Year 5 Maths: Multiplication with Decimals

Introduction to Multiplication with Decimals

Hello, Year 5! Today, we’re going to learn about multiplication with decimals. This is an important skill that will help you in your everyday life, like when you’re shopping or cooking.

What are Decimals?

Decimals are numbers that have a whole part and a fractional part, separated by a decimal point. For example, in the number 3.5, 3 is the whole number and .5 is the decimal part.

How to Multiply Decimals

Multiplying decimals is very similar to multiplying whole numbers. Here’s a step-by-step guide:

1. Ignore the Decimal Points: Start by multiplying the numbers as if they are whole numbers. For example, if you want to multiply 2.5 and 3, first consider them as 25 and 3.
2. Count the Decimal Places: Next, count how many decimal places are in the numbers you are multiplying. In our example, 2.5 has 1 decimal place, and 3 has 0 decimal places. So, that’s a total of 1 decimal place.
3. Multiply the Whole Numbers: Now, multiply the numbers without the decimals: $$25 \times 3 = 75$$
4. Place the Decimal: Finally, put the decimal point back in the answer. Since we counted 1 decimal place earlier, we move the decimal point 1 place to the left in 75. So, the answer is 7.5.

Example

Let’s practice with another example:

Multiply 1.2 and 0.5.

1. Ignore the decimals: 12 and 5.
2. Count the decimal places: 1.2 has 1 decimal place and 0.5 has 1 decimal place. Total is 2.
3. Multiply: $$12 \times 5 = 60$$
4. Place the decimal: Move the decimal 2 places to the left in 60, so the answer is 0.60 or just 0.6.

Key Rules

• Always multiply the numbers as if they are whole numbers first.
• Count the total number of decimal places in both numbers.
• After multiplying, put the decimal point back in the correct place.

Tips and Tricks

• Use Grids or Place Value Charts: Visual aids can help you keep track of where to place the decimal.
• Practice with Money: Think of prices in pounds and pence. This can make it easier to understand how decimals work.
• Check Your Work: Always double-check your calculations to see if the decimal point is in the right place.

Questions

Easy Level Questions

1. What is (0.2 \times 0.3)?
2. What is (1.5 \times 2)?
3. What is (0.4 \times 1.1)?
4. What is (0.6 \times 0.5)?
5. What is (3.0 \times 0.2)?
6. What is (2.5 \times 0.4)?
7. What is (0.9 \times 0.1)?
8. What is (0.7 \times 2)?
9. What is (1.0 \times 3.5)?
10. What is (0.3 \times 0.2)?
11. What is (4.0 \times 0.5)?
12. What is (0.8 \times 0.4)?
13. What is (1.2 \times 1)?
14. What is (0.5 \times 0.6)?
15. What is (0.1 \times 0.3)?
16. What is (2.0 \times 0.3)?
17. What is (0.4 \times 2)?
18. What is (1.5 \times 0.2)?
19. What is (0.6 \times 1.0)?
20. What is (0.3 \times 1.2)?

Medium Level Questions

1. What is (2.5 \times 1.4)?
2. What is (0.75 \times 1.2)?
3. What is (3.5 \times 0.6)?
4. What is (1.8 \times 2.2)?
5. What is (0.9 \times 0.7)?
6. What is (2.4 \times 3.5)?
7. What is (0.6 \times 0.8)?
8. What is (1.5 \times 0.4)?
9. What is (4.2 \times 0.3)?
10. What is (0.5 \times 2.4)?
11. What is (3.3 \times 0.2)?
12. What is (0.9 \times 1.5)?
13. What is (2.0 \times 1.3)?
14. What is (1.2 \times 0.9)?
15. What is (0.4 \times 3.2)?
16. What is (1.6 \times 1.1)?
17. What is (0.8 \times 2.5)?
18. What is (2.1 \times 0.5)?
19. What is (0.5 \times 1.6)?
20. What is (1.0 \times 1.8)?

Hard Level Questions

1. What is (2.75 \times 0.6)?
2. What is (1.25 \times 3.2)?
3. What is (4.5 \times 0.8)?
4. What is (3.6 \times 1.3)?
5. What is (0.56 \times 0.75)?
6. What is (2.3 \times 0.4)?
7. What is (1.1 \times 2.5)?
8. What is (5.5 \times 0.2)?
9. What is (2.0 \times 1.85)?
10. What is (3.3 \times 0.9)?
11. What is (0.75 \times 0.4)?
12. What is (1.9 \times 2.1)?
13. What is (0.45 \times 0.6)?
14. What is (3.0 \times 3.3)?
15. What is (1.4 \times 2.25)?
16. What is (0.2 \times 4.5)?
17. What is (3.7 \times 1.9)?
18. What is (2.9 \times 0.3)?
19. What is (4.4 \times 2.0)?
20. What is (5.1 \times 0.4)?

Answers and Explanations

Easy Level Answers

1. (0.06)
2. (3.0)
3. (0.44)
4. (0.30)
5. (0.60)
6. (1.00)
7. (0.09)
8. (1.4)
9. (3.5)
10. (0.06)
11. (2.0)
12. (0.32)
13. (1.2)
14. (0.30)
15. (0.03)
16. (0.60)
17. (0.8)
18. (0.30)
19. (0.60)
20. (0.36)

Medium Level Answers

1. (3.50)
2. (0.90)
3. (2.10)
4. (3.96)
5. (0.63)
6. (8.40)
7. (0.48)
8. (0.60)
9. (1.26)
10. (1.20)
11. (0.66)
12. (1.35)
13. (2.60)
14. (1.08)
15. (1.28)
16. (1.76)
17. (2.00)
18. (0.80)
19. (0.80)
20. (1.80)

Hard Level Answers

1. (1.65)
2. (4.00)
3. (3.60)
4. (4.68)
5. (0.42)
6. (0.92)
7. (2.75)
8. (1.10)
9. (3.70)
10. (2.97)
11. (0.30)
12. (3.99)
13. (0.27)
14. (9.90)
15. (3.15)
16. (0.90)
17. (7.03)
18. (0.87)
19. (8.80)
20. (2.04)

Happy multiplying, Year 5! Remember, practice makes perfect!