Final answer:
To solve the expression 2/3 x 2/3 - 1/3 x 3/5, multiply and simplify each set of fractions and then subtract the resulting fractions to get 11/45, which is the answer in simplest form.
Step-by-step explanation:
The question asks to solve the following expression 2/3 x 2/3 - 1/3 x 3/5 and to write the answer in simplest form. To solve this, we will perform the multiplication for each set of fractions and then subtract one product from the other. We start with multiplying the numerators together and the denominators together, simplifying as needed. For the first set of fractions, we have (2 x 2) / (3 x 3) which equals 4/9. For the second set, we have (1 x 3) / (3 x 5) which simplifies to 1/5 as the 3 in the numerator and denominator cancel out. The expression simplifies to:
4/9 - 1/5
To subtract these fractions, we need a common denominator. The least common denominator for 9 and 5 is 45. We convert each fraction to an equivalent fraction with a denominator of 45, giving us:
20/45 - 9/45
Subtracting these two fractions, we get:
11/45
This is the simplest form of the expression after performing the subtraction of the fractions.