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?

Answer 1

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.