What is 1/27+512+81-4/3+3375 ?

The solution to 1/27+512+81-4/3+3375 is 3966 19/27

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Popular Pre Algebra >

1/27+512+81-4/3+3375

Solution

\frac{1}{27} + 512 + 81 - \frac{4}{3} + 3375

Solution

3966 \frac{19}{27}

Decimal

3966.70370 \dots

Solution steps

\frac{1}{27} + 512 + 81 - \frac{4}{3} + 3375

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{1}{27} + 512 = \frac{13825}{27}

\frac{1}{27} + 512

Convert element to fraction:

512 = \frac{512 \cdot 27}{27}

= \frac{512 \cdot 27}{27} + \frac{1}{27}

Since the denominators are equal, combine the fractions:

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

= \frac{512 \cdot 27 + 1}{27}

512 \cdot 27 + 1 = 13825

512 \cdot 27 + 1

Multiply the numbers:

512 \cdot 27 = 13824

= 13824 + 1

Add the numbers:

13824 + 1 = 13825

= 13825

= \frac{13825}{27}

= \frac{13825}{27} + 81 - \frac{4}{3} + 3375

\frac{13825}{27} + 81 = \frac{16012}{27}

\frac{13825}{27} + 81

Convert element to fraction:

81 = \frac{81 \cdot 27}{27}

= \frac{81 \cdot 27}{27} + \frac{13825}{27}

Since the denominators are equal, combine the fractions:

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

= \frac{81 \cdot 27 + 13825}{27}

81 \cdot 27 + 13825 = 16012

81 \cdot 27 + 13825

Multiply the numbers:

81 \cdot 27 = 2187

= 2187 + 13825

Add the numbers:

2187 + 13825 = 16012

= 16012

= \frac{16012}{27}

= \frac{16012}{27} - \frac{4}{3} + 3375

\frac{16012}{27} - \frac{4}{3} = \frac{15976}{27}

\frac{16012}{27} - \frac{4}{3}

Least Common Multiplier of

27, 3 : 27

27, 3

Least Common Multiplier (LCM)

Prime factorization of

27 : 3 \cdot 3 \cdot 3

27

27

divides by

327 = 9 \cdot 3

= 3 \cdot 9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3 \cdot 3

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

27

3

= 3 \cdot 3 \cdot 3

Multiply the numbers:

3 \cdot 3 \cdot 3 = 27

= 27

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

27

For

\frac{4}{3} :

multiply the denominator and numerator by

9

\frac{4}{3} = \frac{4 \cdot 9}{3 \cdot 9} = \frac{36}{27}

= \frac{16012}{27} - \frac{36}{27}

Since the denominators are equal, combine the fractions:

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

= \frac{16012 - 36}{27}

Subtract the numbers:

16012 - 36 = 15976

= \frac{15976}{27}

= \frac{15976}{27} + 3375

\frac{15976}{27} + 3375 = \frac{107101}{27}

\frac{15976}{27} + 3375

Convert element to fraction:

3375 = \frac{3375 \cdot 27}{27}

= \frac{3375 \cdot 27}{27} + \frac{15976}{27}

Since the denominators are equal, combine the fractions:

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

= \frac{3375 \cdot 27 + 15976}{27}

3375 \cdot 27 + 15976 = 107101

3375 \cdot 27 + 15976

Multiply the numbers:

3375 \cdot 27 = 91125

= 91125 + 15976

Add the numbers:

91125 + 15976 = 107101

= 107101

= \frac{107101}{27}

= \frac{107101}{27}

Convert improper fractions to mixed numbers:

\frac{107101}{27} = 3966 \frac{19}{27}

\frac{107101}{27} = 3966

Remainder

19

\frac{107101}{27}

Write the problem in long division format

27 \overline{∣ 107101}

Divide

107

27

to get

3

Divide

107

27

to get

3

3 27 \overline{∣ 107101}

Multiply the quotient digit

(3)

by the divisor

27

3 27 \overline{∣ 107101} \underline{81}

Subtract

81

from

107

3 27 \overline{∣ 107101} \underline{81} 26

Bring down the next number of the dividend

3 27 \overline{∣ 107101} \underline{81} 261

3 27 \overline{∣ 107101} \underline{81} 261

Divide

261

27

to get

9

Divide

261

27

to get

9

39 27 \overline{∣ 107101} \underline{81} 261

Multiply the quotient digit

(9)

by the divisor

27

39 27 \overline{∣ 107101} \underline{81} 261 \underline{243}

Subtract

243

from

261

39 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 18

Bring down the next number of the dividend

39 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 180

39 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 180

Divide

180

27

to get

6

Divide

180

27

to get

6

396 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 180

Multiply the quotient digit

(6)

by the divisor

27

396 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 180 \underline{162}

Subtract

162

from

180

396 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 180 \underline{162} 18

Bring down the next number of the dividend

396 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 180 \underline{162} 181

396 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 180 \underline{162} 181

Divide

181

27

to get

6

Divide

181

27

to get

6

3966 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 180 \underline{162} 181

Multiply the quotient digit

(6)

by the divisor

27

3966 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 180 \underline{162} 181 \underline{162}

Subtract

162

from

181

3966 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 180 \underline{162} 181 \underline{162} 19

3966 27 \overline{∣ 107101} \underline{81} 261 \underline{243} 180 \underline{162} 181 \underline{162} 19

The solution for Long Division of

\frac{107101}{27}

3966

with remainder of

19

3966 Remainder 19

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{107101}{27} = 3966 \frac{19}{27}

= 3966 \frac{19}{27}

= 3966 \frac{19}{27}

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What is 1/27+512+81-4/3+3375 ?
The solution to 1/27+512+81-4/3+3375 is 3966 19/27

1/27+512+81-4/3+3375

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What is 1/27+512+81-4/3+3375 ?

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