What is 243/6561+64+81-4/3+1728 ?

The solution to 243/6561+64+81-4/3+1728 is 1871 19/27

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Popular Pre Algebra >

243/6561+64+81-4/3+1728

Solution

\frac{243}{6561} + 64 + 81 - \frac{4}{3} + 1728

Solution

1871 \frac{19}{27}

Decimal

1871.70370 \dots

Solution steps

\frac{243}{6561} + 64 + 81 - \frac{4}{3} + 1728

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

Cancel the common factor:

243

\frac{1}{27}

= \frac{1}{27} + 64 + 81 - \frac{4}{3} + 1728

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{1}{27} + 64 + 81 - \frac{4}{3} + 1728 : \frac{50536}{27}

\frac{1}{27} + 64 + 81 - \frac{4}{3} + 1728

\frac{1}{27} + 64 = \frac{1729}{27}

\frac{1}{27} + 64

Convert element to fraction:

64 = \frac{64 \cdot 27}{27}

= \frac{64 \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{64 \cdot 27 + 1}{27}

64 \cdot 27 + 1 = 1729

64 \cdot 27 + 1

Multiply the numbers:

64 \cdot 27 = 1728

= 1728 + 1

Add the numbers:

1728 + 1 = 1729

= 1729

= \frac{1729}{27}

= \frac{1729}{27} + 81 - \frac{4}{3} + 1728

\frac{1729}{27} + 81 = \frac{3916}{27}

\frac{1729}{27} + 81

Convert element to fraction:

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

= \frac{81 \cdot 27}{27} + \frac{1729}{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 + 1729}{27}

81 \cdot 27 + 1729 = 3916

81 \cdot 27 + 1729

Multiply the numbers:

81 \cdot 27 = 2187

= 2187 + 1729

Add the numbers:

2187 + 1729 = 3916

= 3916

= \frac{3916}{27}

= \frac{3916}{27} - \frac{4}{3} + 1728

\frac{3916}{27} - \frac{4}{3} = \frac{3880}{27}

\frac{3916}{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{3916}{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{3916 - 36}{27}

Subtract the numbers:

3916 - 36 = 3880

= \frac{3880}{27}

= \frac{3880}{27} + 1728

\frac{3880}{27} + 1728 = \frac{50536}{27}

\frac{3880}{27} + 1728

Convert element to fraction:

1728 = \frac{1728 \cdot 27}{27}

= \frac{1728 \cdot 27}{27} + \frac{3880}{27}

Since the denominators are equal, combine the fractions:

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

= \frac{1728 \cdot 27 + 3880}{27}

1728 \cdot 27 + 3880 = 50536

1728 \cdot 27 + 3880

Multiply the numbers:

1728 \cdot 27 = 46656

= 46656 + 3880

Add the numbers:

46656 + 3880 = 50536

= 50536

= \frac{50536}{27}

= \frac{50536}{27}

= \frac{50536}{27}

Convert improper fractions to mixed numbers:

\frac{50536}{27} = 1871 \frac{19}{27}

\frac{50536}{27} = 1871

Remainder

19

\frac{50536}{27}

Write the problem in long division format

27 \overline{∣ 50536}

Divide

50

27

to get

1

Divide

50

27

to get

1

1 27 \overline{∣ 50536}

Multiply the quotient digit

(1)

by the divisor

27

1 27 \overline{∣ 50536} \underline{27}

Subtract

27

from

50

1 27 \overline{∣ 50536} \underline{27} 23

Bring down the next number of the dividend

1 27 \overline{∣ 50536} \underline{27} 235

1 27 \overline{∣ 50536} \underline{27} 235

Divide

235

27

to get

8

Divide

235

27

to get

8

18 27 \overline{∣ 50536} \underline{27} 235

Multiply the quotient digit

(8)

by the divisor

27

18 27 \overline{∣ 50536} \underline{27} 235 \underline{216}

Subtract

216

from

235

18 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 19

Bring down the next number of the dividend

18 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 193

18 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 193

Divide

193

27

to get

7

Divide

193

27

to get

7

187 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 193

Multiply the quotient digit

(7)

by the divisor

27

187 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 193 \underline{189}

Subtract

189

from

193

187 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 193 \underline{189} 4

Bring down the next number of the dividend

187 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 193 \underline{189} 46

187 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 193 \underline{189} 46

Divide

46

27

to get

1

Divide

46

27

to get

1

1871 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 193 \underline{189} 46

Multiply the quotient digit

(1)

by the divisor

27

1871 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 193 \underline{189} 46 \underline{27}

Subtract

27

from

46

1871 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 193 \underline{189} 46 \underline{27} 19

1871 27 \overline{∣ 50536} \underline{27} 235 \underline{216} 193 \underline{189} 46 \underline{27} 19

The solution for Long Division of

\frac{50536}{27}

1871

with remainder of

19

1871 Remainder 19

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{50536}{27} = 1871 \frac{19}{27}

= 1871 \frac{19}{27}

= 1871 \frac{19}{27}

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Frequently Asked Questions (FAQ)

What is 243/6561+64+81-4/3+1728 ?
The solution to 243/6561+64+81-4/3+1728 is 1871 19/27

243/6561+64+81-4/3+1728

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 243/6561+64+81-4/3+1728 ?

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