what number multiplied by the numerator and added to the denominator of the fraction 2/5 makes the resulting fraction 8/9?
Let's denote the number you're looking for as "x".
According to the information given, we have the equation:
x * (numerator of 2/5) + (denominator of 2/5) = numerator of 8/9
In other words:
x * 2 + 5 = 8
To solve this equation for 'x', let's isolate 'x' by subtracting 5 from both sides:
2x = 8 - 5
Simplifying:
2x = 3
Finally, divide both sides by 2 to solve for 'x':
x = 3 / 2
Therefore, the number you are looking for is 3/2.
To solve this problem, we need to find a number that, when multiplied by the numerator and added to the denominator of the fraction 2/5, results in the fraction 8/9.
Let's break down the problem step by step:
1. Start by considering the numerator of the fraction 2/5, which is 2. We want to find a number that, when multiplied by 2 and added to the denominator, produces the numerator of the final fraction, which is 8.
So, we have the equation: number × 2 + 5 = 8.
2. Now, let's solve this equation to find the value of "number."
Subtracting 5 from both sides of the equation, we get: number × 2 = 3.
Then, we divide both sides by 2 to isolate the "number" variable: number = 3/2.
Therefore, the number that needs to be multiplied by the numerator and added to the denominator of the fraction 2/5 to obtain the fraction 8/9 is 3/2.
(2x)/(x+5) = 8/9
cross-multiply
18x = 8x + 40
10x = 40
x = 4