1) Convert the mixed number 3 1/2 to an improper fraction.

Solution: To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction and add the numerator. Then, place the result over the denominator.

3 * 2 + 1 = 7 7/2

Therefore, 3 1/2 as an improper fraction is 7/2.

2) Convert the fraction 5/8 to a mixed number.

Solution: To convert a fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number part, and the remainder becomes the numerator of the fraction part.

5 ÷ 8 = 0 remainder 5

Therefore, 5/8 as a mixed number is 0 5/8.

3) Add the mixed numbers 2 3/4 and 1 2/3.

Solution: To add mixed numbers, first add the whole numbers together. Then, add the fractions together. If the sum of the fractions is an improper fraction, convert it to a mixed number.

2 + 1 = 3 (whole numbers) 3/4 + 2/3 = (9/12) + (8/12) = 17/12

Since 17/12 is an improper fraction, we can convert it to a mixed number.

17 ÷ 12 = 1 remainder 5

Therefore, 2 3/4 + 1 2/3 = 3 5/12.

4) Subtract the fraction 3/5 from the mixed number 4 1/2.

Solution: To subtract a fraction from a mixed number, first convert the mixed number to an improper fraction. Then, subtract the fractions and whole numbers separately.

4 * 2 + 1 = 9 9/2 - 3/5 = (45/10) - (6/10) = 39/10

Since 39/10 is an improper fraction, we can convert it to a mixed number.

39 ÷ 10 = 3 remainder 9

Therefore, 4 1/2 - 3/5 = 3 9/10.

5) Multiply the mixed number 2 1/3 by the fraction 2/5.

Solution: To multiply a mixed number by a fraction, first convert the mixed number to an improper fraction. Then, multiply the numerators together and the denominators together.

2 * 3 + 1 = 7 7/3 * 2/5 = (7 * 2) / (3 * 5) = 14/15

Therefore, 2 1/3 * 2/5 = 14/15.