What is 240-1/5-3/8 ?

The solution to 240-1/5-3/8 is 239 17/40

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Popular Pre Algebra >

240-1/5-3/8

Solution

240 - \frac{1}{5} - \frac{3}{8}

Solution

239 \frac{17}{40}

Decimal

239.425

Solution steps

240 - \frac{1}{5} - \frac{3}{8}

Follow the PEMDAS order of operations

Add and subtract (left to right)

240 - \frac{1}{5} = \frac{1199}{5}

240 - \frac{1}{5}

Convert element to fraction:

240 = \frac{240 \cdot 5}{5}

= \frac{240 \cdot 5}{5} - \frac{1}{5}

Since the denominators are equal, combine the fractions:

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

= \frac{240 \cdot 5 - 1}{5}

240 \cdot 5 - 1 = 1199

240 \cdot 5 - 1

Multiply the numbers:

240 \cdot 5 = 1200

= 1200 - 1

Subtract the numbers:

1200 - 1 = 1199

= 1199

= \frac{1199}{5}

= \frac{1199}{5} - \frac{3}{8}

\frac{1199}{5} - \frac{3}{8} = \frac{9577}{40}

\frac{1199}{5} - \frac{3}{8}

Least Common Multiplier of

5, 8 : 40

5, 8

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

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

5

8

= 5 \cdot 2 \cdot 2 \cdot 2

Multiply the numbers:

5 \cdot 2 \cdot 2 \cdot 2 = 40

= 40

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

40

For

\frac{1199}{5} :

multiply the denominator and numerator by

8

\frac{1199}{5} = \frac{1199 \cdot 8}{5 \cdot 8} = \frac{9592}{40}

For

\frac{3}{8} :

multiply the denominator and numerator by

5

\frac{3}{8} = \frac{3 \cdot 5}{8 \cdot 5} = \frac{15}{40}

= \frac{9592}{40} - \frac{15}{40}

Since the denominators are equal, combine the fractions:

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

= \frac{9592 - 15}{40}

Subtract the numbers:

9592 - 15 = 9577

= \frac{9577}{40}

= \frac{9577}{40}

Convert improper fractions to mixed numbers:

\frac{9577}{40} = 239 \frac{17}{40}

\frac{9577}{40} = 239

Remainder

17

\frac{9577}{40}

Write the problem in long division format

40 \overline{∣ 9577}

Divide

95

40

to get

2

Divide

95

40

to get

2

2 40 \overline{∣ 9577}

Multiply the quotient digit

(2)

by the divisor

40

2 40 \overline{∣ 9577} \underline{80}

Subtract

80

from

95

2 40 \overline{∣ 9577} \underline{80} 15

Bring down the next number of the dividend

2 40 \overline{∣ 9577} \underline{80} 157

2 40 \overline{∣ 9577} \underline{80} 157

Divide

157

40

to get

3

Divide

157

40

to get

3

23 40 \overline{∣ 9577} \underline{80} 157

Multiply the quotient digit

(3)

by the divisor

40

23 40 \overline{∣ 9577} \underline{80} 157 \underline{120}

Subtract

120

from

157

23 40 \overline{∣ 9577} \underline{80} 157 \underline{120} 37

Bring down the next number of the dividend

23 40 \overline{∣ 9577} \underline{80} 157 \underline{120} 377

23 40 \overline{∣ 9577} \underline{80} 157 \underline{120} 377

Divide

377

40

to get

9

Divide

377

40

to get

9

239 40 \overline{∣ 9577} \underline{80} 157 \underline{120} 377

Multiply the quotient digit

(9)

by the divisor

40

239 40 \overline{∣ 9577} \underline{80} 157 \underline{120} 377 \underline{360}

Subtract

360

from

377

239 40 \overline{∣ 9577} \underline{80} 157 \underline{120} 377 \underline{360} 17

239 40 \overline{∣ 9577} \underline{80} 157 \underline{120} 377 \underline{360} 17

The solution for Long Division of

\frac{9577}{40}

239

with remainder of

17

239 Remainder 17

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{9577}{40} = 239 \frac{17}{40}

= 239 \frac{17}{40}

= 239 \frac{17}{40}

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What is 240-1/5-3/8 ?
The solution to 240-1/5-3/8 is 239 17/40

240-1/5-3/8

Solution

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What is 240-1/5-3/8 ?

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