What is 5-6/7+7/8+5/3 ?

The solution to 5-6/7+7/8+5/3 is 6 115/168

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Popular Pre Algebra >

5-6/7+7/8+5/3

Solution

5 - \frac{6}{7} + \frac{7}{8} + \frac{5}{3}

Solution

6 \frac{115}{168}

Decimal

6.68452 \dots

Solution steps

5 - \frac{6}{7} + \frac{7}{8} + \frac{5}{3}

Follow the PEMDAS order of operations

Add and subtract (left to right)

5 - \frac{6}{7} = \frac{29}{7}

5 - \frac{6}{7}

Convert element to fraction:

5 = \frac{5 \cdot 7}{7}

= \frac{5 \cdot 7}{7} - \frac{6}{7}

Since the denominators are equal, combine the fractions:

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

= \frac{5 \cdot 7 - 6}{7}

5 \cdot 7 - 6 = 29

5 \cdot 7 - 6

Multiply the numbers:

5 \cdot 7 = 35

= 35 - 6

Subtract the numbers:

35 - 6 = 29

= 29

= \frac{29}{7}

= \frac{29}{7} + \frac{7}{8} + \frac{5}{3}

\frac{29}{7} + \frac{7}{8} = \frac{281}{56}

\frac{29}{7} + \frac{7}{8}

Least Common Multiplier of

7, 8 : 56

7, 8

Least Common Multiplier (LCM)

Prime factorization of

7 : 7

7

7

is a prime number, therefore no factorization is possible

= 7

Prime factorization of

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

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

7

8

= 7 \cdot 2 \cdot 2 \cdot 2

Multiply the numbers:

7 \cdot 2 \cdot 2 \cdot 2 = 56

= 56

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

56

For

\frac{29}{7} :

multiply the denominator and numerator by

8

\frac{29}{7} = \frac{29 \cdot 8}{7 \cdot 8} = \frac{232}{56}

For

\frac{7}{8} :

multiply the denominator and numerator by

7

\frac{7}{8} = \frac{7 \cdot 7}{8 \cdot 7} = \frac{49}{56}

= \frac{232}{56} + \frac{49}{56}

Since the denominators are equal, combine the fractions:

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

= \frac{232 + 49}{56}

Add the numbers:

232 + 49 = 281

= \frac{281}{56}

= \frac{281}{56} + \frac{5}{3}

\frac{281}{56} + \frac{5}{3} = \frac{1123}{168}

\frac{281}{56} + \frac{5}{3}

Least Common Multiplier of

56, 3 : 168

56, 3

Least Common Multiplier (LCM)

Prime factorization of

56 : 2 \cdot 2 \cdot 2 \cdot 7

56

56

divides by

256 = 28 \cdot 2

= 2 \cdot 28

28

divides by

228 = 14 \cdot 2

= 2 \cdot 2 \cdot 14

14

divides by

214 = 7 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 7

2, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 7

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

56

3

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

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 7 \cdot 3 = 168

= 168

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

168

For

\frac{281}{56} :

multiply the denominator and numerator by

3

\frac{281}{56} = \frac{281 \cdot 3}{56 \cdot 3} = \frac{843}{168}

For

\frac{5}{3} :

multiply the denominator and numerator by

56

\frac{5}{3} = \frac{5 \cdot 56}{3 \cdot 56} = \frac{280}{168}

= \frac{843}{168} + \frac{280}{168}

Since the denominators are equal, combine the fractions:

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

= \frac{843 + 280}{168}

Add the numbers:

843 + 280 = 1123

= \frac{1123}{168}

= \frac{1123}{168}

Convert improper fractions to mixed numbers:

\frac{1123}{168} = 6 \frac{115}{168}

\frac{1123}{168} = 6

Remainder

115

\frac{1123}{168}

Write the problem in long division format

168 \overline{∣ 1123}

Divide

1123

168

to get

6

Divide

1123

168

to get

6

6 168 \overline{∣ 1123}

Multiply the quotient digit

(6)

by the divisor

168

6 168 \overline{∣ 1123} \underline{1008}

Subtract

1008

from

1123

6 168 \overline{∣ 1123} \underline{1008} 115

6 168 \overline{∣ 1123} \underline{1008} 115

The solution for Long Division of

\frac{1123}{168}

6

with remainder of

115

6 Remainder 115

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{1123}{168} = 6 \frac{115}{168}

= 6 \frac{115}{168}

= 6 \frac{115}{168}

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Frequently Asked Questions (FAQ)

What is 5-6/7+7/8+5/3 ?
The solution to 5-6/7+7/8+5/3 is 6 115/168

5-6/7+7/8+5/3

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 5-6/7+7/8+5/3 ?

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