What is 2+(-2/315)-2/5 ?

The solution to 2+(-2/315)-2/5 is 1 187/315

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Popular >

2+(-2/315)-2/5

Solution

2 + (- \frac{2}{315}) - \frac{2}{5}

Solution

1 \frac{187}{315}

Solution steps

2 + (- \frac{2}{315}) - \frac{2}{5}

Follow the PEMDAS order of operations

Add and subtract (left to right)

Apply rule

+ (- a) = - a

+ (- \frac{2}{315}) = - \frac{2}{315}

= 2 - \frac{2}{315} - \frac{2}{5}

2 - \frac{2}{315} = \frac{628}{315}

2 - \frac{2}{315}

Convert element to fraction:

2 = \frac{2 \cdot 315}{315}

= \frac{2 \cdot 315}{315} - \frac{2}{315}

Since the denominators are equal, combine the fractions:

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

= \frac{2 \cdot 315 - 2}{315}

2 \cdot 315 - 2 = 628

2 \cdot 315 - 2

Multiply the numbers:

2 \cdot 315 = 630

= 630 - 2

Subtract the numbers:

630 - 2 = 628

= 628

= \frac{628}{315}

= \frac{628}{315} - \frac{2}{5}

\frac{628}{315} - \frac{2}{5} = \frac{502}{315}

\frac{628}{315} - \frac{2}{5}

Least Common Multiplier of

315, 5 : 315

315, 5

Least Common Multiplier (LCM)

Prime factorization of

315 : 3 \cdot 3 \cdot 5 \cdot 7

315

315

divides by

3315 = 105 \cdot 3

= 3 \cdot 105

105

divides by

3105 = 35 \cdot 3

= 3 \cdot 3 \cdot 35

35

divides by

535 = 7 \cdot 5

= 3 \cdot 3 \cdot 5 \cdot 7

3, 5, 7

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 3 \cdot 5 \cdot 7

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

315

5

= 3 \cdot 3 \cdot 5 \cdot 7

Multiply the numbers:

3 \cdot 3 \cdot 5 \cdot 7 = 315

= 315

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

315

For

\frac{2}{5} :

multiply the denominator and numerator by

63

\frac{2}{5} = \frac{2 \cdot 63}{5 \cdot 63} = \frac{126}{315}

= \frac{628}{315} - \frac{126}{315}

Since the denominators are equal, combine the fractions:

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

= \frac{628 - 126}{315}

Subtract the numbers:

628 - 126 = 502

= \frac{502}{315}

= \frac{502}{315}

Convert improper fractions to mixed numbers:

\frac{502}{315} = 1 \frac{187}{315}

\frac{502}{315} = 1

Remainder

187

\frac{502}{315}

Write the problem in long division format

315 \overline{∣ 502}

Divide

502

315

to get

1

Divide

502

315

to get

1

1 315 \overline{∣ 502}

Multiply the quotient digit

(1)

by the divisor

315

1 315 \overline{∣ 502} \underline{315}

Subtract

315

from

502

1 315 \overline{∣ 502} \underline{315} 187

1 315 \overline{∣ 502} \underline{315} 187

The solution for Long Division of

\frac{502}{315}

1

with remainder of

187

1 Remainder 187

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{502}{315} = 1 \frac{187}{315}

= 1 \frac{187}{315}

= 1 \frac{187}{315}

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48 \div 6 \times 2 - 4

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Frequently Asked Questions (FAQ)

What is 2+(-2/315)-2/5 ?
The solution to 2+(-2/315)-2/5 is 1 187/315