What is 7/9 \div (1/6+2/9) ?

The solution to 7/9 \div (1/6+2/9) is 2

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Popular >

7/9 \div (1/6+2/9)

Solution

\frac{7}{9} \div (\frac{1}{6} + \frac{2}{9})

Solution

2

Solution steps

\frac{7}{9} \div (\frac{1}{6} + \frac{2}{9})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{6} + \frac{2}{9}) : \frac{7}{18}

\frac{1}{6} + \frac{2}{9}

\frac{1}{6} + \frac{2}{9} = \frac{7}{18}

\frac{1}{6} + \frac{2}{9}

Least Common Multiplier of

6, 9 : 18

6, 9

Least Common Multiplier (LCM)

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

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

Multiply each factor the greatest number of times it occurs in either

6

9

= 2 \cdot 3 \cdot 3

Multiply the numbers:

2 \cdot 3 \cdot 3 = 18

= 18

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

18

For

\frac{1}{6} :

multiply the denominator and numerator by

3

\frac{1}{6} = \frac{1 \cdot 3}{6 \cdot 3} = \frac{3}{18}

For

\frac{2}{9} :

multiply the denominator and numerator by

2

\frac{2}{9} = \frac{2 \cdot 2}{9 \cdot 2} = \frac{4}{18}

= \frac{3}{18} + \frac{4}{18}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 + 4}{18}

Add the numbers:

3 + 4 = 7

= \frac{7}{18}

= \frac{7}{18}

= \frac{7}{9} \div \frac{7}{18}

Multiply and divide (left to right)

\frac{7}{9} \div \frac{7}{18} : 2

\frac{7}{9} \div \frac{7}{18}

Apply the fraction rule:

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

= \frac{7}{9} \cdot \frac{18}{7}

Multiply fractions:

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

= \frac{7 \cdot 18}{9 \cdot 7}

Cancel the common factor:

7

= \frac{18}{9}

Divide the numbers:

\frac{18}{9} = 2

= 2

= 2

Popular Examples

5/2-2+1/10

\frac{5}{2} - 2 + \frac{1}{10}

12-[9+(7/6-5/4)-(1/2 \times 3/4)]

12 - [9 + (\frac{7}{6} - \frac{5}{4}) - (\frac{1}{2} \times \frac{3}{4})]

7+2^3

7 + 2^{3}

500+6(3+1)+(8-5)3-2(5+4)

500 + 6 (3 + 1) + (8 - 5) 3 - 2 (5 + 4)

30^2+40^2

3 0^{2} + 4 0^{2}

Frequently Asked Questions (FAQ)

What is 7/9 \div (1/6+2/9) ?
The solution to 7/9 \div (1/6+2/9) is 2