Fraction Arithmetic
Find the value of a + b in the expression below, where a and b are positive integers with no common factors:
6 1 + 1 0 1 = b a .
The answer is 19.
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9 solutions
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take the lcm of 6 and 10..comes out to be 30..so 1/6 +1/10 gives 8/30..simplify 8/30 to get 4/15(question says their hcf is 1) these are the values of a and b..which gives a+b =19
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Can we also simplify it from its cross multiplication which is 16/60? Kindly guide!
the denominator= 610=60 , the numerator=(101)+(6*1)=16, then we have 16\60, by dividing each term by 4 we get 4\15, which equals to a\b, finally by adding 4+15, we gets the answer 19.
Its simple. Represent 1/6+1/10 in the form a/b where a and b are coprime, i.e., a and b have no common divisors other than 1 and then just add a and b.
absolutely right but it would be more better if u also write some explanation
thnk u
1/6 + 1/10 = 8/30 - 8/30 = 4/15 - 4 + 15 = 19
oooops it s lengthy
ah... :) sayang
1/6 +1/10 = 4/15
a = 4 b = 15
a + b = 19
I resolved how you...
the denominator= 6 10=60 , the numerator=(10 1)+(6*1)=16, then we have 16\60, by dividing each term by 4 we get 4\15, which equals to a\b, finally by adding 4+15, we gets the answer 19.
It is simple:
1 0 1 + 6 1 = 1 5 4
15 + 4 = 19
1/6 + 1/10 = a/b
(1×10/6×10) + (1×6/10×6) = a/b So...
10/60 + 6/60 = 16/60 = a/b
16/60 = 8/30 = 4/15 = a/b
A=4 and B=15
a+b = 4+15 = 19
FIRST OF ALL WE WILL TAKE LCM OF 6 AND 10. THE LCM OF 6 AND 10 WILL BE 30. THEN BY SIMPLIFYING WE WILL GET 4/15=a/b. BY COMPARING WE WILL GET a=4,b=15. SO BY ADDING THE VALUES OF a AND b WE WILL GET 19 WHICH IS THE REQUIRED ANSWER.
6 1 + 1 0 1 = 6 0 1 6 = 1 5 4 ⟹ 1 9
Your statement 1 5 4 ⇒ 1 9 seemed to make no sense in logic. (no offense)
first taking L.C.M after solving it we will get the frac. of {a}and {b} is frac.. of {4} {15} then by seeing the numerator terms and denominator terms separated like , a=4 and b=15 put the values of a and b in the form a+b .
By the Mean Value Theorem for Integrals, we find that this is equal to to
∫ − ∞ 0 e 6 x d x + 4 0 1 ∫ 2 0 1 1 2 0 1 5 ∣ 2 0 1 3 − x ∣ d x = 1 5 4
giving our desired result of 4 + 1 5 = 1 9 .
Good job, Cody. I'm upvoting this!
hahahahaha
1/6+1/10=a/b or, (5+3)/30=a/b or, 8/30=a/b or, a/b=4/15
a=4,b=15 a+b=4+15=19