What is 5/3+(6/5+2/3) ?

The solution to 5/3+(6/5+2/3) is 3 8/15

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Popular >

5/3+(6/5+2/3)

Solution

\frac{5}{3} + (\frac{6}{5} + \frac{2}{3})

Solution

3 \frac{8}{15}

Solution steps

\frac{5}{3} + (\frac{6}{5} + \frac{2}{3})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{6}{5} + \frac{2}{3}) : \frac{28}{15}

\frac{6}{5} + \frac{2}{3}

\frac{6}{5} + \frac{2}{3} = \frac{28}{15}

\frac{6}{5} + \frac{2}{3}

Least Common Multiplier of

5, 3 : 15

5, 3

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

5

3

= 5 \cdot 3

Multiply the numbers:

5 \cdot 3 = 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{6}{5} :

multiply the denominator and numerator by

3

\frac{6}{5} = \frac{6 \cdot 3}{5 \cdot 3} = \frac{18}{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}

= \frac{18}{15} + \frac{10}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{18 + 10}{15}

Add the numbers:

18 + 10 = 28

= \frac{28}{15}

= \frac{28}{15}

= \frac{5}{3} + \frac{28}{15}

Add and subtract (left to right)

\frac{5}{3} + \frac{28}{15} : \frac{53}{15}

\frac{5}{3} + \frac{28}{15}

\frac{5}{3} + \frac{28}{15} = \frac{53}{15}

\frac{5}{3} + \frac{28}{15}

Least Common Multiplier of

3, 15 : 15

3, 15

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

3

15

= 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{5}{3} :

multiply the denominator and numerator by

5

\frac{5}{3} = \frac{5 \cdot 5}{3 \cdot 5} = \frac{25}{15}

= \frac{25}{15} + \frac{28}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{25 + 28}{15}

Add the numbers:

25 + 28 = 53

= \frac{53}{15}

= \frac{53}{15}

= \frac{53}{15}

Convert improper fractions to mixed numbers:

\frac{53}{15} = 3 \frac{8}{15}

\frac{53}{15} = 3

Remainder

8

\frac{53}{15}

Write the problem in long division format

15 \overline{∣ 53}

Divide

53

15

to get

3

Divide

53

15

to get

3

3 15 \overline{∣ 53}

Multiply the quotient digit

(3)

by the divisor

15

3 15 \overline{∣ 53} \underline{45}

Subtract

45

from

53

3 15 \overline{∣ 53} \underline{45} 8

3 15 \overline{∣ 53} \underline{45} 8

The solution for Long Division of

\frac{53}{15}

3

with remainder of

8

3 Remainder 8

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{53}{15} = 3 \frac{8}{15}

= 3 \frac{8}{15}

= 3 \frac{8}{15}

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36-4\times (-1)\times (-5)

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1 - \frac{1}{3} + \frac{1}{4}

4(-5)+3

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Frequently Asked Questions (FAQ)

What is 5/3+(6/5+2/3) ?
The solution to 5/3+(6/5+2/3) is 3 8/15