What is 9-5 1/6+4 1/12 ?

The solution to 9-5 1/6+4 1/12 is 7 11/12

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9-5 1/6+4 1/12

Solution

9 - 5 \frac{1}{6} + 4 \frac{1}{12}

Solution

7 \frac{11}{12}

Solution steps

9 - 5 \frac{1}{6} + 4 \frac{1}{12}

Convert mixed numbers to improper fractions:

5 \frac{1}{6} = \frac{31}{6}

5 \frac{1}{6}

Convert mixed numbers to improper fraction:

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

5 \frac{1}{6} = \frac{5 \cdot 6 + 1}{6}

= \frac{31}{6}

= 9 - \frac{31}{6} + 4 \frac{1}{12}

Convert mixed numbers to improper fractions:

4 \frac{1}{12} = \frac{49}{12}

4 \frac{1}{12}

Convert mixed numbers to improper fraction:

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

4 \frac{1}{12} = \frac{4 \cdot 12 + 1}{12}

= \frac{49}{12}

= 9 - \frac{31}{6} + \frac{49}{12}

Follow the PEMDAS order of operations

Add and subtract (left to right)

9 - \frac{31}{6} + \frac{49}{12} : \frac{95}{12}

9 - \frac{31}{6} + \frac{49}{12}

9 - \frac{31}{6} = \frac{23}{6}

9 - \frac{31}{6}

Convert element to fraction:

9 = \frac{9 \cdot 6}{6}

= \frac{9 \cdot 6}{6} - \frac{31}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{9 \cdot 6 - 31}{6}

9 \cdot 6 - 31 = 23

9 \cdot 6 - 31

Multiply the numbers:

9 \cdot 6 = 54

= 54 - 31

Subtract the numbers:

54 - 31 = 23

= 23

= \frac{23}{6}

= \frac{23}{6} + \frac{49}{12}

\frac{23}{6} + \frac{49}{12} = \frac{95}{12}

\frac{23}{6} + \frac{49}{12}

Least Common Multiplier of

6, 12 : 12

6, 12

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

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

6

12

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

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

12

For

\frac{23}{6} :

multiply the denominator and numerator by

2

\frac{23}{6} = \frac{23 \cdot 2}{6 \cdot 2} = \frac{46}{12}

= \frac{46}{12} + \frac{49}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{46 + 49}{12}

Add the numbers:

46 + 49 = 95

= \frac{95}{12}

= \frac{95}{12}

= \frac{95}{12}

Convert improper fractions to mixed numbers:

\frac{95}{12} = 7 \frac{11}{12}

\frac{95}{12} = 7

Remainder

11

\frac{95}{12}

Write the problem in long division format

12 \overline{∣ 95}

Divide

95

12

to get

7

Divide

95

12

to get

7

7 12 \overline{∣ 95}

Multiply the quotient digit

(7)

by the divisor

12

7 12 \overline{∣ 95} \underline{84}

Subtract

84

from

95

7 12 \overline{∣ 95} \underline{84} 11

7 12 \overline{∣ 95} \underline{84} 11

The solution for Long Division of

\frac{95}{12}

7

with remainder of

11

7 Remainder 11

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{95}{12} = 7 \frac{11}{12}

= 7 \frac{11}{12}

= 7 \frac{11}{12}

Popular Examples

6\div 2(3)

6 \div 2 (3)

1+5/8-1/6

1 + \frac{5}{8} - \frac{1}{6}

9+1-5

9 + 1 - 5

3^2+3^2

3^{2} + 3^{2}

3(3)^2

3 (3)^{2}

Frequently Asked Questions (FAQ)

What is 9-5 1/6+4 1/12 ?
The solution to 9-5 1/6+4 1/12 is 7 11/12