What is 5/6-(5/9)/(4/5) ?

The solution to 5/6-(5/9)/(4/5) is 5/36

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5/6-(5/9)÷(4/5)

Solution

5/6 - (5/9) / (4/5)

Solution

\frac{5}{36}

Solution steps

5/6 - (5/9) / (4/5)

Follow the PEMDAS order of operations

Calculate within parentheses

(5/9) : \frac{5}{9}

5/9

5/9 = \frac{5}{9}

= \frac{5}{9}

= 5/6 - \frac{5}{9} / (4/5)

Calculate within parentheses

(4/5) : \frac{4}{5}

4/5

4/5 = \frac{4}{5}

= \frac{4}{5}

= 5/6 - \frac{5}{9} / \frac{4}{5}

Multiply and divide (left to right)

5/6 : \frac{5}{6}

5/6

5/6 = \frac{5}{6}

= \frac{5}{6}

= \frac{5}{6} - \frac{5}{9} / \frac{4}{5}

Multiply and divide (left to right)

\frac{5}{9} / \frac{4}{5} : \frac{25}{36}

\frac{5}{9} / \frac{4}{5}

Apply the fraction rule:

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

= \frac{5}{9} \cdot \frac{5}{4}

Multiply fractions:

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

= \frac{5 \cdot 5}{9 \cdot 4}

Multiply the numbers:

5 \cdot 5 = 25

= \frac{25}{9 \cdot 4}

Multiply the numbers:

9 \cdot 4 = 36

= \frac{25}{36}

= \frac{5}{6} - \frac{25}{36}

Add and subtract (left to right)

\frac{5}{6} - \frac{25}{36} : \frac{5}{36}

\frac{5}{6} - \frac{25}{36}

\frac{5}{6} - \frac{25}{36} = \frac{5}{36}

\frac{5}{6} - \frac{25}{36}

Least Common Multiplier of

6, 36 : 36

6, 36

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

36 : 2 \cdot 2 \cdot 3 \cdot 3

36

36

divides by

236 = 18 \cdot 2

= 2 \cdot 18

18

divides by

218 = 9 \cdot 2

= 2 \cdot 2 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 3

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

6

36

= 2 \cdot 2 \cdot 3 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 \cdot 3 = 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{5}{6} :

multiply the denominator and numerator by

6

\frac{5}{6} = \frac{5 \cdot 6}{6 \cdot 6} = \frac{30}{36}

= \frac{30}{36} - \frac{25}{36}

Since the denominators are equal, combine the fractions:

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

= \frac{30 - 25}{36}

Subtract the numbers:

30 - 25 = 5

= \frac{5}{36}

= \frac{5}{36}

= \frac{5}{36}

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Frequently Asked Questions (FAQ)

What is 5/6-(5/9)/(4/5) ?
The solution to 5/6-(5/9)/(4/5) is 5/36