What is 8 1/10-(6 1/3+1/2) ?

The solution to 8 1/10-(6 1/3+1/2) is 1 4/15

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Popular Pre Algebra >

8 1/10-(6 1/3+1/2)

Solution

8 \frac{1}{10} - (6 \frac{1}{3} + \frac{1}{2})

Solution

1 \frac{4}{15}

Decimal

1.26666 \dots

Solution steps

8 \frac{1}{10} - (6 \frac{1}{3} + \frac{1}{2})

Convert mixed numbers to improper fractions:

8 \frac{1}{10} = \frac{81}{10}

8 \frac{1}{10}

Convert mixed numbers to improper fraction:

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

8 \frac{1}{10} = \frac{8 \cdot 10 + 1}{10}

= \frac{81}{10}

= \frac{81}{10} - (6 \frac{1}{3} + \frac{1}{2})

Convert mixed numbers to improper fractions:

6 \frac{1}{3} = \frac{19}{3}

6 \frac{1}{3}

Convert mixed numbers to improper fraction:

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

6 \frac{1}{3} = \frac{6 \cdot 3 + 1}{3}

= \frac{19}{3}

= \frac{81}{10} - (\frac{19}{3} + \frac{1}{2})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{19}{3} + \frac{1}{2}) : \frac{41}{6}

\frac{19}{3} + \frac{1}{2}

\frac{19}{3} + \frac{1}{2} = \frac{41}{6}

\frac{19}{3} + \frac{1}{2}

Least Common Multiplier of

3, 2 : 6

3, 2

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

3

2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= 6

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

6

For

\frac{19}{3} :

multiply the denominator and numerator by

2

\frac{19}{3} = \frac{19 \cdot 2}{3 \cdot 2} = \frac{38}{6}

For

\frac{1}{2} :

multiply the denominator and numerator by

3

\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}

= \frac{38}{6} + \frac{3}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{38 + 3}{6}

Add the numbers:

38 + 3 = 41

= \frac{41}{6}

= \frac{41}{6}

= \frac{81}{10} - \frac{41}{6}

Add and subtract (left to right)

\frac{81}{10} - \frac{41}{6} : \frac{19}{15}

\frac{81}{10} - \frac{41}{6}

\frac{81}{10} - \frac{41}{6} = \frac{19}{15}

\frac{81}{10} - \frac{41}{6}

Least Common Multiplier of

10, 6 : 30

10, 6

Least Common Multiplier (LCM)

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

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

10

6

= 2 \cdot 5 \cdot 3

Multiply the numbers:

2 \cdot 5 \cdot 3 = 30

= 30

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

30

For

\frac{81}{10} :

multiply the denominator and numerator by

3

\frac{81}{10} = \frac{81 \cdot 3}{10 \cdot 3} = \frac{243}{30}

For

\frac{41}{6} :

multiply the denominator and numerator by

5

\frac{41}{6} = \frac{41 \cdot 5}{6 \cdot 5} = \frac{205}{30}

= \frac{243}{30} - \frac{205}{30}

Since the denominators are equal, combine the fractions:

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

= \frac{243 - 205}{30}

Subtract the numbers:

243 - 205 = 38

= \frac{38}{30}

Cancel the common factor:

2

= \frac{19}{15}

= \frac{19}{15}

= \frac{19}{15}

Convert improper fractions to mixed numbers:

\frac{19}{15} = 1 \frac{4}{15}

\frac{19}{15} = 1

Remainder

4

\frac{19}{15}

Write the problem in long division format

15 \overline{∣ 19}

Divide

19

15

to get

1

Divide

19

15

to get

1

1 15 \overline{∣ 19}

Multiply the quotient digit

(1)

by the divisor

15

1 15 \overline{∣ 19} \underline{15}

Subtract

15

from

19

1 15 \overline{∣ 19} \underline{15} 4

1 15 \overline{∣ 19} \underline{15} 4

The solution for Long Division of

\frac{19}{15}

1

with remainder of

4

1 Remainder 4

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{19}{15} = 1 \frac{4}{15}

= 1 \frac{4}{15}

= 1 \frac{4}{15}

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Frequently Asked Questions (FAQ)

What is 8 1/10-(6 1/3+1/2) ?
The solution to 8 1/10-(6 1/3+1/2) is 1 4/15

8 1/10-(6 1/3+1/2)

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 8 1/10-(6 1/3+1/2) ?

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