What is 3/2+2/3+1/5 ?

The solution to 3/2+2/3+1/5 is 2 11/30

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3/2+2/3+1/5

Solution

3/2 + 2/3 + 1/5

Solution

2 \frac{11}{30}

Solution steps

3/2 + 2/3 + 1/5

Follow the PEMDAS order of operations

Multiply and divide (left to right)

3/2 : \frac{3}{2}

3/2

3/2 = \frac{3}{2}

= \frac{3}{2}

= \frac{3}{2} + 2/3 + 1/5

Multiply and divide (left to right)

2/3 : \frac{2}{3}

2/3

2/3 = \frac{2}{3}

= \frac{2}{3}

= \frac{3}{2} + \frac{2}{3} + 1/5

Multiply and divide (left to right)

1/5 : \frac{1}{5}

1/5

1/5 = \frac{1}{5}

= \frac{1}{5}

= \frac{3}{2} + \frac{2}{3} + \frac{1}{5}

Add and subtract (left to right)

\frac{3}{2} + \frac{2}{3} + \frac{1}{5} : \frac{71}{30}

\frac{3}{2} + \frac{2}{3} + \frac{1}{5}

\frac{3}{2} + \frac{2}{3} = \frac{13}{6}

\frac{3}{2} + \frac{2}{3}

Least Common Multiplier of

2, 3 : 6

2, 3

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

2

3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

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

6

For

\frac{3}{2} :

multiply the denominator and numerator by

3

\frac{3}{2} = \frac{3 \cdot 3}{2 \cdot 3} = \frac{9}{6}

For

\frac{2}{3} :

multiply the denominator and numerator by

2

\frac{2}{3} = \frac{2 \cdot 2}{3 \cdot 2} = \frac{4}{6}

= \frac{9}{6} + \frac{4}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{9 + 4}{6}

Add the numbers:

9 + 4 = 13

= \frac{13}{6}

= \frac{13}{6} + \frac{1}{5}

\frac{13}{6} + \frac{1}{5} = \frac{71}{30}

\frac{13}{6} + \frac{1}{5}

Least Common Multiplier of

6, 5 : 30

6, 5

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

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

6

5

= 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 3 \cdot 5 = 30

= 30

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

30

For

\frac{13}{6} :

multiply the denominator and numerator by

5

\frac{13}{6} = \frac{13 \cdot 5}{6 \cdot 5} = \frac{65}{30}

For

\frac{1}{5} :

multiply the denominator and numerator by

6

\frac{1}{5} = \frac{1 \cdot 6}{5 \cdot 6} = \frac{6}{30}

= \frac{65}{30} + \frac{6}{30}

Since the denominators are equal, combine the fractions:

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

= \frac{65 + 6}{30}

Add the numbers:

65 + 6 = 71

= \frac{71}{30}

= \frac{71}{30}

= \frac{71}{30}

Convert improper fractions to mixed numbers:

\frac{71}{30} = 2 \frac{11}{30}

\frac{71}{30} = 2

Remainder

11

\frac{71}{30}

Write the problem in long division format

30 \overline{∣ 71}

Divide

71

30

to get

2

Divide

71

30

to get

2

2 30 \overline{∣ 71}

Multiply the quotient digit

(2)

by the divisor

30

2 30 \overline{∣ 71} \underline{60}

Subtract

60

from

71

2 30 \overline{∣ 71} \underline{60} 11

2 30 \overline{∣ 71} \underline{60} 11

The solution for Long Division of

\frac{71}{30}

2

with remainder of

11

2 Remainder 11

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{71}{30} = 2 \frac{11}{30}

= 2 \frac{11}{30}

= 2 \frac{11}{30}

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Frequently Asked Questions (FAQ)

What is 3/2+2/3+1/5 ?
The solution to 3/2+2/3+1/5 is 2 11/30