What is 2 5/2+2-8/7+6 ?

The solution to 2 5/2+2-8/7+6 is 11 5/14

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Popular Pre Algebra >

2 5/2+2-8/7+6

Solution

2 \frac{5}{2} + 2 - \frac{8}{7} + 6

Solution

11 \frac{5}{14}

Decimal

11.35714 \dots

Solution steps

2 \frac{5}{2} + 2 - \frac{8}{7} + 6

Convert mixed numbers to improper fractions:

2 \frac{5}{2} = \frac{9}{2}

2 \frac{5}{2}

Convert mixed numbers to improper fraction:

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

2 \frac{5}{2} = \frac{2 \cdot 2 + 5}{2}

= \frac{9}{2}

= \frac{9}{2} + 2 - \frac{8}{7} + 6

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{9}{2} + 2 - \frac{8}{7} + 6 : \frac{159}{14}

\frac{9}{2} + 2 - \frac{8}{7} + 6

\frac{9}{2} + 2 = \frac{13}{2}

\frac{9}{2} + 2

Convert element to fraction:

2 = \frac{2 \cdot 2}{2}

= \frac{2 \cdot 2}{2} + \frac{9}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{2 \cdot 2 + 9}{2}

2 \cdot 2 + 9 = 13

2 \cdot 2 + 9

Multiply the numbers:

2 \cdot 2 = 4

= 4 + 9

Add the numbers:

4 + 9 = 13

= 13

= \frac{13}{2}

= \frac{13}{2} - \frac{8}{7} + 6

\frac{13}{2} - \frac{8}{7} = \frac{75}{14}

\frac{13}{2} - \frac{8}{7}

Least Common Multiplier of

2, 7 : 14

2, 7

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

2

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{13}{2} :

multiply the denominator and numerator by

7

\frac{13}{2} = \frac{13 \cdot 7}{2 \cdot 7} = \frac{91}{14}

For

\frac{8}{7} :

multiply the denominator and numerator by

2

\frac{8}{7} = \frac{8 \cdot 2}{7 \cdot 2} = \frac{16}{14}

= \frac{91}{14} - \frac{16}{14}

Since the denominators are equal, combine the fractions:

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

= \frac{91 - 16}{14}

Subtract the numbers:

91 - 16 = 75

= \frac{75}{14}

= \frac{75}{14} + 6

\frac{75}{14} + 6 = \frac{159}{14}

\frac{75}{14} + 6

Convert element to fraction:

6 = \frac{6 \cdot 14}{14}

= \frac{6 \cdot 14}{14} + \frac{75}{14}

Since the denominators are equal, combine the fractions:

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

= \frac{6 \cdot 14 + 75}{14}

6 \cdot 14 + 75 = 159

6 \cdot 14 + 75

Multiply the numbers:

6 \cdot 14 = 84

= 84 + 75

Add the numbers:

84 + 75 = 159

= 159

= \frac{159}{14}

= \frac{159}{14}

= \frac{159}{14}

Convert improper fractions to mixed numbers:

\frac{159}{14} = 11 \frac{5}{14}

\frac{159}{14} = 11

Remainder

5

\frac{159}{14}

Write the problem in long division format

14 \overline{∣ 159}

Divide

15

14

to get

1

Divide

15

14

to get

1

1 14 \overline{∣ 159}

Multiply the quotient digit

(1)

by the divisor

14

1 14 \overline{∣ 159} \underline{14}

Subtract

14

from

15

1 14 \overline{∣ 159} \underline{14} 1

Bring down the next number of the dividend

1 14 \overline{∣ 159} \underline{14} 19

1 14 \overline{∣ 159} \underline{14} 19

Divide

19

14

to get

1

Divide

19

14

to get

1

11 14 \overline{∣ 159} \underline{14} 19

Multiply the quotient digit

(1)

by the divisor

14

11 14 \overline{∣ 159} \underline{14} 19 \underline{14}

Subtract

14

from

19

11 14 \overline{∣ 159} \underline{14} 19 \underline{14} 5

11 14 \overline{∣ 159} \underline{14} 19 \underline{14} 5

The solution for Long Division of

\frac{159}{14}

11

with remainder of

5

11 Remainder 5

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{159}{14} = 11 \frac{5}{14}

= 11 \frac{5}{14}

= 11 \frac{5}{14}

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Frequently Asked Questions (FAQ)

What is 2 5/2+2-8/7+6 ?
The solution to 2 5/2+2-8/7+6 is 11 5/14

2 5/2+2-8/7+6

Solution

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Frequently Asked Questions (FAQ)

What is 2 5/2+2-8/7+6 ?

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