What is 5/7+(7/14-3/7) ?

The solution to 5/7+(7/14-3/7) is 11/14

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Popular >

5/7+(7/14-3/7)

Solution

\frac{5}{7} + (\frac{7}{14} - \frac{3}{7})

Solution

\frac{11}{14}

Solution steps

\frac{5}{7} + (\frac{7}{14} - \frac{3}{7})

\frac{7}{14} = \frac{1}{2}

Cancel the common factor:

7

\frac{1}{2}

= \frac{5}{7} + \frac{1}{2} - \frac{3}{7}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{5}{7} + \frac{1}{2} - \frac{3}{7} : \frac{11}{14}

\frac{5}{7} + \frac{1}{2} - \frac{3}{7}

\frac{5}{7} + \frac{1}{2} = \frac{17}{14}

\frac{5}{7} + \frac{1}{2}

Least Common Multiplier of

7, 2 : 14

7, 2

Least Common Multiplier (LCM)

Prime factorization of

7 : 7

7

7

is a prime number, therefore no factorization is possible

= 7

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

7

2

= 7 \cdot 2

Multiply the numbers:

7 \cdot 2 = 14

= 14

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

14

For

\frac{5}{7} :

multiply the denominator and numerator by

2

\frac{5}{7} = \frac{5 \cdot 2}{7 \cdot 2} = \frac{10}{14}

For

\frac{1}{2} :

multiply the denominator and numerator by

7

\frac{1}{2} = \frac{1 \cdot 7}{2 \cdot 7} = \frac{7}{14}

= \frac{10}{14} + \frac{7}{14}

Since the denominators are equal, combine the fractions:

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

= \frac{10 + 7}{14}

Add the numbers:

10 + 7 = 17

= \frac{17}{14}

= \frac{17}{14} - \frac{3}{7}

\frac{17}{14} - \frac{3}{7} = \frac{11}{14}

\frac{17}{14} - \frac{3}{7}

Least Common Multiplier of

14, 7 : 14

14, 7

Least Common Multiplier (LCM)

Prime factorization of

14 : 2 \cdot 7

14

14

divides by

214 = 7 \cdot 2

= 2 \cdot 7

2, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 7

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

14

7

= 2 \cdot 7

Multiply the numbers:

2 \cdot 7 = 14

= 14

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

14

For

\frac{3}{7} :

multiply the denominator and numerator by

2

\frac{3}{7} = \frac{3 \cdot 2}{7 \cdot 2} = \frac{6}{14}

= \frac{17}{14} - \frac{6}{14}

Since the denominators are equal, combine the fractions:

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

= \frac{17 - 6}{14}

Subtract the numbers:

17 - 6 = 11

= \frac{11}{14}

= \frac{11}{14}

= \frac{11}{14}

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Frequently Asked Questions (FAQ)

What is 5/7+(7/14-3/7) ?
The solution to 5/7+(7/14-3/7) is 11/14