- 377/259 - 245/448 + 259/340,264 - 426/29,257 + 343,301/15 - 406/48 + 265/436 + 283/407 - 298/367,306 - 407/35 + 250/327,274 = ? Adding ordinary (common) fractions, online calculator, addition operation explained step by step. The answer, written in four ways. As a positive improper fraction (the numerator >= the denominator). As a mixed number. As a decimal number. As a percentage.
- 377/259 - 245/448 + 259/340,264 - 426/29,257 + 343,301/15 - 406/48 + 265/436 + 283/407 - 298/367,306 - 407/35 + 250/327,274 = ?
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: - 377/259 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
377 = 13 × 29
259 = 7 × 37
GCF (13 × 29; 7 × 37) = 1
The fraction: - 245/448 = - (5 × 72)/(26 × 7) = - ((5 × 72) ÷ 7)/((26 × 7) ÷ 7) = - 35/64
The fraction: 259/340,264 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
259 = 7 × 37
340,264 = 23 × 42,533
GCF (7 × 37; 23 × 42,533) = 1
The fraction: - 426/29,257 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
426 = 2 × 3 × 71
29,257 = 17 × 1,721
GCF (2 × 3 × 71; 17 × 1,721) = 1
The fraction: 343,301/15 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
343,301 = 7 × 49,043
15 = 3 × 5
GCF (7 × 49,043; 3 × 5) = 1
The fraction: - 406/48 = - (2 × 7 × 29)/(24 × 3) = - ((2 × 7 × 29) ÷ 2)/((24 × 3) ÷ 2) = - 203/24
The fraction: 265/436 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
265 = 5 × 53
436 = 22 × 109
GCF (5 × 53; 22 × 109) = 1
The fraction: 283/407 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
283 is a prime number
407 = 11 × 37
GCF (283; 11 × 37) = 1
The fraction: - 298/367,306 = - (2 × 149)/(2 × 43 × 4,271) = - ((2 × 149) ÷ 2)/((2 × 43 × 4,271) ÷ 2) = - 149/183,653
The fraction: - 407/35 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
407 = 11 × 37
35 = 5 × 7
GCF (11 × 37; 5 × 7) = 1
The fraction: 250/327,274 = (2 × 53)/(2 × 163,637) = ((2 × 53) ÷ 2)/((2 × 163,637) ÷ 2) = 125/163,637
Rewrite the equivalent simplified operation:
- 377/259 - 245/448 + 259/340,264 - 426/29,257 + 343,301/15 - 406/48 + 265/436 + 283/407 - 298/367,306 - 407/35 + 250/327,274 =
- 377/259 - 35/64 + 259/340,264 - 426/29,257 + 343,301/15 - 203/24 + 265/436 + 283/407 - 149/183,653 - 407/35 + 125/163,637
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: - 377/259
- 377 ÷ 259 = - 1 and the remainder = - 118 ⇒ - 377 = - 1 × 259 - 118
- 377/259 = ( - 1 × 259 - 118)/259 = ( - 1 × 259)/259 - 118/259 = - 1 - 118/259
The fraction: 343,301/15
343,301 ÷ 15 = 22,886 and the remainder = 11 ⇒ 343,301 = 22,886 × 15 + 11
343,301/15 = (22,886 × 15 + 11)/15 = (22,886 × 15)/15 + 11/15 = 22,886 + 11/15
The fraction: - 203/24
- 203 ÷ 24 = - 8 and the remainder = - 11 ⇒ - 203 = - 8 × 24 - 11
- 203/24 = ( - 8 × 24 - 11)/24 = ( - 8 × 24)/24 - 11/24 = - 8 - 11/24
The fraction: - 407/35
- 407 ÷ 35 = - 11 and the remainder = - 22 ⇒ - 407 = - 11 × 35 - 22
- 407/35 = ( - 11 × 35 - 22)/35 = ( - 11 × 35)/35 - 22/35 = - 11 - 22/35
Rewrite the equivalent simplified operation:
- 377/259 - 35/64 + 259/340,264 - 426/29,257 + 343,301/15 - 203/24 + 265/436 + 283/407 - 149/183,653 - 407/35 + 125/163,637 =
- 1 - 118/259 - 35/64 + 259/340,264 - 426/29,257 + 22,886 + 11/15 - 8 - 11/24 + 265/436 + 283/407 - 149/183,653 - 11 - 22/35 + 125/163,637 =
22,866 - 118/259 - 35/64 + 259/340,264 - 426/29,257 + 11/15 - 11/24 + 265/436 + 283/407 - 149/183,653 - 22/35 + 125/163,637
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:
259 = 7 × 37
64 = 26
340,264 = 23 × 42,533
29,257 = 17 × 1,721
15 = 3 × 5
24 = 23 × 3
436 = 22 × 109
407 = 11 × 37
183,653 = 43 × 4,271
35 = 5 × 7
163,637 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 (259; 64; 340,264; 29,257; 15; 24; 436; 407; 183,653; 35; 163,637) = 26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637 = 11,148,733,235,714,896,078,891,085,760
2) Calculate the expanding number of each fraction:
Divide the LCM by the denominator of each fraction.
