Year 6 Maths: Dealing with a Remainder

Understanding Remainders

Hello Year 6! Today, we are going to learn about remainders. This is an important concept in division. Let’s break it down step by step.

What is a Remainder?

When we divide one number by another, sometimes we can’t divide evenly. For example, if we try to divide 10 by 3:

• 3 goes into 10 three times, which makes 9 (3 x 3 = 9).
• If we subtract 9 from 10, we have 1 left over.

This 1 is called the remainder. So we say:

$$10 \div 3 = 3 \text{ remainder } 1$$

Key Rules About Remainders

1. Division Basics: When you divide, you are trying to find out how many times one number fits into another.
2. Whole Numbers: The result of a division can be a whole number with a remainder, or it can be a decimal/fraction.
3. Remainder Less Than Divisor: The remainder will always be less than the number you are dividing by (the divisor).
4. Expressing Remainders: You can express a remainder in different ways:
   • As “remainder” (e.g., 10 ÷ 3 = 3 R1)
   • As a decimal (e.g., 10 ÷ 3 = 3.33)
   • As a fraction (e.g., 10 ÷ 3 = 3 + 1/3)

Tips and Tricks

• Use Counters: If you have some counters or blocks, you can physically divide them to see how many full groups you can make and what’s left over.
• Check Your Work: After finding the quotient and remainder, multiply the divisor by the quotient and add the remainder. It should equal the original number.
• Practice with Real-Life Examples: Think about practical situations, like sharing sweets or toys among friends.

Examples

1. Example 1: Divide 17 by 5.
   • 5 fits into 17 three times (5 x 3 = 15).
   • 17 – 15 = 2, so the remainder is 2.
   • Answer: $$17 \div 5 = 3 \text{ remainder } 2$$
2. Example 2: Divide 23 by 4.
   • 4 fits into 23 five times (4 x 5 = 20).
   • 23 – 20 = 3, so the remainder is 3.
   • Answer: $$23 \div 4 = 5 \text{ remainder } 3$$
3. Example 3: Divide 30 by 6.
   • 6 fits into 30 five times exactly (6 x 5 = 30).
   • There is no remainder.
   • Answer: $$30 \div 6 = 5 \text{ remainder } 0$$

Practice Questions

Easy Level

1. What is $$ 8 \div 3 $$?
2. What is $$ 15 \div 2 $$?
3. What is $$ 10 \div 4 $$?
4. What is $$ 18 \div 5 $$?
5. What is $$ 12 \div 4 $$?
6. What is $$ 9 \div 2 $$?
7. What is $$ 20 \div 6 $$?
8. What is $$ 7 \div 3 $$?
9. What is $$ 14 \div 5 $$?
10. What is $$ 25 \div 4 $$?
11. What is $$ 16 \div 3 $$?
12. What is $$ 11 \div 2 $$?
13. What is $$ 21 \div 5 $$?
14. What is $$ 30 \div 7 $$?
15. What is $$ 27 \div 4 $$?
16. What is $$ 22 \div 3 $$?
17. What is $$ 28 \div 5 $$?
18. What is $$ 32 \div 6 $$?
19. What is $$ 15 \div 6 $$?
20. What is $$ 13 \div 4 $$?

Medium Level

1. What is $$ 34 \div 3 $$?
2. What is $$ 45 \div 7 $$?
3. What is $$ 50 \div 8 $$?
4. What is $$ 39 \div 5 $$?
5. What is $$ 62 \div 9 $$?
6. What is $$ 56 \div 7 $$?
7. What is $$ 70 \div 4 $$?
8. What is $$ 77 \div 6 $$?
9. What is $$ 88 \div 5 $$?
10. What is $$ 91 \div 8 $$?
11. What is $$ 54 \div 7 $$?
12. What is $$ 63 \div 8 $$?
13. What is $$ 72 \div 9 $$?
14. What is $$ 81 \div 6 $$?
15. What is $$ 48 \div 5 $$?
16. What is $$ 90 \div 7 $$?
17. What is $$ 99 \div 10 $$?
18. What is $$ 66 \div 4 $$?
19. What is $$ 44 \div 3 $$?
20. What is $$ 102 \div 11 $$?

Hard Level

1. What is $$ 135 \div 11 $$?
2. What is $$ 250 \div 17 $$?
3. What is $$ 175 \div 12 $$?
4. What is $$ 195 \div 15 $$?
5. What is $$ 360 \div 29 $$?
6. What is $$ 402 \div 21 $$?
7. What is $$ 512 \div 40 $$?
8. What is $$ 275 \div 18 $$?
9. What is $$ 420 \div 34 $$?
10. What is $$ 600 \div 47 $$?
11. What is $$ 750 \div 36 $$?
12. What is $$ 888 \div 37 $$?
13. What is $$ 999 \div 18 $$?
14. What is $$ 1000 \div 33 $$?
15. What is $$ 1500 \div 61 $$?
16. What is $$ 2000 \div 75 $$?
17. What is $$ 3000 \div 89 $$?
18. What is $$ 4500 \div 94 $$?
19. What is $$ 5000 \div 123 $$?
20. What is $$ 6000 \div 200 $$?

Answers

Easy Level Answers

1. 2 R2
2. 7 R1
3. 3 R2
4. 3 R3
5. 3 R0
6. 4 R1
7. 3 R2
8. 2 R1
9. 2 R4
10. 6 R1
11. 5 R1
12. 5 R1
13. 4 R1
14. 4 R2
15. 6 R3
16. 7 R1
17. 5 R3
18. 5 R2
19. 2 R1
20. 3 R1

Medium Level Answers

1. 11 R1
2. 6 R3
3. 6 R2
4. 7 R4
5. 6 R8
6. 8 R0
7. 17 R2
8. 12 R5
9. 17 R3
10. 11 R3
11. 7 R5
12. 7 R7
13. 8 R0
14. 13 R3
15. 9 R3
16. 12 R6
17. 9 R0
18. 16 R2
19. 14 R2
20. 9 R3

Hard Level Answers

1. 12 R3
2. 14 R12
3. 14 R7
4. 13 R0
5. 12 R12
6. 19 R3
7. 12 R32
8. 15 R5
9. 12 R12
10. 12 R24
11. 20 R30
12. 24 R0
13. 55 R9
14. 30 R10
15. 24 R12
16. 80 R0
17. 33 R39
18. 47 R22
19. 40 R60
20. 30 R0

Now, let’s practice these questions and remember, it’s okay to make mistakes. They help us learn! Happy dividing!