What is (31-27)+(1/3-1/4) ?

The solution to (31-27)+(1/3-1/4) is 4 1/12

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(31-27)+(1/3-1/4)

Solution

(31 - 27) + (\frac{1}{3} - \frac{1}{4})

Solution

4 \frac{1}{12}

Solution steps

(31 - 27) + (\frac{1}{3} - \frac{1}{4})

Follow the PEMDAS order of operations

Calculate within parentheses

(31 - 27) : 4

31 - 27

31 - 27 = 4

= 4

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

Calculate within parentheses

(\frac{1}{3} - \frac{1}{4}) : \frac{1}{12}

\frac{1}{3} - \frac{1}{4}

\frac{1}{3} - \frac{1}{4} = \frac{1}{12}

\frac{1}{3} - \frac{1}{4}

Least Common Multiplier of

3, 4 : 12

3, 4

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 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

3

4

= 3 \cdot 2 \cdot 2

Multiply the numbers:

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

multiply the denominator and numerator by

4

\frac{1}{3} = \frac{1 \cdot 4}{3 \cdot 4} = \frac{4}{12}

For

\frac{1}{4} :

multiply the denominator and numerator by

3

\frac{1}{4} = \frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}

= \frac{4}{12} - \frac{3}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{4 - 3}{12}

Subtract the numbers:

4 - 3 = 1

= \frac{1}{12}

= \frac{1}{12}

= 4 + \frac{1}{12}

Add and subtract (left to right)

4 + \frac{1}{12} : \frac{49}{12}

4 + \frac{1}{12}

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

4 + \frac{1}{12}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

4 \cdot 12 + 1 = 49

4 \cdot 12 + 1

Multiply the numbers:

4 \cdot 12 = 48

= 48 + 1

Add the numbers:

48 + 1 = 49

= 49

= \frac{49}{12}

= \frac{49}{12}

= \frac{49}{12}

Convert improper fractions to mixed numbers:

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

\frac{49}{12} = 4

Remainder

1

\frac{49}{12}

Write the problem in long division format

12 \overline{∣ 49}

Divide

49

12

to get

4

Divide

49

12

to get

4

4 12 \overline{∣ 49}

Multiply the quotient digit

(4)

by the divisor

12

4 12 \overline{∣ 49} \underline{48}

Subtract

48

from

49

4 12 \overline{∣ 49} \underline{48} 1

4 12 \overline{∣ 49} \underline{48} 1

The solution for Long Division of

\frac{49}{12}

4

with remainder of

1

4 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

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

= 4 \frac{1}{12}

= 4 \frac{1}{12}

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1/2 (-9)+1

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(81\div 9)+25-17\times 2

(81 \div 9) + 25 - 17 \times 2

-2\times (-7+18)-(9-28\div 7)\times 3

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3^2*5

3^{2} \cdot 5

18\times 3\times 2-1-5\times 2\times 3-9

18 \times 3 \times 2 - 1 - 5 \times 2 \times 3 - 9

Frequently Asked Questions (FAQ)

What is (31-27)+(1/3-1/4) ?
The solution to (31-27)+(1/3-1/4) is 4 1/12