What is 16/25-(8/5-4/15) ?

The solution to 16/25-(8/5-4/15) is -52/75

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Popular Pre Algebra >

16/25-(8/5-4/15)

Solution

\frac{16}{25} - (\frac{8}{5} - \frac{4}{15})

Solution

- \frac{52}{75}

Decimal

- 0.69333 \dots

Solution steps

\frac{16}{25} - (\frac{8}{5} - \frac{4}{15})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{8}{5} - \frac{4}{15}) : \frac{4}{3}

\frac{8}{5} - \frac{4}{15}

\frac{8}{5} - \frac{4}{15} = \frac{4}{3}

\frac{8}{5} - \frac{4}{15}

Least Common Multiplier of

5, 15 : 15

5, 15

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 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

5

15

= 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{8}{5} :

multiply the denominator and numerator by

3

\frac{8}{5} = \frac{8 \cdot 3}{5 \cdot 3} = \frac{24}{15}

= \frac{24}{15} - \frac{4}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{24 - 4}{15}

Subtract the numbers:

24 - 4 = 20

= \frac{20}{15}

Cancel the common factor:

5

= \frac{4}{3}

= \frac{4}{3}

= \frac{16}{25} - \frac{4}{3}

Add and subtract (left to right)

\frac{16}{25} - \frac{4}{3} : - \frac{52}{75}

\frac{16}{25} - \frac{4}{3}

\frac{16}{25} - \frac{4}{3} = - \frac{52}{75}

\frac{16}{25} - \frac{4}{3}

Least Common Multiplier of

25, 3 : 75

25, 3

Least Common Multiplier (LCM)

Prime factorization of

25 : 5 \cdot 5

25

25

divides by

525 = 5 \cdot 5

= 5 \cdot 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

25

3

= 5 \cdot 5 \cdot 3

Multiply the numbers:

5 \cdot 5 \cdot 3 = 75

= 75

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

75

For

\frac{16}{25} :

multiply the denominator and numerator by

3

\frac{16}{25} = \frac{16 \cdot 3}{25 \cdot 3} = \frac{48}{75}

For

\frac{4}{3} :

multiply the denominator and numerator by

25

\frac{4}{3} = \frac{4 \cdot 25}{3 \cdot 25} = \frac{100}{75}

= \frac{48}{75} - \frac{100}{75}

Since the denominators are equal, combine the fractions:

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

= \frac{48 - 100}{75}

Subtract the numbers:

48 - 100 = - 52

= \frac{- 52}{75}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{52}{75}

= - \frac{52}{75}

= - \frac{52}{75}

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Frequently Asked Questions (FAQ)

What is 16/25-(8/5-4/15) ?
The solution to 16/25-(8/5-4/15) is -52/75

16/25-(8/5-4/15)

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 16/25-(8/5-4/15) ?

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