What is 6 4/5-(1/4+7/10) ?

The solution to 6 4/5-(1/4+7/10) is 5 17/20

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6 4/5-(1/4+7/10)

Solution

6 \frac{4}{5} - (\frac{1}{4} + \frac{7}{10})

Solution

5 \frac{17}{20}

Solution steps

6 \frac{4}{5} - (\frac{1}{4} + \frac{7}{10})

Convert mixed numbers to improper fractions:

6 \frac{4}{5} = \frac{34}{5}

6 \frac{4}{5}

Convert mixed numbers to improper fraction:

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

6 \frac{4}{5} = \frac{6 \cdot 5 + 4}{5}

= \frac{34}{5}

= \frac{34}{5} - (\frac{1}{4} + \frac{7}{10})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{4} + \frac{7}{10}) : \frac{19}{20}

\frac{1}{4} + \frac{7}{10}

\frac{1}{4} + \frac{7}{10} = \frac{19}{20}

\frac{1}{4} + \frac{7}{10}

Least Common Multiplier of

4, 10 : 20

4, 10

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5

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

4

10

= 2 \cdot 2 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 5 = 20

= 20

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

20

For

\frac{1}{4} :

multiply the denominator and numerator by

5

\frac{1}{4} = \frac{1 \cdot 5}{4 \cdot 5} = \frac{5}{20}

For

\frac{7}{10} :

multiply the denominator and numerator by

2

\frac{7}{10} = \frac{7 \cdot 2}{10 \cdot 2} = \frac{14}{20}

= \frac{5}{20} + \frac{14}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{5 + 14}{20}

Add the numbers:

5 + 14 = 19

= \frac{19}{20}

= \frac{19}{20}

= \frac{34}{5} - \frac{19}{20}

Add and subtract (left to right)

\frac{34}{5} - \frac{19}{20} : \frac{117}{20}

\frac{34}{5} - \frac{19}{20}

\frac{34}{5} - \frac{19}{20} = \frac{117}{20}

\frac{34}{5} - \frac{19}{20}

Least Common Multiplier of

5, 20 : 20

5, 20

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

20 : 2 \cdot 2 \cdot 5

20

20

divides by

220 = 10 \cdot 2

= 2 \cdot 10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 5

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

5

20

= 5 \cdot 2 \cdot 2

Multiply the numbers:

5 \cdot 2 \cdot 2 = 20

= 20

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

20

For

\frac{34}{5} :

multiply the denominator and numerator by

4

\frac{34}{5} = \frac{34 \cdot 4}{5 \cdot 4} = \frac{136}{20}

= \frac{136}{20} - \frac{19}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{136 - 19}{20}

Subtract the numbers:

136 - 19 = 117

= \frac{117}{20}

= \frac{117}{20}

= \frac{117}{20}

Convert improper fractions to mixed numbers:

\frac{117}{20} = 5 \frac{17}{20}

\frac{117}{20} = 5

Remainder

17

\frac{117}{20}

Write the problem in long division format

20 \overline{∣ 117}

Divide

117

20

to get

5

Divide

117

20

to get

5

5 20 \overline{∣ 117}

Multiply the quotient digit

(5)

by the divisor

20

5 20 \overline{∣ 117} \underline{100}

Subtract

100

from

117

5 20 \overline{∣ 117} \underline{100} 17

5 20 \overline{∣ 117} \underline{100} 17

The solution for Long Division of

\frac{117}{20}

5

with remainder of

17

5 Remainder 17

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{117}{20} = 5 \frac{17}{20}

= 5 \frac{17}{20}

= 5 \frac{17}{20}

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0 - (- 2 \times 1)

Frequently Asked Questions (FAQ)

What is 6 4/5-(1/4+7/10) ?
The solution to 6 4/5-(1/4+7/10) is 5 17/20