What is (-7/6-6/7)-(-7/6-7) ?

The solution to (-7/6-6/7)-(-7/6-7) is 6 1/7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

Evaluate (-7/6-6/7)-(-7/6-7)

Solution

(- 7/6 - 6/7) - (- 7/6 - 7)

Solution

6 \frac{1}{7}

Solution steps

(- 7/6 - 6/7) - (- 7/6 - 7)

Follow the PEMDAS order of operations

Calculate within parentheses

(- 7/6 - 6/7) : - \frac{85}{42}

- 7/6 - 6/7

Multiply and divide (left to right)

- 7/6 : \frac{- 7}{6}

- 7/6

- 7/6 = \frac{- 7}{6}

= \frac{- 7}{6}

= \frac{- 7}{6} - 6/7

Multiply and divide (left to right)

6/7 : \frac{6}{7}

6/7

6/7 = \frac{6}{7}

= \frac{6}{7}

= \frac{- 7}{6} - \frac{6}{7}

Add and subtract (left to right)

\frac{- 7}{6} - \frac{6}{7} : - \frac{85}{42}

\frac{- 7}{6} - \frac{6}{7}

\frac{- 7}{6} - \frac{6}{7} = - \frac{85}{42}

\frac{- 7}{6} - \frac{6}{7}

Apply the fraction rule:

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

= - \frac{7}{6} - \frac{6}{7}

Least Common Multiplier of

6, 7 : 42

6, 7

Least Common Multiplier (LCM)

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

Prime factorization of

7 : 7

7

7

is a prime number, therefore no factorization is possible

= 7

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

6

7

= 2 \cdot 3 \cdot 7

Multiply the numbers:

2 \cdot 3 \cdot 7 = 42

= 42

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

42

For

\frac{7}{6} :

multiply the denominator and numerator by

7

\frac{7}{6} = \frac{7 \cdot 7}{6 \cdot 7} = \frac{49}{42}

For

\frac{6}{7} :

multiply the denominator and numerator by

6

\frac{6}{7} = \frac{6 \cdot 6}{7 \cdot 6} = \frac{36}{42}

= - \frac{49}{42} - \frac{36}{42}

Since the denominators are equal, combine the fractions:

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

= \frac{- 49 - 36}{42}

Subtract the numbers:

- 49 - 36 = - 85

= \frac{- 85}{42}

Apply the fraction rule:

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

= - \frac{85}{42}

= - \frac{85}{42}

= - \frac{85}{42}

= - \frac{85}{42} - (- 7/6 - 7)

Calculate within parentheses

(- 7/6 - 7) : - \frac{49}{6}

- 7/6 - 7

Multiply and divide (left to right)

- 7/6 : \frac{- 7}{6}

- 7/6

- 7/6 = \frac{- 7}{6}

= \frac{- 7}{6}

= \frac{- 7}{6} - 7

Add and subtract (left to right)

\frac{- 7}{6} - 7 : - \frac{49}{6}

\frac{- 7}{6} - 7

\frac{- 7}{6} - 7 = - \frac{49}{6}

\frac{- 7}{6} - 7

Apply the fraction rule:

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

= - \frac{7}{6} - 7

Convert element to fraction:

7 = \frac{7 \cdot 6}{6}

= - \frac{7 \cdot 6}{6} - \frac{7}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{- 7 \cdot 6 - 7}{6}

- 7 \cdot 6 - 7 = - 49

- 7 \cdot 6 - 7

Multiply the numbers:

7 \cdot 6 = 42

= - 42 - 7

Subtract the numbers:

- 42 - 7 = - 49

= - 49

= \frac{- 49}{6}

Apply the fraction rule:

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

= - \frac{49}{6}

= - \frac{49}{6}

= - \frac{49}{6}

= - \frac{85}{42} - (- \frac{49}{6})

Add and subtract (left to right)

- \frac{85}{42} - (- \frac{49}{6}) : \frac{43}{7}

- \frac{85}{42} - (- \frac{49}{6})

Apply rule

- (- a) = + a

- (- \frac{49}{6}) = + \frac{49}{6}

= - \frac{85}{42} + \frac{49}{6}

- \frac{85}{42} + \frac{49}{6} = \frac{43}{7}

- \frac{85}{42} + \frac{49}{6}

Least Common Multiplier of

42, 6 : 42

42, 6

Least Common Multiplier (LCM)

Prime factorization of

42 : 2 \cdot 3 \cdot 7

42

42

divides by

242 = 21 \cdot 2

= 2 \cdot 21

21

divides by

321 = 7 \cdot 3

= 2 \cdot 3 \cdot 7

2, 3, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 7

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

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

42

6

= 2 \cdot 3 \cdot 7

Multiply the numbers:

2 \cdot 3 \cdot 7 = 42

= 42

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

42

For

\frac{49}{6} :

multiply the denominator and numerator by

7

\frac{49}{6} = \frac{49 \cdot 7}{6 \cdot 7} = \frac{343}{42}

= - \frac{85}{42} + \frac{343}{42}

Since the denominators are equal, combine the fractions:

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

= \frac{- 85 + 343}{42}

Add/Subtract the numbers:

- 85 + 343 = 258

= \frac{258}{42}

Cancel the common factor:

6

= \frac{43}{7}

= \frac{43}{7}

= \frac{43}{7}

Convert improper fractions to mixed numbers:

\frac{43}{7} = 6 \frac{1}{7}

\frac{43}{7} = 6

Remainder

1

\frac{43}{7}

Write the problem in long division format

7 \overline{∣ 43}

Divide

43

7

to get

6

Divide

43

7

to get

6

6 7 \overline{∣ 43}

Multiply the quotient digit

(6)

by the divisor

7

6 7 \overline{∣ 43} \underline{42}

Subtract

42

from

43

6 7 \overline{∣ 43} \underline{42} 1

6 7 \overline{∣ 43} \underline{42} 1

The solution for Long Division of

\frac{43}{7}

6

with remainder of

1

6 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{43}{7} = 6 \frac{1}{7}

= 6 \frac{1}{7}

= 6 \frac{1}{7}

Popular Examples

Evaluate 0.5/8 long division

\frac{0.5}{8}

Convert to an Improper Fraction 5 3/5 improper fraction

5 \frac{3}{5}

Evaluate 280÷3 long division

\frac{280}{3}

Convert to a Simplified Fraction 0.064 convert to fraction

0.064

Find the Possible Factors 129 positive factors of

129

Frequently Asked Questions (FAQ)

What is (-7/6-6/7)-(-7/6-7) ?
The solution to (-7/6-6/7)-(-7/6-7) is 6 1/7