What is 32-64/3+32/5 ?

The solution to 32-64/3+32/5 is 17 1/15

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Popular Pre Algebra >

32-64/3+32/5

Solution

32 - \frac{64}{3} + \frac{32}{5}

Solution

17 \frac{1}{15}

Decimal

17.06666 \dots

Solution steps

32 - \frac{64}{3} + \frac{32}{5}

Follow the PEMDAS order of operations

Add and subtract (left to right)

32 - \frac{64}{3} = \frac{32}{3}

32 - \frac{64}{3}

Convert element to fraction:

32 = \frac{32 \cdot 3}{3}

= \frac{32 \cdot 3}{3} - \frac{64}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{32 \cdot 3 - 64}{3}

32 \cdot 3 - 64 = 32

32 \cdot 3 - 64

Multiply the numbers:

32 \cdot 3 = 96

= 96 - 64

Subtract the numbers:

96 - 64 = 32

= 32

= \frac{32}{3}

= \frac{32}{3} + \frac{32}{5}

\frac{32}{3} + \frac{32}{5} = \frac{256}{15}

\frac{32}{3} + \frac{32}{5}

Least Common Multiplier of

3, 5 : 15

3, 5

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Multiply each factor the greatest number of times it occurs in either

3

5

= 3 \cdot 5

Multiply the numbers:

3 \cdot 5 = 15

= 15

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

15

For

\frac{32}{3} :

multiply the denominator and numerator by

5

\frac{32}{3} = \frac{32 \cdot 5}{3 \cdot 5} = \frac{160}{15}

For

\frac{32}{5} :

multiply the denominator and numerator by

3

\frac{32}{5} = \frac{32 \cdot 3}{5 \cdot 3} = \frac{96}{15}

= \frac{160}{15} + \frac{96}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{160 + 96}{15}

Add the numbers:

160 + 96 = 256

= \frac{256}{15}

= \frac{256}{15}

Convert improper fractions to mixed numbers:

\frac{256}{15} = 17 \frac{1}{15}

\frac{256}{15} = 17

Remainder

1

\frac{256}{15}

Write the problem in long division format

15 \overline{∣ 256}

Divide

25

15

to get

1

Divide

25

15

to get

1

1 15 \overline{∣ 256}

Multiply the quotient digit

(1)

by the divisor

15

1 15 \overline{∣ 256} \underline{15}

Subtract

15

from

25

1 15 \overline{∣ 256} \underline{15} 10

Bring down the next number of the dividend

1 15 \overline{∣ 256} \underline{15} 106

1 15 \overline{∣ 256} \underline{15} 106

Divide

106

15

to get

7

Divide

106

15

to get

7

17 15 \overline{∣ 256} \underline{15} 106

Multiply the quotient digit

(7)

by the divisor

15

17 15 \overline{∣ 256} \underline{15} 106 \underline{105}

Subtract

105

from

106

17 15 \overline{∣ 256} \underline{15} 106 \underline{105} 1

17 15 \overline{∣ 256} \underline{15} 106 \underline{105} 1

The solution for Long Division of

\frac{256}{15}

17

with remainder of

1

17 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{256}{15} = 17 \frac{1}{15}

= 17 \frac{1}{15}

= 17 \frac{1}{15}

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Frequently Asked Questions (FAQ)

What is 32-64/3+32/5 ?
The solution to 32-64/3+32/5 is 17 1/15

32-64/3+32/5

Solution

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What is 32-64/3+32/5 ?

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