What is 243/6561+4+81-2/3+512 ?

The solution to 243/6561+4+81-2/3+512 is 596 10/27

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Popular >

243/6561+4+81-2/3+512

Solution

\frac{243}{6561} + 4 + 81 - \frac{2}{3} + 512

Solution

596 \frac{10}{27}

Solution steps

\frac{243}{6561} + 4 + 81 - \frac{2}{3} + 512

\frac{243}{6561} = \frac{1}{27}

Cancel the common factor:

243

\frac{1}{27}

= \frac{1}{27} + 4 + 81 - \frac{2}{3} + 512

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{1}{27} + 4 + 81 - \frac{2}{3} + 512 : \frac{16102}{27}

\frac{1}{27} + 4 + 81 - \frac{2}{3} + 512

\frac{1}{27} + 4 = \frac{109}{27}

\frac{1}{27} + 4

Convert element to fraction:

4 = \frac{4 \cdot 27}{27}

= \frac{4 \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{4 \cdot 27 + 1}{27}

4 \cdot 27 + 1 = 109

4 \cdot 27 + 1

Multiply the numbers:

4 \cdot 27 = 108

= 108 + 1

Add the numbers:

108 + 1 = 109

= 109

= \frac{109}{27}

= \frac{109}{27} + 81 - \frac{2}{3} + 512

\frac{109}{27} + 81 = \frac{2296}{27}

\frac{109}{27} + 81

Convert element to fraction:

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

= \frac{81 \cdot 27}{27} + \frac{109}{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 + 109}{27}

81 \cdot 27 + 109 = 2296

81 \cdot 27 + 109

Multiply the numbers:

81 \cdot 27 = 2187

= 2187 + 109

Add the numbers:

2187 + 109 = 2296

= 2296

= \frac{2296}{27}

= \frac{2296}{27} - \frac{2}{3} + 512

\frac{2296}{27} - \frac{2}{3} = \frac{2278}{27}

\frac{2296}{27} - \frac{2}{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{2}{3} :

multiply the denominator and numerator by

9

\frac{2}{3} = \frac{2 \cdot 9}{3 \cdot 9} = \frac{18}{27}

= \frac{2296}{27} - \frac{18}{27}

Since the denominators are equal, combine the fractions:

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

= \frac{2296 - 18}{27}

Subtract the numbers:

2296 - 18 = 2278

= \frac{2278}{27}

= \frac{2278}{27} + 512

\frac{2278}{27} + 512 = \frac{16102}{27}

\frac{2278}{27} + 512

Convert element to fraction:

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

= \frac{512 \cdot 27}{27} + \frac{2278}{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 + 2278}{27}

512 \cdot 27 + 2278 = 16102

512 \cdot 27 + 2278

Multiply the numbers:

512 \cdot 27 = 13824

= 13824 + 2278

Add the numbers:

13824 + 2278 = 16102

= 16102

= \frac{16102}{27}

= \frac{16102}{27}

= \frac{16102}{27}

Convert improper fractions to mixed numbers:

\frac{16102}{27} = 596 \frac{10}{27}

\frac{16102}{27} = 596

Remainder

10

\frac{16102}{27}

Write the problem in long division format

27 \overline{∣ 16102}

Divide

161

27

to get

5

Divide

161

27

to get

5

5 27 \overline{∣ 16102}

Multiply the quotient digit

(5)

by the divisor

27

5 27 \overline{∣ 16102} \underline{135}

Subtract

135

from

161

5 27 \overline{∣ 16102} \underline{135} 26

Bring down the next number of the dividend

5 27 \overline{∣ 16102} \underline{135} 260

5 27 \overline{∣ 16102} \underline{135} 260

Divide

260

27

to get

9

Divide

260

27

to get

9

59 27 \overline{∣ 16102} \underline{135} 260

Multiply the quotient digit

(9)

by the divisor

27

59 27 \overline{∣ 16102} \underline{135} 260 \underline{243}

Subtract

243

from

260

59 27 \overline{∣ 16102} \underline{135} 260 \underline{243} 17

Bring down the next number of the dividend

59 27 \overline{∣ 16102} \underline{135} 260 \underline{243} 172

59 27 \overline{∣ 16102} \underline{135} 260 \underline{243} 172

Divide

172

27

to get

6

Divide

172

27

to get

6

596 27 \overline{∣ 16102} \underline{135} 260 \underline{243} 172

Multiply the quotient digit

(6)

by the divisor

27

596 27 \overline{∣ 16102} \underline{135} 260 \underline{243} 172 \underline{162}

Subtract

162

from

172

596 27 \overline{∣ 16102} \underline{135} 260 \underline{243} 172 \underline{162} 10

596 27 \overline{∣ 16102} \underline{135} 260 \underline{243} 172 \underline{162} 10

The solution for Long Division of

\frac{16102}{27}

596

with remainder of

10

596 Remainder 10

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{16102}{27} = 596 \frac{10}{27}

= 596 \frac{10}{27}

= 596 \frac{10}{27}

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Frequently Asked Questions (FAQ)

What is 243/6561+4+81-2/3+512 ?
The solution to 243/6561+4+81-2/3+512 is 596 10/27