What is (7/12)/(2/9) ?

The solution to (7/12)/(2/9) is 2 5/8

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Popular >

Write the Fraction in Simplest Form (7/12)÷(2/9)

Solution

(7/12) / (2/9)

Solution

2 \frac{5}{8}

Solution steps

(7/12) / (2/9)

Follow the PEMDAS order of operations

Calculate within parentheses

(7/12) : \frac{7}{12}

7/12

7/12 = \frac{7}{12}

= \frac{7}{12}

= \frac{7}{12} / (2/9)

Calculate within parentheses

(2/9) : \frac{2}{9}

2/9

2/9 = \frac{2}{9}

= \frac{2}{9}

= \frac{7}{12} / \frac{2}{9}

Multiply and divide (left to right)

\frac{7}{12} / \frac{2}{9} : \frac{21}{8}

\frac{7}{12} / \frac{2}{9}

Apply the fraction rule:

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

= \frac{7}{12} \cdot \frac{9}{2}

Cross-cancel common factor:

3

9, 12

Greatest Common Divisor (GCD)

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

Prime factorization of

12 : 2 \cdot 2 \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

The prime factors common to

9, 12

are

= 3

= \frac{7}{4} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{7 \cdot 3}{4 \cdot 2}

Multiply the numbers:

7 \cdot 3 = 21

= \frac{21}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{21}{8}

= \frac{21}{8}

Convert improper fractions to mixed numbers:

\frac{21}{8} = 2 \frac{5}{8}

\frac{21}{8} = 2

Remainder

5

\frac{21}{8}

Write the problem in long division format

8 \overline{∣ 21}

Divide

21

8

to get

2

Divide

21

8

to get

2

2 8 \overline{∣ 21}

Multiply the quotient digit

(2)

by the divisor

8

2 8 \overline{∣ 21} \underline{16}

Subtract

16

from

21

2 8 \overline{∣ 21} \underline{16} 5

2 8 \overline{∣ 21} \underline{16} 5

The solution for Long Division of

\frac{21}{8}

2

with remainder of

5

2 Remainder 5

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{21}{8} = 2 \frac{5}{8}

= 2 \frac{5}{8}

= 2 \frac{5}{8}

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Convert to a Mixed Number 175/12 mixed number

\frac{175}{12}

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Frequently Asked Questions (FAQ)

What is (7/12)/(2/9) ?
The solution to (7/12)/(2/9) is 2 5/8