Introduction to Division with Decimals

Hello, Year 5! Today, we are going to learn about division with decimals. Don’t worry; it’s easier than it sounds!

What is Division?

Division is when we split something into equal parts. For example, if we have 12 sweets and we want to share them between 3 friends, each friend gets 4 sweets.

What are Decimals?

Decimals are numbers that have a whole number part and a fraction part. For example, in the number 4.5, the 4 is the whole number, and the 0.5 is the decimal part.

Why Do We Use Decimals in Division?

Sometimes, when we divide, we might not get a whole number. For example, if we divide 5 by 2, we get 2.5. This means each person gets 2.5 when we share 5 between 2 people.

How to Divide with Decimals

Let’s break down the steps for dividing with decimals:

Step 1: Set Up the Division

Write the division like this:

$$

\text{Dividend} \div \text{Divisor}

$$

For example, if we want to divide 4.5 by 1.5, it looks like this:

$$

4.5 \div 1.5

$$

Step 2: Remove the Decimals

To make it easier, we can remove the decimals by multiplying both numbers by 10, 100, or another power of 10. This makes them whole numbers.

So, for our example:

$$

4.5 \times 10 = 45

$$

$$

1.5 \times 10 = 15

$$

Now, our division looks like this:

$$

45 \div 15

$$

Step 3: Perform the Division

Now, just divide like normal:

$$

45 \div 15 = 3

$$

Step 4: Write the Decimal Back In

Since we multiplied by 10, our answer is still 3.0, but we can simply write it as 3.

Key Rules for Division with Decimals

  1. Make Whole Numbers: Always try to remove the decimals for easier division.
  2. Multiply Both: Remember to multiply both the dividend and the divisor by the same power of 10.
  3. Keep it Neat: Write down your steps neatly to avoid mistakes.

Tips and Tricks

  • Practice makes perfect! The more you practice, the easier it gets.
  • Use a calculator if you’re unsure, but always try to do it by hand first.
  • Check your work! After you get an answer, multiply it back by the divisor to see if you get the original number.

Questions

Easy Level

  1. $3.6 \div 1.2 = ?$
  2. $7.5 \div 2.5 = ?$
  3. $5.0 \div 2.0 = ?$
  4. $4.8 \div 1.6 = ?$
  5. $6.4 \div 0.8 = ?$
  6. $9.0 \div 3.0 = ?$
  7. $8.4 \div 2.1 = ?$
  8. $2.4 \div 0.4 = ?$
  9. $5.6 \div 1.4 = ?$
  10. $10.0 \div 5.0 = ?$
  11. $2.4 \div 1.2 = ?$
  12. $1.5 \div 0.5 = ?$
  13. $3.3 \div 1.1 = ?$
  14. $4.0 \div 0.5 = ?$
  15. $6.0 \div 3.0 = ?$
  16. $8.8 \div 4.4 = ?$
  17. $3.0 \div 1.5 = ?$
  18. $7.2 \div 2.4 = ?$
  19. $9.6 \div 3.2 = ?$
  20. $5.2 \div 1.0 = ?$

Medium Level

  1. $6.3 \div 0.9 = ?$
  2. $8.1 \div 2.7 = ?$
  3. $7.5 \div 1.5 = ?$
  4. $4.9 \div 0.7 = ?$
  5. $5.5 \div 1.1 = ?$
  6. $9.8 \div 0.2 = ?$
  7. $12.6 \div 3.0 = ?$
  8. $15.2 \div 4.0 = ?$
  9. $10.5 \div 2.1 = ?$
  10. $11.0 \div 0.5 = ?$
  11. $14.4 \div 3.6 = ?$
  12. $16.8 \div 2.4 = ?$
  13. $18.0 \div 6.0 = ?$
  14. $20.0 \div 10.0 = ?$
  15. $22.5 \div 2.5 = ?$
  16. $24.0 \div 8.0 = ?$
  17. $25.0 \div 5.0 = ?$
  18. $27.0 \div 1.5 = ?$
  19. $30.0 \div 3.0 = ?$
  20. $28.8 \div 4.8 = ?$

Hard Level

  1. $7.25 \div 0.25 = ?$
  2. $9.75 \div 0.15 = ?$
  3. $14.4 \div 2.4 = ?$
  4. $18.9 \div 3.3 = ?$
  5. $22.5 \div 1.5 = ?$
  6. $33.0 \div 0.3 = ?$
  7. $45.6 \div 3.6 = ?$
  8. $56.0 \div 0.8 = ?$
  9. $78.4 \div 1.6 = ?$
  10. $81.0 \div 9.0 = ?$
  11. $99.9 \div 9.9 = ?$
  12. $150.0 \div 15.0 = ?$
  13. $200.0 \div 20.0 = ?$
  14. $250.5 \div 5.5 = ?$
  15. $300.0 \div 30.0 = ?$
  16. $360.0 \div 12.0 = ?$
  17. $420.0 \div 21.0 = ?$
  18. $480.0 \div 24.0 = ?$
  19. $540.0 \div 18.0 = ?$
  20. $600.0 \div 60.0 = ?$

Answers

Easy Level Answers:

  1. 3.0
  2. 3.0
  3. 2.5
  4. 3.0
  5. 8.0
  6. 3.0
  7. 4.0
  8. 6.0
  9. 4.0
  10. 2.0
  11. 2.0
  12. 3.0
  13. 3.0
  14. 8.0
  15. 2.0
  16. 2.0
  17. 2.0
  18. 3.0
  19. 3.0
  20. 5.2

Medium Level Answers:

  1. 7.0
  2. 3.0
  3. 5.0
  4. 7.0
  5. 5.0
  6. 49.0
  7. 4.2
  8. 3.8
  9. 5.0
  10. 22.0
  11. 4.0
  12. 3.0
  13. 5.0
  14. 40.0
  15. 9.0
  16. 7.0
  17. 20.0
  18. 18.0
  19. 10.0
  20. 6.0

Hard Level Answers:

  1. 29.0
  2. 65.0
  3. 6.0
  4. 5.7
  5. 15.0
  6. 110.0
  7. 12.6
  8. 70.0
  9. 49.0
  10. 9.0
  11. 10.0
  12. 10.0
  13. 10.0
  14. 45.5
  15. 10.0
  16. 30.0
  17. 20.0
  18. 20.0
  19. 30.0
  20. 10.0

Now you have a good understanding of division with decimals! Keep practising, and you will become a pro in no time!