- 118/259 : 11,148,733,235,714,896,078,891,085,760 ÷ 259 = (26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637) ÷ (7 × 37) = 43,045,302,068,397,282,157,880,640
- 35/64 : 11,148,733,235,714,896,078,891,085,760 ÷ 64 = (26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637) ÷ 26 = 174,198,956,808,045,251,232,673,215
259/340,264 : 11,148,733,235,714,896,078,891,085,760 ÷ 340,264 = (26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637) ÷ (23 × 42,533) = 32,764,950,849,090,400,626,840
- 426/29,257 : 11,148,733,235,714,896,078,891,085,760 ÷ 29,257 = (26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637) ÷ (17 × 1,721) = 381,062,078,672,280,004,063,680
11/15 : 11,148,733,235,714,896,078,891,085,760 ÷ 15 = (26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637) ÷ (3 × 5) = 743,248,882,380,993,071,926,072,384
- 11/24 : 11,148,733,235,714,896,078,891,085,760 ÷ 24 = (26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637) ÷ (23 × 3) = 464,530,551,488,120,669,953,795,240
265/436 : 11,148,733,235,714,896,078,891,085,760 ÷ 436 = (26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637) ÷ (22 × 109) = 25,570,489,072,740,587,336,906,160
283/407 : 11,148,733,235,714,896,078,891,085,760 ÷ 407 = (26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637) ÷ (11 × 37) = 27,392,464,952,616,452,282,287,680
- 149/183,653 : 11,148,733,235,714,896,078,891,085,760 ÷ 183,653 = (26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637) ÷ (43 × 4,271) = 60,705,424,010,034,663,625,920
- 22/35 : 11,148,733,235,714,896,078,891,085,760 ÷ 35 = (26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637) ÷ (5 × 7) = 318,535,235,306,139,887,968,316,736
125/163,637 : 11,148,733,235,714,896,078,891,085,760 ÷ 163,637 = (26 × 3 × 5 × 7 × 11 × 17 × 37 × 43 × 109 × 1,721 × 4,271 × 42,533 × 163,637) ÷ 163,637 = 68,130,882,598,158,705,420,480
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.
22,866 - 118/259 - 35/64 + 259/340,264 - 426/29,257 + 11/15 - 11/24 + 265/436 + 283/407 - 149/183,653 - 22/35 + 125/163,637 =
22,866 - (43,045,302,068,397,282,157,880,640 × 118)/(43,045,302,068,397,282,157,880,640 × 259) - (174,198,956,808,045,251,232,673,215 × 35)/(174,198,956,808,045,251,232,673,215 × 64) + (32,764,950,849,090,400,626,840 × 259)/(32,764,950,849,090,400,626,840 × 340,264) - (381,062,078,672,280,004,063,680 × 426)/(381,062,078,672,280,004,063,680 × 29,257) + (743,248,882,380,993,071,926,072,384 × 11)/(743,248,882,380,993,071,926,072,384 × 15) - (464,530,551,488,120,669,953,795,240 × 11)/(464,530,551,488,120,669,953,795,240 × 24) + (25,570,489,072,740,587,336,906,160 × 265)/(25,570,489,072,740,587,336,906,160 × 436) + (27,392,464,952,616,452,282,287,680 × 283)/(27,392,464,952,616,452,282,287,680 × 407) - (60,705,424,010,034,663,625,920 × 149)/(60,705,424,010,034,663,625,920 × 183,653) - (318,535,235,306,139,887,968,316,736 × 22)/(318,535,235,306,139,887,968,316,736 × 35) + (68,130,882,598,158,705,420,480 × 125)/(68,130,882,598,158,705,420,480 × 163,637) =
22,866 - 5,079,345,644,070,879,294,629,915,520/11,148,733,235,714,896,078,891,085,760 - 6,096,963,488,281,583,793,143,562,525/11,148,733,235,714,896,078,891,085,760 + 8,486,122,269,914,413,762,351,560/11,148,733,235,714,896,078,891,085,760 - 162,332,445,514,391,281,731,127,680/11,148,733,235,714,896,078,891,085,760 + 8,175,737,706,190,923,791,186,796,224/11,148,733,235,714,896,078,891,085,760 - 5,109,836,066,369,327,369,491,747,640/11,148,733,235,714,896,078,891,085,760 + 6,776,179,604,276,255,644,280,132,400/11,148,733,235,714,896,078,891,085,760 + 7,752,067,581,590,455,995,887,413,440/11,148,733,235,714,896,078,891,085,760 - 9,045,108,177,495,164,880,262,080/11,148,733,235,714,896,078,891,085,760 - 7,007,775,176,735,077,535,302,968,192/11,148,733,235,714,896,078,891,085,760 + 8,516,360,324,769,838,177,560,000/11,148,733,235,714,896,078,891,085,760 =
22,866 + ( - 5,079,345,644,070,879,294,629,915,520 - 6,096,963,488,281,583,793,143,562,525 + 8,486,122,269,914,413,762,351,560 - 162,332,445,514,391,281,731,127,680 + 8,175,737,706,190,923,791,186,796,224 - 5,109,836,066,369,327,369,491,747,640 + 6,776,179,604,276,255,644,280,132,400 + 7,752,067,581,590,455,995,887,413,440 - 9,045,108,177,495,164,880,262,080 - 7,007,775,176,735,077,535,302,968,192 + 8,516,360,324,769,838,177,560,000)/11,148,733,235,714,896,078,891,085,760 =
22,866 - 744,310,554,496,434,755,885,330,013/11,148,733,235,714,896,078,891,085,760
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:
744,310,554,496,434,755,885,330,013 = 238 × 10,781 × 251,162,788,531
11,148,733,235,714,896,078,891,085,760 = 242 × 72 × 1,523 × 33,967,980,119
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 (744,310,554,496,434,755,885,330,013; 11,148,733,235,714,896,078,891,085,760) = GCF (238 × 10,781 × 251,162,788,531; 242 × 72 × 1,523 × 33,967,980,119) = 238
The fraction can be reduced (simplified):
Divide both the numerator and denominator by their greatest common factor, GCF.
