- 340/211 - 204/331,204 - 335/5 - 249/317,211 + 341/10 + 215/300,208 + 302,218/298,224 + 315/14 - 242/344 - 201/328 - 186/349 = ? Adding ordinary (common) fractions, online calculator, addition operation explained step by step. The answer, written in four ways. As a negative improper fraction (the numerator >= the denominator). As a mixed number. As a decimal number. As a percentage.

- 340/211 - 204/331,204 - 335/5 - 249/317,211 + 341/10 + 215/300,208 + 302,218/298,224 + 315/14 - 242/344 - 201/328 - 186/349 = ?

Simplify the operation

Reduce (simplify) the fractions to their lowest terms equivalents:

To fully reduce a fraction, to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.


* Why do we reduce (simplify) the fractions?


By reducing the values of the numerators and denominators of fractions, further calculations with these fractions become easier to do.


A fully reduced (simplified) fraction is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.

* * *

The fraction: - 340/211 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
340 = 22 × 5 × 17
211 is a prime number
GCF (22 × 5 × 17; 211) = 1


The fraction: - 204/331,204 = - (22 × 3 × 17)/(22 × 31 × 2,671) = - ((22 × 3 × 17) ÷ 22 )/((22 × 31 × 2,671) ÷ 22 ) = - 51/82,801


The fraction: - 335/5 = - (5 × 67)/5 = - ((5 × 67) ÷ 5)/(5 ÷ 5) = - 67/1 = - 67


The fraction: - 249/317,211 = - (3 × 83)/(3 × 43 × 2,459) = - ((3 × 83) ÷ 3)/((3 × 43 × 2,459) ÷ 3) = - 83/105,737


The fraction: 341/10 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
341 = 11 × 31
10 = 2 × 5
GCF (11 × 31; 2 × 5) = 1


The fraction: 215/300,208 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
215 = 5 × 43
300,208 = 24 × 29 × 647
GCF (5 × 43; 24 × 29 × 647) = 1


The fraction: 302,218/298,224 = (2 × 7 × 21,587)/(24 × 32 × 19 × 109) = ((2 × 7 × 21,587) ÷ 2)/((24 × 32 × 19 × 109) ÷ 2) = 151,109/149,112


The fraction: 315/14 = (32 × 5 × 7)/(2 × 7) = ((32 × 5 × 7) ÷ 7)/((2 × 7) ÷ 7) = 45/2


The fraction: - 242/344 = - (2 × 112)/(23 × 43) = - ((2 × 112) ÷ 2)/((23 × 43) ÷ 2) = - 121/172


The fraction: - 201/328 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
201 = 3 × 67
328 = 23 × 41
GCF (3 × 67; 23 × 41) = 1


The fraction: - 186/349 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
186 = 2 × 3 × 31
349 is a prime number
GCF (2 × 3 × 31; 349) = 1



Rewrite the equivalent simplified operation:

- 340/211 - 204/331,204 - 335/5 - 249/317,211 + 341/10 + 215/300,208 + 302,218/298,224 + 315/14 - 242/344 - 201/328 - 186/349 =


- 340/211 - 51/82,801 - 67 - 83/105,737 + 341/10 + 215/300,208 + 151,109/149,112 + 45/2 - 121/172 - 201/328 - 186/349 =


- 67 - 340/211 - 51/82,801 - 83/105,737 + 341/10 + 215/300,208 + 151,109/149,112 + 45/2 - 121/172 - 201/328 - 186/349

Rewrite the improper fractions:

An improper fraction: the value of the numerator is larger than or equal to the value of the denominator.

A proper fraction: the value of the numerator is smaller than the value of the denominator.


Each improper fraction will be rewritten as a whole number and a proper fraction, both having the same sign: divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below.


Why do we rewrite the improper fractions?

By reducing the value of the numerator of a fraction the calculations are getting easier to perform.

