What is 2\div 3\times 8\div 6\times 9\div 4 ?

The solution to 2\div 3\times 8\div 6\times 9\div 4 is 2

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2\div 3\times 8\div 6\times 9\div 4

Solution

2 \div 3 \times 8 \div 6 \times 9 \div 4

Solution

2

Solution steps

2 \div 3 \times 8 \div 6 \times 9 \div 4

Follow the PEMDAS order of operations

Multiply and divide (left to right)

2 \div 3 = \frac{2}{3}

= \frac{2}{3} \times 8 \div 6 \times 9 \div 4

\frac{2}{3} \times 8 = \frac{16}{3}

\frac{2}{3} \cdot 8

Convert element to fraction:

8 = \frac{8}{1}

= \frac{2}{3} \cdot \frac{8}{1}

Apply the fraction rule:

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

= \frac{2 \cdot 8}{3 \cdot 1}

Multiply the numbers:

2 \cdot 8 = 16

= \frac{16}{3 \cdot 1}

Multiply the numbers:

3 \cdot 1 = 3

= \frac{16}{3}

= \frac{16}{3} \div 6 \times 9 \div 4

\frac{16}{3} \div 6 = \frac{8}{9}

\frac{16}{3} \div 6

Convert element to fraction:

6 = \frac{6}{1}

= \frac{16}{3} \div \frac{6}{1}

Apply the fraction rule:

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

= \frac{16}{3} \cdot \frac{1}{6}

Cross-cancel common factor:

2

16, 6

Greatest Common Divisor (GCD)

Prime factorization of

16 : 2 \cdot 2 \cdot 2 \cdot 2

16

16

divides by

216 = 8 \cdot 2

= 2 \cdot 8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 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

16, 6

are

= 2

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

Multiply fractions:

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

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

Multiply the numbers:

8 \cdot 1 = 8

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

Multiply the numbers:

3 \cdot 3 = 9

= \frac{8}{9}

= \frac{8}{9} \times 9 \div 4

\frac{8}{9} \times 9 = 8

\frac{8}{9} \cdot 9

Convert element to fraction:

9 = \frac{9}{1}

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

Cross-cancel common factor:

9

= \frac{8}{1}

Divide the numbers:

\frac{8}{1} = 8

= 8

= 8 \div 4

8 \div 4 = 2

= 2

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Frequently Asked Questions (FAQ)

What is 2\div 3\times 8\div 6\times 9\div 4 ?
The solution to 2\div 3\times 8\div 6\times 9\div 4 is 2