- 744,310,554,496,434,755,885,330,013/11,148,733,235,714,896,078,891,085,760 =
- (238 × 10,781 × 251,162,788,531)/(242 × 72 × 1,523 × 33,967,980,119) =
- ((238 × 10,781 × 251,162,788,531) ÷ 238)/((242 × 72 × 1,523 × 33,967,980,119) ÷ 238) =
- (10,781 × 251,162,788,531)/(24 × 72 × 1,523 × 33,967,980,119) =
- 2,707,786,023,152,711/40,558,855,237,449,810
Rewrite the equivalent simplified operation:
22,866 - 744,310,554,496,434,755,885,330,013/11,148,733,235,714,896,078,891,085,760 =
22,866 - 2,707,786,023,152,711/40,558,855,237,449,810
Rewrite the intermediate result
As a positive 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.
22,866 - 2,707,786,023,152,711/40,558,855,237,449,810 =
(22,866 × 40,558,855,237,449,810)/40,558,855,237,449,810 - 2,707,786,023,152,711/40,558,855,237,449,810 =
(22,866 × 40,558,855,237,449,810 - 2,707,786,023,152,711)/40,558,855,237,449,810 =
9.274160760735E+20/40,558,855,237,449,810
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:
9.274160760735E+20 ÷ 40,558,855,237,449,810 = 22,865 and the remainder = 3.7851069214228E+16 ⇒
9.274160760735E+20 = 22,865 × 40,558,855,237,449,810 + 3.7851069214228E+16 ⇒
9.274160760735E+20/40,558,855,237,449,810 =
(22,865 × 40,558,855,237,449,810 + 3.7851069214228E+16)/40,558,855,237,449,810 =
(22,865 × 40,558,855,237,449,810)/40,558,855,237,449,810 + 3.7851069214228E+16/40,558,855,237,449,810 =
22,865 + 3.7851069214228E+16/40,558,855,237,449,810 =
22,865 3.7851069214228E+16/40,558,855,237,449,810
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
22,865 + 3.7851069214228E+16/40,558,855,237,449,810 =
22,865 + 3.7851069214228E+16 ÷ 40,558,855,237,449,810 ≈
22,865.933238105284 ≈
22,865.93
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.
22,865.933238105284 =
22,865.933238105284 × 100/100 =
(22,865.933238105284 × 100)/100 =
2,286,593.323810528428/100 ≈
2,286,593.323810528428% ≈
2,286,593.32%
The final answer:
:: written in four ways ::
As a positive improper fraction:
(the numerator >= the denominator)
- 377/259 - 245/448 + 259/340,264 - 426/29,257 + 343,301/15 - 406/48 + 265/436 + 283/407 - 298/367,306 - 407/35 + 250/327,274 = 9.274160760735E+20/40,558,855,237,449,810
As a mixed number (also called a mixed fraction):
- 377/259 - 245/448 + 259/340,264 - 426/29,257 + 343,301/15 - 406/48 + 265/436 + 283/407 - 298/367,306 - 407/35 + 250/327,274 = 22,865 3.7851069214228E+16/40,558,855,237,449,810
As a decimal number:
- 377/259 - 245/448 + 259/340,264 - 426/29,257 + 343,301/15 - 406/48 + 265/436 + 283/407 - 298/367,306 - 407/35 + 250/327,274 ≈ 22,865.93
As a percentage:
- 377/259 - 245/448 + 259/340,264 - 426/29,257 + 343,301/15 - 406/48 + 265/436 + 283/407 - 298/367,306 - 407/35 + 250/327,274 ≈ 2,286,593.32%
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.
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