* * *

The fraction: - 340/211


- 340 ÷ 211 = - 1 and the remainder = - 129 ⇒ - 340 = - 1 × 211 - 129


- 340/211 = ( - 1 × 211 - 129)/211 = ( - 1 × 211)/211 - 129/211 = - 1 - 129/211


The fraction: 341/10


341 ÷ 10 = 34 and the remainder = 1 ⇒ 341 = 34 × 10 + 1


341/10 = (34 × 10 + 1)/10 = (34 × 10)/10 + 1/10 = 34 + 1/10


The fraction: 151,109/149,112


151,109 ÷ 149,112 = 1 and the remainder = 1,997 ⇒ 151,109 = 1 × 149,112 + 1,997


151,109/149,112 = (1 × 149,112 + 1,997)/149,112 = (1 × 149,112)/149,112 + 1,997/149,112 = 1 + 1,997/149,112


The fraction: 45/2


45 ÷ 2 = 22 and the remainder = 1 ⇒ 45 = 22 × 2 + 1


45/2 = (22 × 2 + 1)/2 = (22 × 2)/2 + 1/2 = 22 + 1/2



Rewrite the equivalent simplified operation:

- 67 - 340/211 - 51/82,801 - 83/105,737 + 341/10 + 215/300,208 + 151,109/149,112 + 45/2 - 121/172 - 201/328 - 186/349 =


- 67 - 1 - 129/211 - 51/82,801 - 83/105,737 + 34 + 1/10 + 215/300,208 + 1 + 1,997/149,112 + 22 + 1/2 - 121/172 - 201/328 - 186/349 =


- 11 - 129/211 - 51/82,801 - 83/105,737 + 1/10 + 215/300,208 + 1,997/149,112 + 1/2 - 121/172 - 201/328 - 186/349

Perform the operation of calculating the fractions.

To add or subtract fractions we need them to have equal denominators (the same common denominator).

To calculate the fractions' operation we have to:


1) find their common denominator


2) then calculate the expanding number of each fraction


3) then make their denominators the same by expanding the fractions to equivalent forms - which all have equal denominators (the same denominator)


* The common denominator is nothing else than the least common multiple (LCM) of the denominators of the fractions.


The LCM will be the common denominator of the fractions that we work with.


1) Find the common denominator
Calculate the LCM of the denominators:

The prime factorization of the denominators:


211 is a prime number


82,801 = 31 × 2,671


105,737 = 43 × 2,459


10 = 2 × 5


300,208 = 24 × 29 × 647


149,112 = 23 × 32 × 19 × 109


2 is a prime number


172 = 22 × 43


328 = 23 × 41


349 is a prime number


Multiply all the unique prime factors: if there are repeating prime factors we only take them once, and only the ones having the highest exponent (the highest powers).


LCM (211; 82,801; 105,737; 10; 300,208; 149,112; 2; 172; 328; 349) = 24 × 32 × 5 × 19 × 29 × 31 × 41 × 43 × 109 × 211 × 349 × 647 × 2,459 × 2,671 = 739,552,788,705,018,454,169,687,280



2) Calculate the expanding number of each fraction:

Divide the LCM by the denominator of each fraction.


- 129/211 : 739,552,788,705,018,454,169,687,280 ÷ 211 = (24 × 32 × 5 × 19 × 29 × 31 × 41 × 43 × 109 × 211 × 349 × 647 × 2,459 × 2,671) ÷ 211 = 3,504,989,519,928,997,413,126,480


- 51/82,801 : 739,552,788,705,018,454,169,687,280 ÷ 82,801 = (24 × 32 × 5 × 19 × 29 × 31 × 41 × 43 × 109 × 211 × 349 × 647 × 2,459 × 2,671) ÷ (31 × 2,671) = 8,931,689,094,395,218,103,280


- 83/105,737 : 739,552,788,705,018,454,169,687,280 ÷ 105,737 = (24 × 32 × 5 × 19 × 29 × 31 × 41 × 43 × 109 × 211 × 349 × 647 × 2,459 × 2,671) ÷ (43 × 2,459) = 6,994,266,800,694,349,699,440


1/10 : 739,552,788,705,018,454,169,687,280 ÷ 10 = (24 × 32 × 5 × 19 × 29 × 31 × 41 × 43 × 109 × 211 × 349 × 647 × 2,459 × 2,671) ÷ (2 × 5) = 73,955,278,870,501,845,416,968,728


