By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?
Lets look at a sample
4/8 reduced by 50% 2/8
reduce den by 25% 2/2 = 1
4/8 is 1/2 so compare it to 1 it is doubled.
1/2 divided by 1/4 = 1/2 x 4 = 2
So.... whats the answer?
the answer is 33.(3)
To find the percentage decrease in a fraction, we need to compare the original fraction to the new fraction after the decrease. Let's assume the original fraction is represented by (numerator / denominator).
Step 1: Calculate the new numerator after the decrease.
If the numerator is decreased by 50%, it means it is multiplied by (1 - 50%) or 0.5.
New Numerator = Original Numerator * 0.5
Step 2: Calculate the new denominator after the decrease.
If the denominator is decreased by 25%, it means it is multiplied by (1 - 25%) or 0.75.
New Denominator = Original Denominator * 0.75
Step 3: Calculate the new fraction.
New Fraction = New Numerator / New Denominator
Step 4: Calculate the decrease in the fraction.
Decrease = Original Fraction - New Fraction
Step 5: Calculate the percentage decrease.
Percentage Decrease = (Decrease / Original Fraction) * 100
Let's calculate the percentage decrease for an example:
Assume the original fraction is 8/12.
Step 1: Calculate the new numerator.
New Numerator = 8 * 0.5 = 4
Step 2: Calculate the new denominator.
New Denominator = 12 * 0.75 = 9
Step 3: Calculate the new fraction.
New Fraction = 4/9
Step 4: Calculate the decrease.
Decrease = (8/12) - (4/9) = (8/12) - (16/36) = (24/36) - (16/36) = 8/36 = 2/9
Step 5: Calculate the percentage decrease.
Percentage Decrease = (2/9) / (8/12) * 100 = (2/9) / (2/3) * 100 = (2/9) * (3/2) * 100 = 1/3 * 100 = 33.33%
Therefore, the fraction will decrease by approximately 33.33%.