What is 1/27+128+81-4/3+2197 ?

The solution to 1/27+128+81-4/3+2197 is 2404 19/27

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Popular Pre Algebra >

1/27+128+81-4/3+2197

Solution

\frac{1}{27} + 128 + 81 - \frac{4}{3} + 2197

Solution

2404 \frac{19}{27}

Decimal

2404.70370 \dots

Solution steps

\frac{1}{27} + 128 + 81 - \frac{4}{3} + 2197

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{1}{27} + 128 = \frac{3457}{27}

\frac{1}{27} + 128

Convert element to fraction:

128 = \frac{128 \cdot 27}{27}

= \frac{128 \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{128 \cdot 27 + 1}{27}

128 \cdot 27 + 1 = 3457

128 \cdot 27 + 1

Multiply the numbers:

128 \cdot 27 = 3456

= 3456 + 1

Add the numbers:

3456 + 1 = 3457

= 3457

= \frac{3457}{27}

= \frac{3457}{27} + 81 - \frac{4}{3} + 2197

\frac{3457}{27} + 81 = \frac{5644}{27}

\frac{3457}{27} + 81

Convert element to fraction:

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

= \frac{81 \cdot 27}{27} + \frac{3457}{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 + 3457}{27}

81 \cdot 27 + 3457 = 5644

81 \cdot 27 + 3457

Multiply the numbers:

81 \cdot 27 = 2187

= 2187 + 3457

Add the numbers:

2187 + 3457 = 5644

= 5644

= \frac{5644}{27}

= \frac{5644}{27} - \frac{4}{3} + 2197

\frac{5644}{27} - \frac{4}{3} = \frac{5608}{27}

\frac{5644}{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{5644}{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{5644 - 36}{27}

Subtract the numbers:

5644 - 36 = 5608

= \frac{5608}{27}

= \frac{5608}{27} + 2197

\frac{5608}{27} + 2197 = \frac{64927}{27}

\frac{5608}{27} + 2197

Convert element to fraction:

2197 = \frac{2197 \cdot 27}{27}

= \frac{2197 \cdot 27}{27} + \frac{5608}{27}

Since the denominators are equal, combine the fractions:

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

= \frac{2197 \cdot 27 + 5608}{27}

2197 \cdot 27 + 5608 = 64927

2197 \cdot 27 + 5608

Multiply the numbers:

2197 \cdot 27 = 59319

= 59319 + 5608

Add the numbers:

59319 + 5608 = 64927

= 64927

= \frac{64927}{27}

= \frac{64927}{27}

Convert improper fractions to mixed numbers:

\frac{64927}{27} = 2404 \frac{19}{27}

\frac{64927}{27} = 2404

Remainder

19

\frac{64927}{27}

Write the problem in long division format

27 \overline{∣ 64927}

Divide

64

27

to get

2

Divide

64

27

to get

2

2 27 \overline{∣ 64927}

Multiply the quotient digit

(2)

by the divisor

27

2 27 \overline{∣ 64927} \underline{54}

Subtract

54

from

64

2 27 \overline{∣ 64927} \underline{54} 10

Bring down the next number of the dividend

2 27 \overline{∣ 64927} \underline{54} 109

2 27 \overline{∣ 64927} \underline{54} 109

Divide

109

27

to get

4

Divide

109

27

to get

4

24 27 \overline{∣ 64927} \underline{54} 109

Multiply the quotient digit

(4)

by the divisor

27

24 27 \overline{∣ 64927} \underline{54} 109 \underline{108}

Subtract

108

from

109

24 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 1

Bring down the next number of the dividend

24 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 12

24 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 12

Divide

12

27

to get

0

Divide

12

27

to get

0

240 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 12

Multiply the quotient digit

(0)

by the divisor

27

240 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 12 \underline{0}

Subtract

0

from

12

240 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 12 \underline{0} 12

Bring down the next number of the dividend

240 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 12 \underline{0} 127

240 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 12 \underline{0} 127

Divide

127

27

to get

4

Divide

127

27

to get

4

2404 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 12 \underline{0} 127

Multiply the quotient digit

(4)

by the divisor

27

2404 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 12 \underline{0} 127 \underline{108}

Subtract

108

from

127

2404 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 12 \underline{0} 127 \underline{108} 19

2404 27 \overline{∣ 64927} \underline{54} 109 \underline{108} 12 \underline{0} 127 \underline{108} 19

The solution for Long Division of

\frac{64927}{27}

2404

with remainder of

19

2404 Remainder 19

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{64927}{27} = 2404 \frac{19}{27}

= 2404 \frac{19}{27}

= 2404 \frac{19}{27}

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Frequently Asked Questions (FAQ)

What is 1/27+128+81-4/3+2197 ?
The solution to 1/27+128+81-4/3+2197 is 2404 19/27

1/27+128+81-4/3+2197

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 1/27+128+81-4/3+2197 ?

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