What is (5/8)/(4/6) ?

The solution to (5/8)/(4/6) is 15/16

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(5/8)/(4/6)

(5/8) / (4/6)

\frac{15}{16}

Solution steps

(5/8) / (4/6)

Follow the PEMDAS order of operations

Calculate within parentheses

(5/8) : \frac{5}{8}

5/8

5/8 = \frac{5}{8}

= \frac{5}{8}

= \frac{5}{8} / (4/6)

Calculate within parentheses

(4/6) : \frac{4}{6}

4/6

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

= \frac{4}{6}

= \frac{5}{8} / \frac{4}{6}

Multiply and divide (left to right)

\frac{5}{8} / \frac{4}{6} : \frac{15}{16}

\frac{5}{8} / \frac{4}{6}

Apply the fraction rule:

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

= \frac{5}{8} \cdot \frac{6}{4}

Cross-cancel common factor:

2

6, 8

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

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

The prime factors common to

6, 8

are

= 2

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

Multiply fractions:

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

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

Multiply the numbers:

5 \cdot 3 = 15

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

Multiply the numbers:

4 \cdot 4 = 16

= \frac{15}{16}

= \frac{15}{16}

(34 - 45) - (- 34 - 45)

- 1^{2} - 1 + 2

(- 100) + (- 25) + (+ 200)

\frac{3}{4} - (\frac{3}{2} - \frac{1}{4})

10 - (- 2)^{2}