What is 2 2/3+5\div 12 ?

The solution to 2 2/3+5\div 12 is 3 1/12

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Popular >

2 2/3+5\div 12

Solution

2 \frac{2}{3} + 5 \div 12

Solution

3 \frac{1}{12}

Solution steps

2 \frac{2}{3} + 5 \div 12

Convert mixed numbers to improper fractions:

2 \frac{2}{3} = \frac{8}{3}

2 \frac{2}{3}

Convert mixed numbers to improper fraction:

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

2 \frac{2}{3} = \frac{2 \cdot 3 + 2}{3}

= \frac{8}{3}

= \frac{8}{3} + 5 \div 12

Follow the PEMDAS order of operations

Multiply and divide (left to right)

5 \div 12 : \frac{5}{12}

5 \div 12

5 \div 12 = \frac{5}{12}

= \frac{5}{12}

= \frac{8}{3} + \frac{5}{12}

Add and subtract (left to right)

\frac{8}{3} + \frac{5}{12} : \frac{37}{12}

\frac{8}{3} + \frac{5}{12}

\frac{8}{3} + \frac{5}{12} = \frac{37}{12}

\frac{8}{3} + \frac{5}{12}

Least Common Multiplier of

3, 12 : 12

3, 12

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 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

3

12

= 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{8}{3} :

multiply the denominator and numerator by

4

\frac{8}{3} = \frac{8 \cdot 4}{3 \cdot 4} = \frac{32}{12}

= \frac{32}{12} + \frac{5}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{32 + 5}{12}

Add the numbers:

32 + 5 = 37

= \frac{37}{12}

= \frac{37}{12}

= \frac{37}{12}

Convert improper fractions to mixed numbers:

\frac{37}{12} = 3 \frac{1}{12}

\frac{37}{12} = 3

Remainder

1

\frac{37}{12}

Write the problem in long division format

12 \overline{∣ 37}

Divide

37

12

to get

3

Divide

37

12

to get

3

3 12 \overline{∣ 37}

Multiply the quotient digit

(3)

by the divisor

12

3 12 \overline{∣ 37} \underline{36}

Subtract

36

from

37

3 12 \overline{∣ 37} \underline{36} 1

3 12 \overline{∣ 37} \underline{36} 1

The solution for Long Division of

\frac{37}{12}

3

with remainder of

1

3 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{37}{12} = 3 \frac{1}{12}

= 3 \frac{1}{12}

= 3 \frac{1}{12}

Popular Examples

(5-(-2)-3+(-12)-(15-(-7)))/(-2)

\frac{5 - ( - 2 ) - 3 + ( - 12 ) - ( 15 - ( - 7 ) )}{- 2}

3/2 (11/3-2/7)

\frac{3}{2} (\frac{11}{3} - \frac{2}{7})

2\times [(-12+36)\div 6+(8-5)\div (-3)]-6

2 \times [(- 12 + 36) \div 6 + (8 - 5) \div (- 3)] - 6

14+18\div 2*18-7

14 + 18 \div 2 \cdot 18 - 7

2-2/3 (3)

2 - \frac{2}{3} (3)

Frequently Asked Questions (FAQ)

What is 2 2/3+5\div 12 ?
The solution to 2 2/3+5\div 12 is 3 1/12