215/300,208 : 739,552,788,705,018,454,169,687,280 ÷ 300,208 = (24 × 32 × 5 × 19 × 29 × 31 × 41 × 43 × 109 × 211 × 349 × 647 × 2,459 × 2,671) ÷ (24 × 29 × 647) = 2,463,467,957,899,251,366,285


1,997/149,112 : 739,552,788,705,018,454,169,687,280 ÷ 149,112 = (24 × 32 × 5 × 19 × 29 × 31 × 41 × 43 × 109 × 211 × 349 × 647 × 2,459 × 2,671) ÷ (23 × 32 × 19 × 109) = 4,959,713,428,195,037,650,690


1/2 : 739,552,788,705,018,454,169,687,280 ÷ 2 = (24 × 32 × 5 × 19 × 29 × 31 × 41 × 43 × 109 × 211 × 349 × 647 × 2,459 × 2,671) ÷ 2 = 369,776,394,352,509,227,084,843,640


- 121/172 : 739,552,788,705,018,454,169,687,280 ÷ 172 = (24 × 32 × 5 × 19 × 29 × 31 × 41 × 43 × 109 × 211 × 349 × 647 × 2,459 × 2,671) ÷ (22 × 43) = 4,299,725,515,726,851,477,730,740


- 201/328 : 739,552,788,705,018,454,169,687,280 ÷ 328 = (24 × 32 × 5 × 19 × 29 × 31 × 41 × 43 × 109 × 211 × 349 × 647 × 2,459 × 2,671) ÷ (23 × 41) = 2,254,734,111,905,544,067,590,510


- 186/349 : 739,552,788,705,018,454,169,687,280 ÷ 349 = (24 × 32 × 5 × 19 × 29 × 31 × 41 × 43 × 109 × 211 × 349 × 647 × 2,459 × 2,671) ÷ 349 = 2,119,062,431,819,537,117,964,720


3) Make the fractions' denominators the same:

Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated at the step 2, above. This way all the fractions will have the same denominator.


Then keep the common denominator and work only with the numerators of the fractions.


- 11 - 129/211 - 51/82,801 - 83/105,737 + 1/10 + 215/300,208 + 1,997/149,112 + 1/2 - 121/172 - 201/328 - 186/349 =


- 11 - (3,504,989,519,928,997,413,126,480 × 129)/(3,504,989,519,928,997,413,126,480 × 211) - (8,931,689,094,395,218,103,280 × 51)/(8,931,689,094,395,218,103,280 × 82,801) - (6,994,266,800,694,349,699,440 × 83)/(6,994,266,800,694,349,699,440 × 105,737) + (73,955,278,870,501,845,416,968,728 × 1)/(73,955,278,870,501,845,416,968,728 × 10) + (2,463,467,957,899,251,366,285 × 215)/(2,463,467,957,899,251,366,285 × 300,208) + (4,959,713,428,195,037,650,690 × 1,997)/(4,959,713,428,195,037,650,690 × 149,112) + (369,776,394,352,509,227,084,843,640 × 1)/(369,776,394,352,509,227,084,843,640 × 2) - (4,299,725,515,726,851,477,730,740 × 121)/(4,299,725,515,726,851,477,730,740 × 172) - (2,254,734,111,905,544,067,590,510 × 201)/(2,254,734,111,905,544,067,590,510 × 328) - (2,119,062,431,819,537,117,964,720 × 186)/(2,119,062,431,819,537,117,964,720 × 349) =


- 11 - 452,143,648,070,840,666,293,315,920/739,552,788,705,018,454,169,687,280 - 455,516,143,814,156,123,267,280/739,552,788,705,018,454,169,687,280 - 580,524,144,457,631,025,053,520/739,552,788,705,018,454,169,687,280 + 73,955,278,870,501,845,416,968,728/739,552,788,705,018,454,169,687,280 + 529,645,610,948,339,043,751,275/739,552,788,705,018,454,169,687,280 + 9,904,547,716,105,490,188,427,930/739,552,788,705,018,454,169,687,280 + 369,776,394,352,509,227,084,843,640/739,552,788,705,018,454,169,687,280 - 520,266,787,402,949,028,805,419,540/739,552,788,705,018,454,169,687,280 - 453,201,556,493,014,357,585,692,510/739,552,788,705,018,454,169,687,280 - 394,145,612,318,433,903,941,437,920/739,552,788,705,018,454,169,687,280 =


