Answer:
1449/2691
Step-by-step explanation:
Let the fraction be x/y. Then, we have two conditions:
(1) x + y = 4140
(2) x/y = 7/13
(3) 13x = 7y Multiplied each side by the lcd (13y)
(4) y = 4140 - x Subtracted x from each side of (1)
13x = 7(4140 - x) Substituted (4) into (3)
13x = 28 980 - 7x Distributed the 7
20x = 28 980 Added 7x to each side
(5) x = 1449
1449 + y = 4140 Substituted (5) into (1)
y = 2691 Subtracted 1449 from each side
The original fraction was 1449/2691.
Check:
(1) 1449 + 2691 = 4140 (2) 1449/2691 = 7/13
4140 = 4140 7/13 = 7/13
OK.
The original fractions if the sum of the numerator and the denominator of the certain fraction is equal to 4,140 is 1449/269
Fractions are written as a ratio of two integers.
Let the numerator be "x" and the denominator be "y"
The sum of the numerator and the denominator will be x + y
x + y = 4140 ...........1
If the fraction was reduced, the result was 7/13, hence;
x/y = 7/13
x = 7/13 y .............. 2
Substitute equation 2 into 1
7/13 y + y = 4140
20y/13 = 4140
y/13 = 207
y = 2691
From equation 1, x = 4140 - y
x = 4140 - 2691
x = 1449
Hence the original fractions if the sum of the numerator and the denominator of the certain fraction is equal to 4,140 is 1449/2691
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