Paige decided to paint 4/5 of the rooms in her home last year. By the end of the year, Paige completed 2/3 of the rooms. How much of Paige's home was painted last year?
To find out how much of Paige's home was painted last year, we need to find the fraction of the total number of rooms that were painted.
First, let's represent the number of rooms in Paige's home as x.
Paige decided to paint 4/5 of the rooms last year, so the number of rooms painted is (4/5)x.
By the end of the year, Paige completed 2/3 of the rooms, so the number of rooms painted is (2/3)x.
Since both fractions represent the same number of rooms painted, we can set them equal to each other:
(4/5)x = (2/3)x
To get rid of the fractions, we can multiply both sides of the equation by the denominators:
3 * (4/5)x = 5 * (2/3)x
12/5x = 10/3x
Now we can cancel out the x from both sides:
12/5 = 10/3
To solve for x, we can cross multiply:
12 * 3 = 10 * 5
36 = 50
Since this equation is not true, it means that there is no value for x that satisfies the equation.
Therefore, there is no accurate way to determine how much of Paige's home was painted last year based on the given information.
To determine how much of the home Paige painted, we can multiply 4/5 by the total number of rooms in the home, which is represented by the fraction 1. This gives us 4/5 * 1 = 4/5 of the home painted.
Since Paige completed 2/3 of the rooms in her home last year, we can represent this as 2/3 * 1 = 2/3 of the home painted.
Since these two fractions represent the same thing (how much of Paige's home she painted last year), they are equal to each other. So, 4/5 = 2/3.
To find the fraction that represents the portion of Paige's home that was painted last year, we can multiply both sides of the equation by the least common denominator of the two fractions, which in this case is 15. Doing so, we get 15 * 4/5 = 15 * 2/3.
Multiplying these fractions gives us 60/5 = 30/3.
Reducing these fractions gives us 12 = 10/3.
So, 10/3 of Paige's home was painted last year.