What is -1/3000+242+6/125 ?

The solution to -1/3000+242+6/125 is 242 143/3000

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Popular Pre Algebra >

-1/3000+242+6/125

Solution

- \frac{1}{3000} + 242 + \frac{6}{125}

Solution

242 \frac{143}{3000}

Decimal

242.04766 \dots

Solution steps

- \frac{1}{3000} + 242 + \frac{6}{125}

Follow the PEMDAS order of operations

Add and subtract (left to right)

- \frac{1}{3000} + 242 = \frac{725999}{3000}

- \frac{1}{3000} + 242

Convert element to fraction:

242 = \frac{242 \cdot 3000}{3000}

= \frac{242 \cdot 3000}{3000} - \frac{1}{3000}

Since the denominators are equal, combine the fractions:

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

= \frac{242 \cdot 3000 - 1}{3000}

242 \cdot 3000 - 1 = 725999

242 \cdot 3000 - 1

Multiply the numbers:

242 \cdot 3000 = 726000

= 726000 - 1

Subtract the numbers:

726000 - 1 = 725999

= 725999

= \frac{725999}{3000}

= \frac{725999}{3000} + \frac{6}{125}

\frac{725999}{3000} + \frac{6}{125} = \frac{726143}{3000}

\frac{725999}{3000} + \frac{6}{125}

Least Common Multiplier of

3000, 125 : 3000

3000, 125

Least Common Multiplier (LCM)

Prime factorization of

3000 : 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5

3000

3000

divides by

23000 = 1500 \cdot 2

= 2 \cdot 1500

1500

divides by

21500 = 750 \cdot 2

= 2 \cdot 2 \cdot 750

750

divides by

2750 = 375 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 375

375

divides by

3375 = 125 \cdot 3

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 125

125

divides by

5125 = 25 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5

Prime factorization of

125 : 5 \cdot 5 \cdot 5

125

125

divides by

5125 = 25 \cdot 5

= 5 \cdot 25

25

divides by

525 = 5 \cdot 5

= 5 \cdot 5 \cdot 5

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

3000

125

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 = 3000

= 3000

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

3000

For

\frac{6}{125} :

multiply the denominator and numerator by

24

\frac{6}{125} = \frac{6 \cdot 24}{125 \cdot 24} = \frac{144}{3000}

= \frac{725999}{3000} + \frac{144}{3000}

Since the denominators are equal, combine the fractions:

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

= \frac{725999 + 144}{3000}

Add the numbers:

725999 + 144 = 726143

= \frac{726143}{3000}

= \frac{726143}{3000}

Convert improper fractions to mixed numbers:

\frac{726143}{3000} = 242 \frac{143}{3000}

\frac{726143}{3000} = 242

Remainder

143

\frac{726143}{3000}

Write the problem in long division format

3000 \overline{∣ 726143}

Divide

7261

3000

to get

2

Divide

7261

3000

to get

2

2 3000 \overline{∣ 726143}

Multiply the quotient digit

(2)

by the divisor

3000

2 3000 \overline{∣ 726143} \underline{6000}

Subtract

6000

from

7261

2 3000 \overline{∣ 726143} \underline{6000} 1261

Bring down the next number of the dividend

2 3000 \overline{∣ 726143} \underline{6000} 12614

2 3000 \overline{∣ 726143} \underline{6000} 12614

Divide

12614

3000

to get

4

Divide

12614

3000

to get

4

24 3000 \overline{∣ 726143} \underline{6000} 12614

Multiply the quotient digit

(4)

by the divisor

3000

24 3000 \overline{∣ 726143} \underline{6000} 12614 \underline{12000}

Subtract

12000

from

12614

24 3000 \overline{∣ 726143} \underline{6000} 12614 \underline{12000} 614

Bring down the next number of the dividend

24 3000 \overline{∣ 726143} \underline{6000} 12614 \underline{12000} 6143

24 3000 \overline{∣ 726143} \underline{6000} 12614 \underline{12000} 6143

Divide

6143

3000

to get

2

Divide

6143

3000

to get

2

242 3000 \overline{∣ 726143} \underline{6000} 12614 \underline{12000} 6143

Multiply the quotient digit

(2)

by the divisor

3000

242 3000 \overline{∣ 726143} \underline{6000} 12614 \underline{12000} 6143 \underline{6000}

Subtract

6000

from

6143

242 3000 \overline{∣ 726143} \underline{6000} 12614 \underline{12000} 6143 \underline{6000} 143

242 3000 \overline{∣ 726143} \underline{6000} 12614 \underline{12000} 6143 \underline{6000} 143

The solution for Long Division of

\frac{726143}{3000}

242

with remainder of

143

242 Remainder 143

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{726143}{3000} = 242 \frac{143}{3000}

= 242 \frac{143}{3000}

= 242 \frac{143}{3000}

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Frequently Asked Questions (FAQ)

What is -1/3000+242+6/125 ?
The solution to -1/3000+242+6/125 is 242 143/3000

-1/3000+242+6/125

Solution

Solution

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Frequently Asked Questions (FAQ)

What is -1/3000+242+6/125 ?

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