lara and maria finished 3/4 of their homework assignment. lara did 1/4 more of the assignment than maria. what fraction of the assignment did each girl finish?
3/4 = 6/8. do you see why? If one finished 1/4 more, that is the same as saying 2/8. Subtract 2 from 6 and that leaves 4/8 (which is the same, by the way, as 2/4 or 1/2. Divide that in 2 and each girl finished 2/8 (or 1/4) = 4/8 (1/2) leaving the 2/8 (1/4) extra of the one girl.
To find out what fraction of the assignment each girl finished, we can break down the information given step-by-step.
Let's start by assigning variables to the fractions of the homework assignment completed by Lara and Maria. Let L represent Lara's fraction and M represent Maria's fraction.
According to the question, Lara and Maria finished a total of 3/4 of the assignment combined. So, we can write the following equation:
L + M = 3/4
The question also states that Lara did 1/4 more of the assignment than Maria. This can be written as:
L = M + 1/4
Now we have two equations:
Equation 1: L + M = 3/4
Equation 2: L = M + 1/4
To solve for the values of L and M, we can substitute Equation 2 into Equation 1:
(M + 1/4) + M = 3/4
Combine like terms:
2M + 1/4 = 3/4
Subtract 1/4 from both sides:
2M = 3/4 - 1/4
2M = 2/4
Simplify:
2M = 1/2
Divide both sides by 2:
M = 1/4
Now, substitute the value of M back into Equation 2 to solve for L:
L = (1/4) + 1/4
L = 2/4
L = 1/2
Therefore, Lara finished 1/2 of the assignment, and Maria finished 1/4 of the assignment.