Reciprocal Sum Equality

Algebra Level 1

If a a and b b are coprime positive integers such that

1 2 + 1 3 + 1 4 + 1 5 = a b , \frac {1}{2} + \frac {1}{3} + \frac {1}{4} + \frac {1}{5} =\frac {a}{b},

what is the value of a + b a+b ?


The answer is 137.

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Arron Kau by Arron Kau

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12 solutions

1/2+1/3+1/4+1/5 =a/b

(30+20+15+12)/60=77/60

77/60=a/b

a=77 b=66

a+b=137

10 Helpful 0 Interesting 0 Brilliant 0 Confused

char ..go jep! hahaha

Da Zhi Zhang - 7 years, 10 months ago

how you can doing this way please ....

Laura Al-taib - 7 years, 10 months ago

ahhy grabe jud katalino mo....

Majieddah Guiana - 7 years, 10 months ago

144/120=77/60

are the same 77 + 60 = 137

Dini Yah - 7 years, 10 months ago

Wow thank :)

Ivandro Ismael - 7 years, 10 months ago

aiH ganun jiji galing (y)

Ammierol Momando - 7 years, 10 months ago

Wow thank very much...^_^

Ahmad Aminnuddin - 7 years, 10 months ago

I thought a was 87

Bryan Anofa - 7 years, 10 months ago

You wrote 66 instead of 60

Miguel Angel Ordóñez Silis - 5 years, 8 months ago

Calculate the LCM between 2, 3, 4 and 5 (it's 60). 30 + 20 + 15 + 12 60 \frac{30+20+15+12}{60} = 77 60 \frac{77}{60} . Now, just do 77+60=137. And there we have it!

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Good approach of taking the LCM initially, to reduce the need to add fractions numerous times. This can help cut down calculation mistakes.

Jose, I liked how you made your solution short and to the point. It helped me a lot!

Castor Grande - 7 years, 10 months ago
Anubhav Mishra
Jul 30, 2013

1/2+1/3=5/6 5/6+1/4=13/12 13/12+1/5=77/60 77 and 60 are coprimes and positive therefore, a+b=77+60=137

2 Helpful 0 Interesting 0 Brilliant 0 Confused

what are the copprime numbers ?

Ankit Gupta - 7 years, 10 months ago
Castor Grande
Aug 4, 2013

First, you must multiply all the denominators together because without a common denominator, you cannot add fractions.

2 x 3 x 4 x 5 =

The product of this equation is now the common denominator of this set of fractions.

120

Now, divide the common denominator by each of the previous denominators to determine the new numerator for each of the fractions.

1/2 = 60/120, 1/3 = 40/120, 1/4 = 30/120, 1/5 = 24/120

Then, add the fractions together.

60/120 + 40/120 + 30/120 + 24/120 = 154/120

DO NOT convert the sum into this: 1 34/120 Because then you have changed the value of a and b! Reduce the fraction, leaving it in the same form of a fraction as it is.

77/60

Now add a (numerator) and b (denominator) together to get the sum of a + b.

77 + 60 = 137

The problem is now solved.

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Fikri Kurniawan
Aug 1, 2013

just do copy paste in to google .. you will get it

0 Helpful 0 Interesting 0 Brilliant 0 Confused

1/2 + 1/3 + 1/4 + 1/5 = 30/60 + 20/60 + 15/60 + 12/60 = 77/60 a = 77, b = 60 a + b = 137

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ronald Salim
Jul 29, 2013

LCM of 2,3,4,5 = 60

60/2 + 60/3 + 60/4 + 60/5 = 77/60 = a/b

a+b=137

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Matheus Pinto
Jul 29, 2013

1/2+1/3+1/4+1/5=a/b

MMC(2, 3, 4, 5) = 2^2 . 3 . 5 = 60

30+20+15+12/60= a/b

77/60=a/b

77+60= 137

0 Helpful 0 Interesting 0 Brilliant 0 Confused

you can understand me how you can formated that '30+20+15+12/60= a/b' beacuse is not clair for me please

Laura Al-taib - 7 years, 10 months ago
Pat Pat Labra
Jul 29, 2013

1/2 + 1/ 3 + 1/ 4 + 1/5 = a/b

a/b= 77/60

a+b = 77 + 60 = 137

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Alice Xirinayi
Jul 29, 2013

1/2 + 1/3 + 1/4 + 1/5 = 77/60

therefore, a=77, b=60

77+60=137

0 Helpful 0 Interesting 0 Brilliant 0 Confused

1/2+1/3+1/4+1/5 = a/b, 30+20+15+12/60 = a/b , 77/60=a/b , a+b = 77+60 = 137

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Vipin Tiwari
Jul 28, 2013

1/2+1/3+1/4+1/5=3+2/6+5+4/9=154/120=77/60 .therefore value of a is 77 and the value of b is 60 i.e. a+b=77+60=137

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