If a certain number is added to the numerator and denominator of 11/13, the result is 11/12. Find the number.
(11+x)/(13+x) = 11/12
132 + 12x = 143+11x
x = 11
check:
(11+11)/(13+11)
= 22/24
= 11/12
Oh, I love math! Let's solve this problem together... Or should I say, "math-terpiece"!
To find the number that needs to be added, we can start by setting up the equation. Let's call the unknown number "x".
The original fraction is 11/13. This can be written as:
(11 + x) / (13 + x) = 11/12
Now, let's cross-multiply:
12(11 + x) = 11(13 + x)
Simplifying, we get:
132 + 12x = 143 + 11x
Subtracting 11x from both sides, we have:
x = 143 - 132
Simplifying further, we find:
x = 11
Hooray! The number that needs to be added to both the numerator and denominator is 11. Now go impress your friends with your "math-ical" skills!
Let's solve this problem step by step.
Step 1: Express the given information as an equation.
Let's call the number we need to find "x". According to the problem, if we add x to both the numerator and denominator of 11/13, we get 11/12. We can write this as the following equation:
(11 + x) / (13 + x) = 11/12
Step 2: Cross-multiply the equation.
To eliminate the fractions, we can cross-multiply the equation:
12 * (11 + x) = 11 * (13 + x)
Simplifying this equation gives us:
132 + 12x = 143 + 11x
Step 3: Solve for x.
Now, we can solve the equation for x:
12x - 11x = 143 - 132
x = 11
Therefore, the number we are looking for is 11.
To find the number that needs to be added to both the numerator and denominator of 11/13, we can set up an equation. Let's say the number we are looking for is represented by 'x'.
So, we have the equation:
(11 + x) / (13 + x) = 11/12
Now, we can cross-multiply to solve for 'x'. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction and vice versa.
(11 + x) * 12 = 11 * (13 + x)
Expanding this equation, we get:
132 + 12x = 143 + 11x
Next, we can simplify the equation by combining like terms:
12x - 11x = 143 - 132
1x = 11
Therefore, the number 'x' that needs to be added to both the numerator and denominator of 11/13 is 11.