Year 5 Maths: Decimal Division with a Remainder

Understanding Decimal Division with a Remainder

Hello Year 5! Today we are going to learn about decimal division with a remainder. This is a way of dividing numbers that aren’t whole (like 1.5 or 2.3) and can sometimes leave us with extra bits, called a remainder. Let’s break it down step by step.

What is Division?

First, let’s remember what division is. When we divide, we are splitting something into equal parts. For example, if you have 10 sweets and you want to share them with 2 friends, you would do:

$$

10 \div 2 = 5

$$

This means each friend gets 5 sweets.

What Happens with Decimals?

Now, sometimes we have to divide decimal numbers. Let’s say we want to divide 5.6 by 2.

Example:

$$

5.6 \div 2

$$

Steps to Divide Decimals:

1. Ignore the Decimal for Now: Think of 5.6 as 56 (but remember to place the decimal back later).
2. Do the Division: Now divide 56 by 2. $$56 \div 2 = 28$$
3. Add the Decimal Back: Since we took the decimal out, we need to put it back. Since there is one number after the decimal in 5.6, we add it back to make it: $$2.8$$

What is a Remainder?

Sometimes when we divide, we might not get a whole number. This is where the remainder comes in. A remainder is what’s left over when we can’t divide evenly.

Example:

If we divide 5.7 by 2:

1. Ignore the Decimal: Think of it as 57.
2. Do the Division: $$57 \div 2 = 28 \text{ remainder } 1$$ (because 2 goes into 57 twenty-eight times and leaves 1 left over).
3. Add the Decimal Back:
   • Since we have 1 remaining, we need to express that as a decimal.
   • We’ll put the remainder over the divisor:
   $$5.7 \div 2 = 2.8 \text{ remainder } 1$$
   • To express this as a decimal, we can also do:
   $$5.7 \div 2 = 2.85$$

Key Rules for Decimal Division with a Remainder

1. Ignore the Decimal: Divide the numbers as if they are whole numbers.
2. Remember the Decimal: Bring back the decimal point in your answer.
3. Identify Remainders: If you can’t divide evenly, note the remainder.
4. Convert Remainders: Optionally, convert the remainder into a decimal.

Tips and Tricks

• Practice makes perfect! The more you practice, the easier it will get.
• Write down your steps clearly to avoid mistakes.
• Use a number line if you’re struggling to visualise the division.

Questions for Practice

Easy Level

1. $$1.2 \div 2 = ?$$
2. $$3.4 \div 1 = ?$$
3. $$4.5 \div 5 = ?$$
4. $$6.6 \div 3 = ?$$
5. $$10.0 \div 5 = ?$$
6. $$5.5 \div 1 = ?$$
7. $$7.4 \div 2 = ?$$
8. $$8.8 \div 4 = ?$$
9. $$9.9 \div 3 = ?$$
10. $$2.0 \div 2 = ?$$

Medium Level

11. $$4.8 \div 2 = ?$$
12. $$5.9 \div 3 = ?$$
13. $$6.1 \div 2 = ?$$
14. $$7.5 \div 4 = ?$$
15. $$8.4 \div 2 = ?$$
16. $$10.5 \div 3 = ?$$
17. $$5.7 \div 2 = ?$$
18. $$2.6 \div 2 = ?$$
19. $$9.1 \div 3 = ?$$
20. $$3.3 \div 1 = ?$$

Hard Level

21. $$12.5 \div 4 = ?$$
22. $$15.3 \div 3 = ?$$
23. $$19.8 \div 5 = ?$$
24. $$20.6 \div 6 = ?$$
25. $$25.9 \div 4 = ?$$
26. $$30.2 \div 5 = ?$$
27. $$40.4 \div 8 = ?$$
28. $$50.7 \div 3 = ?$$
29. $$60.5 \div 4 = ?$$
30. $$75.1 \div 7 = ?$$

Answers and Explanations

Easy Level Answers

1. $$0.6$$
2. $$3.4$$
3. $$0.9$$
4. $$2.2$$
5. $$2.0$$
6. $$5.5$$
7. $$3.7$$
8. $$2.2$$
9. $$3.3$$
10. $$1.0$$

Medium Level Answers

11. $$2.4$$
12. $$1.97$$ (1 remainder 2)
13. $$3.05$$
14. $$1.875$$ (1 remainder 1)
15. $$4.2$$
16. $$3.5$$
17. $$2.85$$ (2 remainder 1)
18. $$1.3$$
19. $$3.03$$
20. $$3.3$$

Hard Level Answers

21. $$3.125$$
22. $$5.1$$
23. $$3.96$$
24. $$3.43$$
25. $$6.475$$ (6 remainder 3)
26. $$6.04$$
27. $$5.05$$
28. $$16.9$$
29. $$15.125$$
30. $$10.5$$

Great job today, Year 5! Remember to keep practicing your decimal division with remainders!