What is 2/3-3/4+4/5-5/6+6/7 ?

The solution to 2/3-3/4+4/5-5/6+6/7 is 311/420

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Popular >

2/3-3/4+4/5-5/6+6/7

Solution

2/3 - 3/4 + 4/5 - 5/6 + 6/7

Solution

\frac{311}{420}

Solution steps

2/3 - 3/4 + 4/5 - 5/6 + 6/7

Follow the PEMDAS order of operations

Multiply and divide (left to right)

2/3 : \frac{2}{3}

2/3

2/3 = \frac{2}{3}

= \frac{2}{3}

= \frac{2}{3} - 3/4 + 4/5 - 5/6 + 6/7

Multiply and divide (left to right)

3/4 : \frac{3}{4}

3/4

3/4 = \frac{3}{4}

= \frac{3}{4}

= \frac{2}{3} - \frac{3}{4} + 4/5 - 5/6 + 6/7

Multiply and divide (left to right)

4/5 : \frac{4}{5}

4/5

4/5 = \frac{4}{5}

= \frac{4}{5}

= \frac{2}{3} - \frac{3}{4} + \frac{4}{5} - 5/6 + 6/7

Multiply and divide (left to right)

5/6 : \frac{5}{6}

5/6

5/6 = \frac{5}{6}

= \frac{5}{6}

= \frac{2}{3} - \frac{3}{4} + \frac{4}{5} - \frac{5}{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{2}{3} - \frac{3}{4} + \frac{4}{5} - \frac{5}{6} + \frac{6}{7}

Add and subtract (left to right)

\frac{2}{3} - \frac{3}{4} + \frac{4}{5} - \frac{5}{6} + \frac{6}{7} : \frac{311}{420}

\frac{2}{3} - \frac{3}{4} + \frac{4}{5} - \frac{5}{6} + \frac{6}{7}

\frac{2}{3} - \frac{3}{4} = - \frac{1}{12}

\frac{2}{3} - \frac{3}{4}

Least Common Multiplier of

3, 4 : 12

3, 4

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

3

4

= 3 \cdot 2 \cdot 2

Multiply the numbers:

3 \cdot 2 \cdot 2 = 12

= 12

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

12

For

\frac{2}{3} :

multiply the denominator and numerator by

4

\frac{2}{3} = \frac{2 \cdot 4}{3 \cdot 4} = \frac{8}{12}

For

\frac{3}{4} :

multiply the denominator and numerator by

3

\frac{3}{4} = \frac{3 \cdot 3}{4 \cdot 3} = \frac{9}{12}

= \frac{8}{12} - \frac{9}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{8 - 9}{12}

Subtract the numbers:

8 - 9 = - 1

= \frac{- 1}{12}

Apply the fraction rule:

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

= - \frac{1}{12}

= - \frac{1}{12} + \frac{4}{5} - \frac{5}{6} + \frac{6}{7}

- \frac{1}{12} + \frac{4}{5} = \frac{43}{60}

- \frac{1}{12} + \frac{4}{5}

Least Common Multiplier of

12, 5 : 60

12, 5

Least Common Multiplier (LCM)

Prime factorization of

12 : 2 \cdot 2 \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 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

12

5

= 2 \cdot 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 3 \cdot 5 = 60

= 60

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

60

For

\frac{1}{12} :

multiply the denominator and numerator by

5

\frac{1}{12} = \frac{1 \cdot 5}{12 \cdot 5} = \frac{5}{60}

For

\frac{4}{5} :

multiply the denominator and numerator by

12

\frac{4}{5} = \frac{4 \cdot 12}{5 \cdot 12} = \frac{48}{60}

= - \frac{5}{60} + \frac{48}{60}

Since the denominators are equal, combine the fractions:

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

= \frac{- 5 + 48}{60}

Add/Subtract the numbers:

- 5 + 48 = 43

= \frac{43}{60}

= \frac{43}{60} - \frac{5}{6} + \frac{6}{7}

\frac{43}{60} - \frac{5}{6} = - \frac{7}{60}

\frac{43}{60} - \frac{5}{6}

Least Common Multiplier of

60, 6 : 60

60, 6

Least Common Multiplier (LCM)

Prime factorization of

60 : 2 \cdot 2 \cdot 3 \cdot 5

60

60

divides by

260 = 30 \cdot 2

= 2 \cdot 30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 5

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

60

6

= 2 \cdot 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 3 \cdot 5 = 60

= 60

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

60

For

\frac{5}{6} :

multiply the denominator and numerator by

10

\frac{5}{6} = \frac{5 \cdot 10}{6 \cdot 10} = \frac{50}{60}

= \frac{43}{60} - \frac{50}{60}

Since the denominators are equal, combine the fractions:

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

= \frac{43 - 50}{60}

Subtract the numbers:

43 - 50 = - 7

= \frac{- 7}{60}

Apply the fraction rule:

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

= - \frac{7}{60}

= - \frac{7}{60} + \frac{6}{7}

- \frac{7}{60} + \frac{6}{7} = \frac{311}{420}

- \frac{7}{60} + \frac{6}{7}

Least Common Multiplier of

60, 7 : 420

60, 7

Least Common Multiplier (LCM)

Prime factorization of

60 : 2 \cdot 2 \cdot 3 \cdot 5

60

60

divides by

260 = 30 \cdot 2

= 2 \cdot 30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 5

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

60

7

= 2 \cdot 2 \cdot 3 \cdot 5 \cdot 7

Multiply the numbers:

2 \cdot 2 \cdot 3 \cdot 5 \cdot 7 = 420

= 420

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

420

For

\frac{7}{60} :

multiply the denominator and numerator by

7

\frac{7}{60} = \frac{7 \cdot 7}{60 \cdot 7} = \frac{49}{420}

For

\frac{6}{7} :

multiply the denominator and numerator by

60

\frac{6}{7} = \frac{6 \cdot 60}{7 \cdot 60} = \frac{360}{420}

= - \frac{49}{420} + \frac{360}{420}

Since the denominators are equal, combine the fractions:

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

= \frac{- 49 + 360}{420}

Add/Subtract the numbers:

- 49 + 360 = 311

= \frac{311}{420}

= \frac{311}{420}

= \frac{311}{420}

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Frequently Asked Questions (FAQ)

What is 2/3-3/4+4/5-5/6+6/7 ?
The solution to 2/3-3/4+4/5-5/6+6/7 is 311/420