What is 7/6+5/2-3+1/5 ?

The solution to 7/6+5/2-3+1/5 is 13/15

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Popular >

7/6+5/2-3+1/5

Solution

\frac{7}{6} + \frac{5}{2} - 3 + \frac{1}{5}

Solution

\frac{13}{15}

Solution steps

\frac{7}{6} + \frac{5}{2} - 3 + \frac{1}{5}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{7}{6} + \frac{5}{2} = \frac{11}{3}

\frac{7}{6} + \frac{5}{2}

Least Common Multiplier of

6, 2 : 6

6, 2

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

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

6

2

= 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{5}{2} :

multiply the denominator and numerator by

3

\frac{5}{2} = \frac{5 \cdot 3}{2 \cdot 3} = \frac{15}{6}

= \frac{7}{6} + \frac{15}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{7 + 15}{6}

Add the numbers:

7 + 15 = 22

= \frac{22}{6}

Cancel the common factor:

2

= \frac{11}{3}

= \frac{11}{3} - 3 + \frac{1}{5}

\frac{11}{3} - 3 = \frac{2}{3}

\frac{11}{3} - 3

Convert element to fraction:

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

= - \frac{3 \cdot 3}{3} + \frac{11}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{- 3 \cdot 3 + 11}{3}

- 3 \cdot 3 + 11 = 2

- 3 \cdot 3 + 11

Multiply the numbers:

3 \cdot 3 = 9

= - 9 + 11

Add/Subtract the numbers:

- 9 + 11 = 2

= 2

= \frac{2}{3}

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

\frac{2}{3} + \frac{1}{5} = \frac{13}{15}

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

Least Common Multiplier of

3, 5 : 15

3, 5

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 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

3

5

= 3 \cdot 5

Multiply the numbers:

3 \cdot 5 = 15

= 15

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

15

For

\frac{2}{3} :

multiply the denominator and numerator by

5

\frac{2}{3} = \frac{2 \cdot 5}{3 \cdot 5} = \frac{10}{15}

For

\frac{1}{5} :

multiply the denominator and numerator by

3

\frac{1}{5} = \frac{1 \cdot 3}{5 \cdot 3} = \frac{3}{15}

= \frac{10}{15} + \frac{3}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{10 + 3}{15}

Add the numbers:

10 + 3 = 13

= \frac{13}{15}

= \frac{13}{15}

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30^2+16^2

3 0^{2} + 1 6^{2}

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Frequently Asked Questions (FAQ)

What is 7/6+5/2-3+1/5 ?
The solution to 7/6+5/2-3+1/5 is 13/15