1. Convert the following improper fractions into mixed numbers:
    (a) 17/5 = 3 2/5
    (b) 23/4 = 5 3/4
    (c) 19/6 = 3 1/6
    (d) 45/8 = 5 5/8
    (e) 32/7 = 4 4/7
    (f) 29/3 = 9 2/3
    (g) 14/5 = 2 4/5

2. Multiply the following mixed numbers and simplify the result:
    (a) 2 1/2 × 3 1/3 = 5/2 × 10/3 = 50/6 = 8 1/3
    (b) 4 2/5 × 2 1/2 = 22/5 × 5/2 = 110/10 = 11
    (c) 1 3/4 × 5 2/3 = 7/4 × 17/3 = 119/12 = 9 11/12
    (d) 3 1/5 × 6 1/4 = 16/5 × 25/4 = 400/20 = 20
    (e) 7 2/3 × 1 1/6 = 23/3 × 7/6 = 161/18 = 8 17/18
    (f) 2 3/7 × 4 3/5 = 17/7 × 23/5 = 391/35 = 11 6/35
    (g) 5 1/2 × 2 3/8 = 11/2 × 19/8 = 209/16 = 13 1/16

3. Find the fraction of the given numbers:
    (a) 1/4 of 28 = 7
    (b) 2/5 of 45 = 18
    (c) 3/8 of 64 = 24
    (d) 5/6 of 72 = 60
    (e) 2/3 of 90 = 60
    (f) 4/7 of 49 = 28
    (g) 3/5 of 100 = 60

4. A jug contains 6 litres of juice. Riya drinks 2/3 of it. How much juice is left in the jug?
    2/3 of 6 = 4 litres. Juice left = 6 – 4 = 2 litres

5. Divide the following fractions and simplify:
    (a) 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2
    (b) 7/8 ÷ 2/3 = 7/8 × 3/2 = 21/16 = 1 5/16
    (c) 5/6 ÷ 1/4 = 5/6 × 4/1 = 20/6 = 3 1/3
    (d) 2/5 ÷ 3/7 = 2/5 × 7/3 = 14/15
    (e) 4/9 ÷ 2/3 = 4/9 × 3/2 = 12/18 = 2/3
    (f) 6/7 ÷ 5/6 = 6/7 × 6/5 = 36/35 = 1 1/35
    (g) 8/11 ÷ 4/5 = 8/11 × 5/4 = 40/44 = 10/11

6. A water tank holds 9 litres of water. A pipe fills 3/4 of the tank in one hour. How many litres does it fill in one hour?
    3/4 of 9 = 27/4 = 6.75 litres

7. Add the following fractions and reduce them to the lowest form:
    (a) 2/5 + 3/10 = 4/10 + 3/10 = 7/10
    (b) 4/9 + 5/18 = 8/18 + 5/18 = 13/18
    (c) 7/8 + 1/4 = 7/8 + 2/8 = 9/8 = 1 1/8
    (d) 3/7 + 2/3 = (9 + 14)/21 = 23/21 = 1 2/21
    (e) 5/6 + 1/2 = 10/12 + 6/12 = 16/12 = 4/3 = 1 1/3
    (f) 1/3 + 3/4 = 4/12 + 9/12 = 13/12 = 1 1/12
    (g) 2/9 + 4/5 = (10 + 36)/45 = 46/45 = 1 1/45

8. Reena baked 3 1/2 trays of cookies and her friend baked 2 2/3 trays. How many trays of cookies did they bake together?
    3 1/2 + 2 2/3 = 7/2 + 8/3 = (21 + 16)/6 = 37/6 = 6 1/6 trays

9. Subtract the following fractions and simplify the results:
    (a) 5/6 – 1/3 = 5/6 – 2/6 = 3/6 = 1/2
    (b) 7/8 – 3/4 = 7/8 – 6/8 = 1/8
    (c) 9/10 – 2/5 = 9/10 – 4/10 = 5/10 = 1/2
    (d) 3/4 – 1/6 = 9/12 – 2/12 = 7/12
    (e) 11/12 – 5/6 = 11/12 – 10/12 = 1/12
    (f) 4/5 – 2/7 = (28 – 10)/35 = 18/35
    (g) 7/9 – 1/3 = 7/9 – 3/9 = 4/9

10. Arjun ran 2 1/4 km in the morning and 1 3/4 km in the evening. What is the total distance he ran in a day?
    2 1/4 + 1 3/4 = 9/4 + 7/4 = 16/4 = 4 km