What is (2/3-1/5)+8/15 ?

The solution to (2/3-1/5)+8/15 is 1

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Popular >

(2/3-1/5)+8/15

Solution

(\frac{2}{3} - \frac{1}{5}) + \frac{8}{15}

Solution

1

Solution steps

(\frac{2}{3} - \frac{1}{5}) + \frac{8}{15}

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{2}{3} - \frac{1}{5}) : \frac{7}{15}

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

\frac{2}{3} - \frac{1}{5} = \frac{7}{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}

Subtract the numbers:

10 - 3 = 7

= \frac{7}{15}

= \frac{7}{15}

= \frac{7}{15} + \frac{8}{15}

Add and subtract (left to right)

\frac{7}{15} + \frac{8}{15} : 1

\frac{7}{15} + \frac{8}{15}

\frac{7}{15} + \frac{8}{15} = 1

\frac{7}{15} + \frac{8}{15}

Apply rule

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

= \frac{7 + 8}{15}

Add the numbers:

7 + 8 = 15

= \frac{15}{15}

Apply rule

\frac{a}{a} = 1

= 1

= 1

= 1

Popular Examples

1/4 (1)^2

\frac{1}{4} (1)^{2}

4^2+6

4^{2} + 6

(2\times 4+12)\times (6-4)

(2 \times 4 + 12) \times (6 - 4)

20+5*9

20 + 5 \cdot 9

2^4+2^2

2^{4} + 2^{2}

Frequently Asked Questions (FAQ)

What is (2/3-1/5)+8/15 ?
The solution to (2/3-1/5)+8/15 is 1