What is 13/5 \div (7/9-5/12) ?

The solution to 13/5 \div (7/9-5/12) is 7 1/5

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13/5 \div (7/9-5/12)

Solution

\frac{13}{5} \div (\frac{7}{9} - \frac{5}{12})

Solution

7 \frac{1}{5}

Solution steps

\frac{13}{5} \div (\frac{7}{9} - \frac{5}{12})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{7}{9} - \frac{5}{12}) : \frac{13}{36}

\frac{7}{9} - \frac{5}{12}

\frac{7}{9} - \frac{5}{12} = \frac{13}{36}

\frac{7}{9} - \frac{5}{12}

Least Common Multiplier of

9, 12 : 36

9, 12

Least Common Multiplier (LCM)

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

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

9

12

= 3 \cdot 3 \cdot 2 \cdot 2

Multiply the numbers:

3 \cdot 3 \cdot 2 \cdot 2 = 36

= 36

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

36

For

\frac{7}{9} :

multiply the denominator and numerator by

4

\frac{7}{9} = \frac{7 \cdot 4}{9 \cdot 4} = \frac{28}{36}

For

\frac{5}{12} :

multiply the denominator and numerator by

3

\frac{5}{12} = \frac{5 \cdot 3}{12 \cdot 3} = \frac{15}{36}

= \frac{28}{36} - \frac{15}{36}

Since the denominators are equal, combine the fractions:

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

= \frac{28 - 15}{36}

Subtract the numbers:

28 - 15 = 13

= \frac{13}{36}

= \frac{13}{36}

= \frac{13}{5} \div \frac{13}{36}

Multiply and divide (left to right)

\frac{13}{5} \div \frac{13}{36} : \frac{36}{5}

\frac{13}{5} \div \frac{13}{36}

Apply the fraction rule:

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

= \frac{13}{5} \cdot \frac{36}{13}

Cross-cancel:

13

= \frac{36}{5}

= \frac{36}{5}

Convert improper fractions to mixed numbers:

\frac{36}{5} = 7 \frac{1}{5}

\frac{36}{5} = 7

Remainder

1

\frac{36}{5}

Write the problem in long division format

5 \overline{∣ 36}

Divide

36

5

to get

7

Divide

36

5

to get

7

7 5 \overline{∣ 36}

Multiply the quotient digit

(7)

by the divisor

5

7 5 \overline{∣ 36} \underline{35}

Subtract

35

from

36

7 5 \overline{∣ 36} \underline{35} 1

7 5 \overline{∣ 36} \underline{35} 1

The solution for Long Division of

\frac{36}{5}

7

with remainder of

1

7 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{36}{5} = 7 \frac{1}{5}

= 7 \frac{1}{5}

= 7 \frac{1}{5}

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Frequently Asked Questions (FAQ)

What is 13/5 \div (7/9-5/12) ?
The solution to 13/5 \div (7/9-5/12) is 7 1/5