Mixed Numbers and Improper Fractions

Problem: Convert 11/4 to a mixed number.

Solution:

Step 1: Divide 11 by 4. Quotient = 2, Remainder = 3.

Step 2: Mixed number = 2 3/4.

Answer: 11/4 = 2 3/4

Problem: Convert 17/5 to a mixed number.

Solution:

Step 1: 17 ÷ 5 = 3 remainder 2.

Step 2: Mixed number = 3 2/5.

Answer: 17/5 = 3 2/5

Problem: Convert 2 3/7 to an improper fraction.

Solution:

Step 1: Multiply whole number by denominator: 2 × 7 = 14.

Step 2: Add numerator: 14 + 3 = 17.

Step 3: Write over the same denominator: 17/7.

Answer: 2 3/7 = 17/7

Problem: Convert 4 1/3 to an improper fraction.

Solution:

Step 1: 4 × 3 = 12.

Step 2: 12 + 1 = 13.

Step 3: 13/3.

Answer: 4 1/3 = 13/3

Problem: Convert 8/8 to a mixed number.

Solution:

Step 1: 8 ÷ 8 = 1 remainder 0.

Step 2: Since remainder is 0, the result is just a whole number.

Answer: 8/8 = 1

Problem: Convert 23/6 to a mixed number.

Solution:

Step 1: 23 ÷ 6 = 3 remainder 5.

Step 2: Mixed number = 3 5/6.

Answer: 23/6 = 3 5/6

Problem: Aditi baked 13 chapatis. She arranged them in groups of 4 on each plate. How many full plates did she fill, and how many chapatis were left over? Write as a mixed number.

Solution:

Step 1: Total chapatis = 13, chapatis per plate = 4.

Step 2: 13 ÷ 4 = 3 remainder 1.

Step 3: Mixed number = 3 1/4 plates.

Answer: Aditi filled 3 full plates with 1 chapati left over (3 1/4 plates).

Problem: Which is greater: 2 1/3 or 9/4?

Solution:

Step 1: Convert both to improper fractions: 2 1/3 = 7/3, 9/4 stays as 9/4.

Step 2: Cross multiply: 7 × 4 = 28 and 3 × 9 = 27.

Step 3: 28 > 27.

Answer: 2 1/3 (= 7/3) > 9/4

Problem: Rahul has 3 1/2 litres of milk. Write this as an improper fraction.

Solution:

Step 1: 3 × 2 = 6.

Step 2: 6 + 1 = 7.

Step 3: 7/2.

Answer: 3 1/2 litres = 7/2 litres