What is (1/5+1/6)+22/15 ?

The solution to (1/5+1/6)+22/15 is 1 5/6

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Popular Pre Algebra >

(1/5+1/6)+22/15

Solution

(\frac{1}{5} + \frac{1}{6}) + \frac{22}{15}

Solution

1 \frac{5}{6}

Decimal

1.83333 \dots

Solution steps

(\frac{1}{5} + \frac{1}{6}) + \frac{22}{15}

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{5} + \frac{1}{6}) : \frac{11}{30}

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

\frac{1}{5} + \frac{1}{6} = \frac{11}{30}

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

Least Common Multiplier of

5, 6 : 30

5, 6

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

5

6

= 5 \cdot 2 \cdot 3

Multiply the numbers:

5 \cdot 2 \cdot 3 = 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{1}{5} :

multiply the denominator and numerator by

6

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

For

\frac{1}{6} :

multiply the denominator and numerator by

5

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

= \frac{6}{30} + \frac{5}{30}

Since the denominators are equal, combine the fractions:

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

= \frac{6 + 5}{30}

Add the numbers:

6 + 5 = 11

= \frac{11}{30}

= \frac{11}{30}

= \frac{11}{30} + \frac{22}{15}

Add and subtract (left to right)

\frac{11}{30} + \frac{22}{15} : \frac{11}{6}

\frac{11}{30} + \frac{22}{15}

\frac{11}{30} + \frac{22}{15} = \frac{11}{6}

\frac{11}{30} + \frac{22}{15}

Least Common Multiplier of

30, 15 : 30

30, 15

Least Common Multiplier (LCM)

Prime factorization of

30 : 2 \cdot 3 \cdot 5

30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 5

Prime factorization of

15 : 3 \cdot 5

15

15

divides by

315 = 5 \cdot 3

= 3 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5

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

30

15

= 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{22}{15} :

multiply the denominator and numerator by

2

\frac{22}{15} = \frac{22 \cdot 2}{15 \cdot 2} = \frac{44}{30}

= \frac{11}{30} + \frac{44}{30}

Since the denominators are equal, combine the fractions:

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

= \frac{11 + 44}{30}

Add the numbers:

11 + 44 = 55

= \frac{55}{30}

Cancel the common factor:

5

= \frac{11}{6}

= \frac{11}{6}

= \frac{11}{6}

Convert improper fractions to mixed numbers:

\frac{11}{6} = 1 \frac{5}{6}

\frac{11}{6} = 1

Remainder

5

\frac{11}{6}

Write the problem in long division format

6 \overline{∣ 11}

Divide

11

6

to get

1

Divide

11

6

to get

1

1 6 \overline{∣ 11}

Multiply the quotient digit

(1)

by the divisor

6

1 6 \overline{∣ 11} \underline{6}

Subtract

6

from

11

1 6 \overline{∣ 11} \underline{6} 5

1 6 \overline{∣ 11} \underline{6} 5

The solution for Long Division of

\frac{11}{6}

1

with remainder of

5

1 Remainder 5

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{11}{6} = 1 \frac{5}{6}

= 1 \frac{5}{6}

= 1 \frac{5}{6}

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Frequently Asked Questions (FAQ)

What is (1/5+1/6)+22/15 ?
The solution to (1/5+1/6)+22/15 is 1 5/6

(1/5+1/6)+22/15

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is (1/5+1/6)+22/15 ?

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