What is 4\div 12\times 8\div 24 ?

The solution to 4\div 12\times 8\div 24 is 1/9

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Popular >

4\div 12\times 8\div 24

Solution

4 \div 12 \times 8 \div 24

Solution

\frac{1}{9}

Solution steps

4 \div 12 \times 8 \div 24

Follow the PEMDAS order of operations

Multiply and divide (left to right)

4 \div 12 = \frac{4}{12}

= \frac{4}{12} \times 8 \div 24

\frac{4}{12} \times 8 = \frac{8}{3}

\frac{4}{12} \cdot 8

Cancel the numbers:

\frac{4}{12} = \frac{1}{3}

= \frac{1}{3} \cdot 8

\frac{1}{3} \cdot 8 = \frac{8}{3}

\frac{1}{3} \cdot 8

Convert element to fraction:

8 = \frac{8}{1}

= \frac{1}{3} \cdot \frac{8}{1}

Apply the fraction rule:

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

= \frac{1 \cdot 8}{3 \cdot 1}

Multiply the numbers:

1 \cdot 8 = 8

= \frac{8}{3 \cdot 1}

Multiply the numbers:

3 \cdot 1 = 3

= \frac{8}{3}

= \frac{8}{3}

= \frac{8}{3} \div 24

\frac{8}{3} \div 24 = \frac{1}{9}

\frac{8}{3} \div 24

Convert element to fraction:

24 = \frac{24}{1}

= \frac{8}{3} \div \frac{24}{1}

Apply the fraction rule:

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

= \frac{8}{3} \cdot \frac{1}{24}

Cross-cancel common factor:

8

8, 24

Greatest Common Divisor (GCD)

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

Prime factorization of

24 : 2 \cdot 2 \cdot 2 \cdot 3

24

24

divides by

224 = 12 \cdot 2

= 2 \cdot 12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 3

The prime factors common to

8, 24

are

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 1 = 1

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

Multiply the numbers:

3 \cdot 3 = 9

= \frac{1}{9}

= \frac{1}{9}

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Frequently Asked Questions (FAQ)

What is 4\div 12\times 8\div 24 ?
The solution to 4\div 12\times 8\div 24 is 1/9