- 11 + ( - 452,143,648,070,840,666,293,315,920 - 455,516,143,814,156,123,267,280 - 580,524,144,457,631,025,053,520 + 73,955,278,870,501,845,416,968,728 + 529,645,610,948,339,043,751,275 + 9,904,547,716,105,490,188,427,930 + 369,776,394,352,509,227,084,843,640 - 520,266,787,402,949,028,805,419,540 - 453,201,556,493,014,357,585,692,510 - 394,145,612,318,433,903,941,437,920)/739,552,788,705,018,454,169,687,280 =


- 11 - 1,366,627,778,023,444,842,040,195,117/739,552,788,705,018,454,169,687,280


Fully reduce (simplify) the fraction to its lowest terms equivalent:

To fully reduce a fraction, to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.


A fully reduced (simplified) fraction is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.


Calculate the greatest common factor, GCF,
of the numerator and denominator of the fraction:

The prime factorizations of the numerator and denominator:


1,366,627,778,023,444,842,040,195,117 = 239 × 5 × 17 × 29,245,664,080,189


739,552,788,705,018,454,169,687,280 = 237 × 5 × 13 × 887 × 178,907 × 521,669


Multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).


GCF (1,366,627,778,023,444,842,040,195,117; 739,552,788,705,018,454,169,687,280) = GCF (239 × 5 × 17 × 29,245,664,080,189; 237 × 5 × 13 × 887 × 178,907 × 521,669) = 237 × 5


The fraction can be reduced (simplified):

Divide both the numerator and denominator by their greatest common factor, GCF.


- 1,366,627,778,023,444,842,040,195,117/739,552,788,705,018,454,169,687,280 =


- (239 × 5 × 17 × 29,245,664,080,189)/(237 × 5 × 13 × 887 × 178,907 × 521,669) =


- ((239 × 5 × 17 × 29,245,664,080,189) ÷ (237 × 5))/((237 × 5 × 13 × 887 × 178,907 × 521,669) ÷ (237 × 5)) =


- (22 × 17 × 29,245,664,080,189)/(13 × 887 × 178,907 × 521,669) =


- 1,988,705,157,452,852/1,076,190,948,813,773



Rewrite the equivalent simplified operation:

- 11 - 1,366,627,778,023,444,842,040,195,117/739,552,788,705,018,454,169,687,280 =


- 11 - 1,988,705,157,452,852/1,076,190,948,813,773


Rewrite the intermediate result

As a negative improper fraction:
(the numerator >= the denominator)

An improper fraction: the value of the numerator is larger than or equal to the value of the denominator.


- 11 - 1,988,705,157,452,852/1,076,190,948,813,773 =


( - 11 × 1,076,190,948,813,773)/1,076,190,948,813,773 - 1,988,705,157,452,852/1,076,190,948,813,773 =


( - 11 × 1,076,190,948,813,773 - 1,988,705,157,452,852)/1,076,190,948,813,773 =


- 13,826,805,594,404,355/1,076,190,948,813,773

As a mixed number (also called a mixed fraction):

A mixed number: a whole number and a proper fraction, both having the same sign.


A proper fraction: the value of the numerator is smaller than the value of the denominator.


Divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below:


- 13,826,805,594,404,355 ÷ 1,076,190,948,813,773 = - 12 and the remainder = - 9.1251420863908E+14 ⇒


- 13,826,805,594,404,355 = - 12 × 1,076,190,948,813,773 - 9.1251420863908E+14 ⇒


- 13,826,805,594,404,355/1,076,190,948,813,773 =


( - 12 × 1,076,190,948,813,773 - 9.1251420863908E+14)/1,076,190,948,813,773 =


( - 12 × 1,076,190,948,813,773)/1,076,190,948,813,773 - 9.1251420863908E+14/1,076,190,948,813,773 =


- 12 - 9.1251420863908E+14/1,076,190,948,813,773 =


- 12 9.1251420863908E+14/1,076,190,948,813,773

As a decimal number:

Simply divide the numerator by the denominator, without a remainder, as shown below:


- 12 - 9.1251420863908E+14/1,076,190,948,813,773 =


- 12 - 9.1251420863908E+14 ÷ 1,076,190,948,813,773 ≈


- 12.847911060435 ≈


- 12.85

As a percentage:

A percentage value p% is equal to the fraction: p/100, for any decimal number p. So, we need to change the form of the number calculated above, to show a denominator of 100.


