5 \cdot 3}

Multiply the numbers:

5 \cdot 3 = 15

= \frac{14}{15}

= \frac{14}{15}

\frac{85}{8}

40 \cdot 10

100 - 33

t h e \frac{285}{180}

4.2