Final answer:
Quotients are calculated by dividing the numerator by the denominator; improper fractions are converted to mixed numbers. In this case, 7/3 simplifies to 2 1/3, 3/7 remains unchanged, 5/4 simplifies to 1 1/4, and 2/5 remains as is.
Step-by-step explanation:
To find each of the given quotients and express them in their simplest form, we need to see if the fractions are improper (the numerator is larger than the denominator) and then convert them to mixed numbers if necessary. Here's how to calculate and simplify each one:
- a) 7/3: This is an improper fraction. To convert it to a mixed number, we divide 7 by 3 which gives us 2 with a remainder of 1. So, the mixed number is 2 1/3.
- b) 3/7: This is a proper fraction (the numerator is smaller than the denominator) and it is already in its simplest form, so the answer is 3/7.
- c) 5/4: This is an improper fraction. To convert it to a mixed number, we divide 5 by 4 which gives us 1 with a remainder of 1. Thus, the mixed number is 1 1/4.
- d) 2/5: This is a proper fraction and cannot be simplified further, so the answer remains 2/5.