What is 1 5/12-(1/6+3/4) ?

The solution to 1 5/12-(1/6+3/4) is 1/2

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1 5/12-(1/6+3/4)

Solution

1 \frac{5}{12} - (\frac{1}{6} + \frac{3}{4})

Solution

\frac{1}{2}

Solution steps

1 \frac{5}{12} - (\frac{1}{6} + \frac{3}{4})

Convert mixed numbers to improper fractions:

1 \frac{5}{12} = \frac{17}{12}

1 \frac{5}{12}

Convert mixed numbers to improper fraction:

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

1 \frac{5}{12} = \frac{1 \cdot 12 + 5}{12}

= \frac{17}{12}

= \frac{17}{12} - (\frac{1}{6} + \frac{3}{4})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{6} + \frac{3}{4}) : \frac{11}{12}

\frac{1}{6} + \frac{3}{4}

\frac{1}{6} + \frac{3}{4} = \frac{11}{12}

\frac{1}{6} + \frac{3}{4}

Least Common Multiplier of

6, 4 : 12

6, 4

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

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

6

4

= 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{1}{6} :

multiply the denominator and numerator by

2

\frac{1}{6} = \frac{1 \cdot 2}{6 \cdot 2} = \frac{2}{12}

For

\frac{3}{4} :

multiply the denominator and numerator by

3

\frac{3}{4} = \frac{3 \cdot 3}{4 \cdot 3} = \frac{9}{12}

= \frac{2}{12} + \frac{9}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{2 + 9}{12}

Add the numbers:

2 + 9 = 11

= \frac{11}{12}

= \frac{11}{12}

= \frac{17}{12} - \frac{11}{12}

Add and subtract (left to right)

\frac{17}{12} - \frac{11}{12} : \frac{1}{2}

\frac{17}{12} - \frac{11}{12}

\frac{17}{12} - \frac{11}{12} = \frac{1}{2}

\frac{17}{12} - \frac{11}{12}

Apply rule

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

= \frac{17 - 11}{12}

Subtract the numbers:

17 - 11 = 6

= \frac{6}{12}

Cancel the common factor:

6

= \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2}

Popular Examples

(3/8+1/4)*16

(\frac{3}{8} + \frac{1}{4}) \cdot 16

24^2+30^2

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

7-9\div 9+4(4-3)-7

7 - 9 \div 9 + 4 (4 - 3) - 7

6^2-5(6)-5

6^{2} - 5 (6) - 5

6^2-5(6)-8

6^{2} - 5 (6) - 8

Frequently Asked Questions (FAQ)

What is 1 5/12-(1/6+3/4) ?
The solution to 1 5/12-(1/6+3/4) is 1/2