If a certain number is added to the numerator and denominator of 5/9, the result is 2/3. Find the number.
(5+x)/(9+x) = 2/3
3(5+x) = 2(9+x)
and so on
To solve this problem, follow these steps:
1. Start with the given fraction 5/9.
2. Add the same number to both the numerator and the denominator. Let's call this number "x".
3. The new fraction is (5+x)/(9+x).
4. According to the problem, this new fraction is equal to 2/3.
5. Set up an equation using the information from steps 3 and 4: (5+x)/(9+x) = 2/3.
6. Cross-multiply to eliminate the fractions: (5+x) * 3 = 2 * (9+x).
7. Solve the resulting equation: 15 + 3x = 18 + 2x.
8. Simplify the equation: 3x - 2x = 18 - 15.
9. Combine like terms: x = 3.
Therefore, the number that needs to be added to both the numerator and the denominator of 5/9 is 3.