What is 64-128/3+64/5 ?

The solution to 64-128/3+64/5 is 34 2/15

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Popular >

64-128/3+64/5

Solution

64 - \frac{128}{3} + \frac{64}{5}

Solution

34 \frac{2}{15}

Solution steps

64 - \frac{128}{3} + \frac{64}{5}

Follow the PEMDAS order of operations

Add and subtract (left to right)

64 - \frac{128}{3} = \frac{64}{3}

64 - \frac{128}{3}

Convert element to fraction:

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

= \frac{64 \cdot 3}{3} - \frac{128}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{64 \cdot 3 - 128}{3}

64 \cdot 3 - 128 = 64

64 \cdot 3 - 128

Multiply the numbers:

64 \cdot 3 = 192

= 192 - 128

Subtract the numbers:

192 - 128 = 64

= 64

= \frac{64}{3}

= \frac{64}{3} + \frac{64}{5}

\frac{64}{3} + \frac{64}{5} = \frac{512}{15}

\frac{64}{3} + \frac{64}{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{64}{3} :

multiply the denominator and numerator by

5

\frac{64}{3} = \frac{64 \cdot 5}{3 \cdot 5} = \frac{320}{15}

For

\frac{64}{5} :

multiply the denominator and numerator by

3

\frac{64}{5} = \frac{64 \cdot 3}{5 \cdot 3} = \frac{192}{15}

= \frac{320}{15} + \frac{192}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{320 + 192}{15}

Add the numbers:

320 + 192 = 512

= \frac{512}{15}

= \frac{512}{15}

Convert improper fractions to mixed numbers:

\frac{512}{15} = 34 \frac{2}{15}

\frac{512}{15} = 34

Remainder

2

\frac{512}{15}

Write the problem in long division format

15 \overline{∣ 512}

Divide

51

15

to get

3

Divide

51

15

to get

3

3 15 \overline{∣ 512}

Multiply the quotient digit

(3)

by the divisor

15

3 15 \overline{∣ 512} \underline{45}

Subtract

45

from

51

3 15 \overline{∣ 512} \underline{45} 6

Bring down the next number of the dividend

3 15 \overline{∣ 512} \underline{45} 62

3 15 \overline{∣ 512} \underline{45} 62

Divide

62

15

to get

4

Divide

62

15

to get

4

34 15 \overline{∣ 512} \underline{45} 62

Multiply the quotient digit

(4)

by the divisor

15

34 15 \overline{∣ 512} \underline{45} 62 \underline{60}

Subtract

60

from

62

34 15 \overline{∣ 512} \underline{45} 62 \underline{60} 2

34 15 \overline{∣ 512} \underline{45} 62 \underline{60} 2

The solution for Long Division of

\frac{512}{15}

34

with remainder of

2

34 Remainder 2

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{512}{15} = 34 \frac{2}{15}

= 34 \frac{2}{15}

= 34 \frac{2}{15}

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Frequently Asked Questions (FAQ)

What is 64-128/3+64/5 ?
The solution to 64-128/3+64/5 is 34 2/15