What is -5/13 × (-27)-13/15 ?

The solution to -5/13 × (-27)-13/15 is 9 101/195

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Popular Pre Algebra >

-5/13 × (-27)-13/15

Solution

- \frac{5}{13} \times (- 27) - \frac{13}{15}

Solution

9 \frac{101}{195}

Decimal

9.51794 \dots

Solution steps

- \frac{5}{13} (- 27) - \frac{13}{15}

Follow the PEMDAS order of operations

Multiply and divide (left to right)

- \frac{5}{13} (- 27) : \frac{135}{13}

- \frac{5}{13} (- 27)

Apply rule

- a \cdot (- b) = a \cdot b

- \frac{5}{13} (- 27) = \frac{5}{13} \cdot 27

Convert element to fraction:

27 = \frac{27}{1}

= \frac{5}{13} \cdot \frac{27}{1}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{5 \cdot 27}{13 \cdot 1}

Multiply the numbers:

5 \cdot 27 = 135

= \frac{135}{13 \cdot 1}

Multiply the numbers:

13 \cdot 1 = 13

= \frac{135}{13}

= \frac{135}{13} - \frac{13}{15}

Add and subtract (left to right)

\frac{135}{13} - \frac{13}{15} : \frac{1856}{195}

\frac{135}{13} - \frac{13}{15}

\frac{135}{13} - \frac{13}{15} = \frac{1856}{195}

\frac{135}{13} - \frac{13}{15}

Least Common Multiplier of

13, 15 : 195

13, 15

Least Common Multiplier (LCM)

Prime factorization of

13 : 13

13

13

is a prime number, therefore no factorization is possible

= 13

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

13

15

= 13 \cdot 3 \cdot 5

Multiply the numbers:

13 \cdot 3 \cdot 5 = 195

= 195

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

195

For

\frac{135}{13} :

multiply the denominator and numerator by

15

\frac{135}{13} = \frac{135 \cdot 15}{13 \cdot 15} = \frac{2025}{195}

For

\frac{13}{15} :

multiply the denominator and numerator by

13

\frac{13}{15} = \frac{13 \cdot 13}{15 \cdot 13} = \frac{169}{195}

= \frac{2025}{195} - \frac{169}{195}

Since the denominators are equal, combine the fractions:

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

= \frac{2025 - 169}{195}

Subtract the numbers:

2025 - 169 = 1856

= \frac{1856}{195}

= \frac{1856}{195}

= \frac{1856}{195}

Convert improper fractions to mixed numbers:

\frac{1856}{195} = 9 \frac{101}{195}

\frac{1856}{195} = 9

Remainder

101

\frac{1856}{195}

Write the problem in long division format

195 \overline{∣ 1856}

Divide

1856

195

to get

9

Divide

1856

195

to get

9

9 195 \overline{∣ 1856}

Multiply the quotient digit

(9)

by the divisor

195

9 195 \overline{∣ 1856} \underline{1755}

Subtract

1755

from

1856

9 195 \overline{∣ 1856} \underline{1755} 101

9 195 \overline{∣ 1856} \underline{1755} 101

The solution for Long Division of

\frac{1856}{195}

9

with remainder of

101

9 Remainder 101

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{1856}{195} = 9 \frac{101}{195}

= 9 \frac{101}{195}

= 9 \frac{101}{195}

Popular Examples

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Frequently Asked Questions (FAQ)

What is -5/13 × (-27)-13/15 ?
The solution to -5/13 × (-27)-13/15 is 9 101/195

-5/13 × (-27)-13/15

Solution

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Frequently Asked Questions (FAQ)

What is -5/13 × (-27)-13/15 ?

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