What is 3 1/3+5^2/3+3^5/6 ?

The solution to 3 1/3+5^2/3+3^5/6 is 52 1/6

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Popular Pre Algebra >

3 1/3+5^2/3+3^5/6

Solution

3 \frac{1}{3} + 5^{2} /3 + 3^{5} /6

Solution

52 \frac{1}{6}

Decimal

52.16666 \dots

Solution steps

3 \frac{1}{3} + 5^{2} /3 + 3^{5} /6

Convert mixed numbers to improper fractions:

3 \frac{1}{3} = \frac{10}{3}

3 \frac{1}{3}

Convert mixed numbers to improper fraction:

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

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

= \frac{10}{3}

= \frac{10}{3} + 5^{2} /3 + 3^{5} /6

Follow the PEMDAS order of operations

Calculate exponents

5^{2} : 25

5^{2}

5^{2} = 25

= 25

= \frac{10}{3} + 25/3 + 3^{5} /6

Calculate exponents

3^{5} : 243

3^{5}

3^{5} = 243

= 243

= \frac{10}{3} + 25/3 + 243/6

Multiply and divide (left to right)

25/3 : \frac{25}{3}

25/3

25/3 = \frac{25}{3}

= \frac{25}{3}

= \frac{10}{3} + \frac{25}{3} + 243/6

Multiply and divide (left to right)

243/6 : \frac{243}{6}

243/6

243/6 = \frac{243}{6}

= \frac{243}{6}

= \frac{10}{3} + \frac{25}{3} + \frac{243}{6}

Add and subtract (left to right)

\frac{10}{3} + \frac{25}{3} + \frac{243}{6} : \frac{313}{6}

\frac{10}{3} + \frac{25}{3} + \frac{243}{6}

\frac{10}{3} + \frac{25}{3} = \frac{35}{3}

\frac{10}{3} + \frac{25}{3}

Apply rule

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

= \frac{10 + 25}{3}

Add the numbers:

10 + 25 = 35

= \frac{35}{3}

= \frac{35}{3} + \frac{243}{6}

\frac{35}{3} + \frac{243}{6} = \frac{313}{6}

\frac{35}{3} + \frac{243}{6}

Cancel

\frac{243}{6} : \frac{81}{2}

\frac{243}{6}

Cancel the common factor:

3

= \frac{81}{2}

= \frac{35}{3} + \frac{81}{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{35}{3} :

multiply the denominator and numerator by

2

\frac{35}{3} = \frac{35 \cdot 2}{3 \cdot 2} = \frac{70}{6}

For

\frac{81}{2} :

multiply the denominator and numerator by

3

\frac{81}{2} = \frac{81 \cdot 3}{2 \cdot 3} = \frac{243}{6}

= \frac{70}{6} + \frac{243}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{70 + 243}{6}

Add the numbers:

70 + 243 = 313

= \frac{313}{6}

= \frac{313}{6}

= \frac{313}{6}

Convert improper fractions to mixed numbers:

\frac{313}{6} = 52 \frac{1}{6}

\frac{313}{6} = 52

Remainder

1

\frac{313}{6}

Write the problem in long division format

6 \overline{∣ 313}

Divide

31

6

to get

5

Divide

31

6

to get

5

5 6 \overline{∣ 313}

Multiply the quotient digit

(5)

by the divisor

6

5 6 \overline{∣ 313} \underline{30}

Subtract

30

from

31

5 6 \overline{∣ 313} \underline{30} 1

Bring down the next number of the dividend

5 6 \overline{∣ 313} \underline{30} 13

5 6 \overline{∣ 313} \underline{30} 13

Divide

13

6

to get

2

Divide

13

6

to get

2

52 6 \overline{∣ 313} \underline{30} 13

Multiply the quotient digit

(2)

by the divisor

6

52 6 \overline{∣ 313} \underline{30} 13 \underline{12}

Subtract

12

from

13

52 6 \overline{∣ 313} \underline{30} 13 \underline{12} 1

52 6 \overline{∣ 313} \underline{30} 13 \underline{12} 1

The solution for Long Division of

\frac{313}{6}

52

with remainder of

1

52 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{313}{6} = 52 \frac{1}{6}

= 52 \frac{1}{6}

= 52 \frac{1}{6}

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What is 3 1/3+5^2/3+3^5/6 ?
The solution to 3 1/3+5^2/3+3^5/6 is 52 1/6

3 1/3+5^2/3+3^5/6

Solution

Solution

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What is 3 1/3+5^2/3+3^5/6 ?

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