What is (3+1/4)-(2+1/6) ?

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

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(3+1/4)-(2+1/6)

Solution

(3 + \frac{1}{4}) - (2 + \frac{1}{6})

Solution

1 \frac{1}{12}

Solution steps

(3 + \frac{1}{4}) - (2 + \frac{1}{6})

Follow the PEMDAS order of operations

Calculate within parentheses

(3 + \frac{1}{4}) : \frac{13}{4}

3 + \frac{1}{4}

3 + \frac{1}{4} = \frac{13}{4}

3 + \frac{1}{4}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

3 \cdot 4 + 1 = 13

3 \cdot 4 + 1

Multiply the numbers:

3 \cdot 4 = 12

= 12 + 1

Add the numbers:

12 + 1 = 13

= 13

= \frac{13}{4}

= \frac{13}{4}

= \frac{13}{4} - (2 + \frac{1}{6})

Calculate within parentheses

(2 + \frac{1}{6}) : \frac{13}{6}

2 + \frac{1}{6}

2 + \frac{1}{6} = \frac{13}{6}

2 + \frac{1}{6}

Convert element to fraction:

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

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

2 \cdot 6 + 1 = 13

2 \cdot 6 + 1

Multiply the numbers:

2 \cdot 6 = 12

= 12 + 1

Add the numbers:

12 + 1 = 13

= 13

= \frac{13}{6}

= \frac{13}{6}

= \frac{13}{4} - \frac{13}{6}

Add and subtract (left to right)

\frac{13}{4} - \frac{13}{6} : \frac{13}{12}

\frac{13}{4} - \frac{13}{6}

\frac{13}{4} - \frac{13}{6} = \frac{13}{12}

\frac{13}{4} - \frac{13}{6}

Least Common Multiplier of

4, 6 : 12

4, 6

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

4

6

= 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{13}{4} :

multiply the denominator and numerator by

3

\frac{13}{4} = \frac{13 \cdot 3}{4 \cdot 3} = \frac{39}{12}

For

\frac{13}{6} :

multiply the denominator and numerator by

2

\frac{13}{6} = \frac{13 \cdot 2}{6 \cdot 2} = \frac{26}{12}

= \frac{39}{12} - \frac{26}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{39 - 26}{12}

Subtract the numbers:

39 - 26 = 13

= \frac{13}{12}

= \frac{13}{12}

= \frac{13}{12}

Convert improper fractions to mixed numbers:

\frac{13}{12} = 1 \frac{1}{12}

\frac{13}{12} = 1

Remainder

1

\frac{13}{12}

Write the problem in long division format

12 \overline{∣ 13}

Divide

13

12

to get

1

Divide

13

12

to get

1

1 12 \overline{∣ 13}

Multiply the quotient digit

(1)

by the divisor

12

1 12 \overline{∣ 13} \underline{12}

Subtract

12

from

13

1 12 \overline{∣ 13} \underline{12} 1

1 12 \overline{∣ 13} \underline{12} 1

The solution for Long Division of

\frac{13}{12}

1

with remainder of

1

1 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{13}{12} = 1 \frac{1}{12}

= 1 \frac{1}{12}

= 1 \frac{1}{12}

Popular Examples

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2^{20} + 2^{20}

-4(2-3-1)+2(8-5)+3(4-5)

- 4 (2 - 3 - 1) + 2 (8 - 5) + 3 (4 - 5)

9-3\div 1/3+1

9 - 3 \div \frac{1}{3} + 1

(7-2+4)-(2-5)

(7 - 2 + 4) - (2 - 5)

2(0)^2

2 (0)^{2}

Frequently Asked Questions (FAQ)

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