To do that, multiply the number by the fraction 100/100.


The value of the fraction 100/100 = 1, so by multiplying the number by this fraction the result is not changing, only the form.


- 12.847911060435 =


- 12.847911060435 × 100/100 =


( - 12.847911060435 × 100)/100 =


- 1,284.791106043485/100


- 1,284.791106043485% ≈


- 1,284.79%



The final answer:
:: written in four ways ::

As a negative improper fraction:
(the numerator >= the denominator)
- 340/211 - 204/331,204 - 335/5 - 249/317,211 + 341/10 + 215/300,208 + 302,218/298,224 + 315/14 - 242/344 - 201/328 - 186/349 = - 13,826,805,594,404,355/1,076,190,948,813,773

As a mixed number (also called a mixed fraction):
- 340/211 - 204/331,204 - 335/5 - 249/317,211 + 341/10 + 215/300,208 + 302,218/298,224 + 315/14 - 242/344 - 201/328 - 186/349 = - 12 9.1251420863908E+14/1,076,190,948,813,773

As a decimal number:
- 340/211 - 204/331,204 - 335/5 - 249/317,211 + 341/10 + 215/300,208 + 302,218/298,224 + 315/14 - 242/344 - 201/328 - 186/349 ≈ - 12.85

As a percentage:
- 340/211 - 204/331,204 - 335/5 - 249/317,211 + 341/10 + 215/300,208 + 302,218/298,224 + 315/14 - 242/344 - 201/328 - 186/349 ≈ - 1,284.79%

How are the numbers written: comma ',' used as a thousands separator; point '.' as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The symbols used: '/' fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.

Other similar operations:

How to add the common ordinary fractions:
- 348/220 + 206/331,213 - 347/10 + 255/317,218 + 346/14 - 223/300,217 - 302,221/298,233 + 322/20 + 250/355 - 207/334 + 195/361

Add common ordinary fractions, online calculator:

Fractions additions: the latest fractions added by the users

How to: Adding ordinary (simple, common) fractions. Steps.

There are two cases regarding the denominators when we add ordinary fractions:

  • A. the fractions have like denominators;
  • B. the fractions have unlike denominators.

A. How to add ordinary fractions that have like denominators?

  • Simply add the numerators of the fractions.
  • The denominator of the resulting fraction will be the common denominator of the fractions.
  • Reduce the resulting fraction.

An example of adding ordinary fractions that have like denominators, with explanations

B. To add fractions with different denominators (unlike denominators), build up the fractions to the same denominator. How is it done?

  • 1. Reduce the fractions to the lowest terms (simplifying).

  • 2. Calculate the least common multiple, LCM, of all the fractions' new denominators:

    • LCM is going to be the common denominator of the added fractions.
    • Factor all the new denominators of the reduced fractions (run the prime factorization).
    • The least common multiple, LCM, is the product of all the unique prime factors of the denominators, taken by the largest exponents.
    • Calculate LCM, the least common multiple of numbers.

  • 3. Calculate each fraction's expanding number:

    • The expanding number is the non-zero number that will be used to multiply both the numerator and the denominator of each fraction, in order to build all the fractions up to the same common denominator.
    • Divide the least common multiple, LCM, calculated above, by each fraction's denominator, in order to calculate each fraction's expanding number.
  • 4. Expand each fraction:

    • Multiply each fraction's both numerator and denominator by expanding number.
    • At this point, fractions are built up to the same denominator.
  • 5. Add the fractions:

    • In order to add all the fractions simply add all the fractions' numerators.
    • The end fraction will have as a denominator the least common multiple, LCM, calculated above.
  • 6. Reduce the end fraction to the lowest terms, if needed.


Read the rest of this article, here > How to add ordinary (common) fractions

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