What is 1-6/5-(6/5+1/10) ?

The solution to 1-6/5-(6/5+1/10) is -3/2

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1-6/5-(6/5+1/10)

Solution

1 - \frac{6}{5} - (\frac{6}{5} + \frac{1}{10})

Solution

- \frac{3}{2}

Solution steps

1 - \frac{6}{5} - (\frac{6}{5} + \frac{1}{10})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{6}{5} + \frac{1}{10}) : \frac{13}{10}

\frac{6}{5} + \frac{1}{10}

\frac{6}{5} + \frac{1}{10} = \frac{13}{10}

\frac{6}{5} + \frac{1}{10}

Least Common Multiplier of

5, 10 : 10

5, 10

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5

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

5

10

= 5 \cdot 2

Multiply the numbers:

5 \cdot 2 = 10

= 10

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

10

For

\frac{6}{5} :

multiply the denominator and numerator by

2

\frac{6}{5} = \frac{6 \cdot 2}{5 \cdot 2} = \frac{12}{10}

= \frac{12}{10} + \frac{1}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{12 + 1}{10}

Add the numbers:

12 + 1 = 13

= \frac{13}{10}

= \frac{13}{10}

= 1 - \frac{6}{5} - \frac{13}{10}

Add and subtract (left to right)

1 - \frac{6}{5} - \frac{13}{10} : - \frac{3}{2}

1 - \frac{6}{5} - \frac{13}{10}

1 - \frac{6}{5} = - \frac{1}{5}

1 - \frac{6}{5}

Convert element to fraction:

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

= \frac{1 \cdot 5}{5} - \frac{6}{5}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 5 - 6}{5}

1 \cdot 5 - 6 = - 1

1 \cdot 5 - 6

Multiply the numbers:

1 \cdot 5 = 5

= 5 - 6

Subtract the numbers:

5 - 6 = - 1

= - 1

= \frac{- 1}{5}

Apply the fraction rule:

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

= - \frac{1}{5}

= - \frac{1}{5} - \frac{13}{10}

- \frac{1}{5} - \frac{13}{10} = - \frac{3}{2}

- \frac{1}{5} - \frac{13}{10}

Least Common Multiplier of

5, 10 : 10

5, 10

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5

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

5

10

= 5 \cdot 2

Multiply the numbers:

5 \cdot 2 = 10

= 10

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

10

For

\frac{1}{5} :

multiply the denominator and numerator by

2

\frac{1}{5} = \frac{1 \cdot 2}{5 \cdot 2} = \frac{2}{10}

= - \frac{2}{10} - \frac{13}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{- 2 - 13}{10}

Subtract the numbers:

- 2 - 13 = - 15

= \frac{- 15}{10}

Apply the fraction rule:

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

= - \frac{15}{10}

Cancel the common factor:

5

= - \frac{3}{2}

= - \frac{3}{2}

= - \frac{3}{2}

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Frequently Asked Questions (FAQ)

What is 1-6/5-(6/5+1/10) ?
The solution to 1-6/5-(6/5+1/10) is -3/2