If 1 is subtracted from the numerator and from the denominator of a fraction, the value obtained is 1/2. If 1 is added to its numerator and to its denominator, the resulting value is 2/3. Find the fraction.
Answers
Given: If 1 is subtracted from the numerator and from the denominator of a fraction, the value obtained is 1/2. If 1 is added to its numerator and to its denominator, the resulting value is 2/3.
To find: Find the fraction.
Solution:
- Let the fraction be x/y, then:
- According to the first statement, we get:
x-1/y-1 = 1/2
- Solving this, we get:
2(x-1) = y-1
2x - 2 = y - 1
2x - y - 1 = 0 .....................(i)
- According to the second statement, we get:
x+1/y+1 = 2/3
- Solving this, we get:
3(x+1) = 2(y+1)
3x + 3 = 2y + 2
3x - 2y + 1 = 0 .....................(ii)
- Now solving: 2(i) - (ii), we get:
4x - 2y - 2 = 0
- 3x + 2y - 1 = 0
x - 3 = 0
x = 3
- Putting x in (i), we get:
2(3) - y - 1 = 0
6 - y - 1 = 0
y = 5
x/y = 3/5
Answer:
So the fraction is 3/5.
Answer:
the fraction is 3/5
Step-by-step explanation:
Let the numerator of the fraction be x and its denominator be y,
i.e. let the fraction be x
y .
x
y
– 1
– 1 = 1
2 — (1)
+
+
x
y
1
1 = 2
3 — (2)
From (1),
2(x – 1) = y – 1
2x – 2 = y – 1
y = 2x – 1 — (3)
Substitute (3) into (2):
+
+
x
x
1
2 – 1 1 = 2
3
3(x + 1) = 4x
3x + 3 = 4x
x = 3
Substitute x = 3 into (3):
y = 2(3) – 1
= 5
The fraction is 3 /5