What is 8/12\times 6/9\times 5/8 ?

The solution to 8/12\times 6/9\times 5/8 is 5/18

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Popular >

8/12\times 6/9\times 5/8

Solution

8/12 \times 6/9 \times 5/8

Solution

\frac{5}{18}

Solution steps

8/12 \times 6/9 \times 5/8

Follow the PEMDAS order of operations

Multiply and divide (left to right)

8/12 = \frac{8}{12}

= \frac{8}{12} \times 6/9 \times 5/8

\frac{8}{12} \times 6 = 4

\frac{8}{12} \cdot 6

Cancel

\frac{8}{12} : \frac{2}{3}

\frac{8}{12}

Factor the number:

8 = 4 \cdot 2

= \frac{4 \cdot 2}{12}

Factor the number:

12 = 4 \cdot 3

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

Cancel the common factor:

4

= \frac{2}{3}

= \frac{2}{3} \cdot 6

\frac{2}{3} \cdot 6 = 4

\frac{2}{3} \cdot 6

Convert element to fraction:

6 = \frac{6}{1}

= \frac{2}{3} \cdot \frac{6}{1}

Apply the fraction rule:

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

= \frac{2 \cdot 6}{3 \cdot 1}

Cancel

\frac{2 \cdot 6}{3 \cdot 1} : 4

\frac{2 \cdot 6}{3 \cdot 1}

Multiply the numbers:

3 \cdot 1 = 3

= \frac{2 \cdot 6}{3}

Divide the numbers:

\frac{6}{3} = 2

= 2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4

= 4

= 4

= 4/9 \times 5/8

4/9 = \frac{4}{9}

= \frac{4}{9} \times 5/8

\frac{4}{9} \times 5 = \frac{20}{9}

\frac{4}{9} \cdot 5

Convert element to fraction:

5 = \frac{5}{1}

= \frac{4}{9} \cdot \frac{5}{1}

Apply the fraction rule:

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

= \frac{4 \cdot 5}{9 \cdot 1}

Multiply the numbers:

4 \cdot 5 = 20

= \frac{20}{9 \cdot 1}

Multiply the numbers:

9 \cdot 1 = 9

= \frac{20}{9}

= \frac{20}{9} /8

\frac{20}{9} /8 = \frac{5}{18}

\frac{20}{9} /8

Convert element to fraction:

8 = \frac{8}{1}

= \frac{20}{9} \div \frac{8}{1}

Apply the fraction rule:

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

= \frac{20}{9} \cdot \frac{1}{8}

Cross-cancel common factor:

4

20, 8

Greatest Common Divisor (GCD)

Prime factorization of

20 : 2 \cdot 2 \cdot 5

20

20

divides by

220 = 10 \cdot 2

= 2 \cdot 10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 5

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

20, 8

are

= 2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4

= \frac{5}{9} \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{5 \cdot 1}{9 \cdot 2}

Multiply the numbers:

5 \cdot 1 = 5

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

Multiply the numbers:

9 \cdot 2 = 18

= \frac{5}{18}

= \frac{5}{18}

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Frequently Asked Questions (FAQ)

What is 8/12\times 6/9\times 5/8 ?
The solution to 8/12\times 6/9\times 5/8 is 5/18