What is (9+5/9)-(3 1/6-2) ?

The solution to (9+5/9)-(3 1/6-2) is 8 7/18

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(9+5/9)-(3 1/6-2)

Solution

(9 + \frac{5}{9}) - (3 \frac{1}{6} - 2)

Solution

8 \frac{7}{18}

Solution steps

(9 + \frac{5}{9}) - (3 \frac{1}{6} - 2)

Convert mixed numbers to improper fractions:

3 \frac{1}{6} = \frac{19}{6}

3 \frac{1}{6}

Convert mixed numbers to improper fraction:

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

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

= \frac{19}{6}

= (9 + \frac{5}{9}) - (\frac{19}{6} - 2)

Follow the PEMDAS order of operations

Calculate within parentheses

(9 + \frac{5}{9}) : \frac{86}{9}

9 + \frac{5}{9}

9 + \frac{5}{9} = \frac{86}{9}

9 + \frac{5}{9}

Convert element to fraction:

9 = \frac{9 \cdot 9}{9}

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

Since the denominators are equal, combine the fractions:

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

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

9 \cdot 9 + 5 = 86

9 \cdot 9 + 5

Multiply the numbers:

9 \cdot 9 = 81

= 81 + 5

Add the numbers:

81 + 5 = 86

= 86

= \frac{86}{9}

= \frac{86}{9}

= \frac{86}{9} - (\frac{19}{6} - 2)

Calculate within parentheses

(\frac{19}{6} - 2) : \frac{7}{6}

\frac{19}{6} - 2

\frac{19}{6} - 2 = \frac{7}{6}

\frac{19}{6} - 2

Convert element to fraction:

2 = \frac{2 \cdot 6}{6}

= - \frac{2 \cdot 6}{6} + \frac{19}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{- 2 \cdot 6 + 19}{6}

- 2 \cdot 6 + 19 = 7

- 2 \cdot 6 + 19

Multiply the numbers:

2 \cdot 6 = 12

= - 12 + 19

Add/Subtract the numbers:

- 12 + 19 = 7

= 7

= \frac{7}{6}

= \frac{7}{6}

= \frac{86}{9} - \frac{7}{6}

Add and subtract (left to right)

\frac{86}{9} - \frac{7}{6} : \frac{151}{18}

\frac{86}{9} - \frac{7}{6}

\frac{86}{9} - \frac{7}{6} = \frac{151}{18}

\frac{86}{9} - \frac{7}{6}

Least Common Multiplier of

9, 6 : 18

9, 6

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

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

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

9

6

= 3 \cdot 3 \cdot 2

Multiply the numbers:

3 \cdot 3 \cdot 2 = 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{86}{9} :

multiply the denominator and numerator by

2

\frac{86}{9} = \frac{86 \cdot 2}{9 \cdot 2} = \frac{172}{18}

For

\frac{7}{6} :

multiply the denominator and numerator by

3

\frac{7}{6} = \frac{7 \cdot 3}{6 \cdot 3} = \frac{21}{18}

= \frac{172}{18} - \frac{21}{18}

Since the denominators are equal, combine the fractions:

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

= \frac{172 - 21}{18}

Subtract the numbers:

172 - 21 = 151

= \frac{151}{18}

= \frac{151}{18}

= \frac{151}{18}

Convert improper fractions to mixed numbers:

\frac{151}{18} = 8 \frac{7}{18}

\frac{151}{18} = 8

Remainder

7

\frac{151}{18}

Write the problem in long division format

18 \overline{∣ 151}

Divide

151

18

to get

8

Divide

151

18

to get

8

8 18 \overline{∣ 151}

Multiply the quotient digit

(8)

by the divisor

18

8 18 \overline{∣ 151} \underline{144}

Subtract

144

from

151

8 18 \overline{∣ 151} \underline{144} 7

8 18 \overline{∣ 151} \underline{144} 7

The solution for Long Division of

\frac{151}{18}

8

with remainder of

7

8 Remainder 7

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{151}{18} = 8 \frac{7}{18}

= 8 \frac{7}{18}

= 8 \frac{7}{18}

Popular Examples

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(7 - 2) \div 5

50(2\div 3)

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- 2 (- 2) - 5

2^2-2^2

2^{2} - 2^{2}

4\times 7+3(6-4)-2

4 \times 7 + 3 (6 - 4) - 2

Frequently Asked Questions (FAQ)

What is (9+5/9)-(3 1/6-2) ?
The solution to (9+5/9)-(3 1/6-2) is 8 7/18