Year 5 Maths: Long Multiplication

Hello Year 5! Today, we’re going to learn about long multiplication. This is a method we use to multiply larger numbers together. Let’s break it down step by step.

What is Long Multiplication?

Long multiplication is a way to multiply numbers that have more than one digit. It helps us when the numbers get bigger than what we can easily multiply in our heads.

Step-by-Step Guide

1. Write the Numbers Down: Write the bigger number on top and the smaller number underneath it. Make sure to line them up by their rightmost digits.Example: 23 x 45
2. Multiply the Bottom Number: Start with the digit on the right of the bottom number. Multiply this digit by each digit of the top number, starting from the right.For example:
   • Multiply 5 (from 45) by 3 (from 23): $$5 \times 3 = 15$$ . Write down 5 and carry over 1.
   • Multiply 5 by 2 (from 23): $$5 \times 2 = 10$$ . Add the carried over 1: $$10 + 1 = 11$$ . Write down 11.
   Your work will look like this: 23 x 45 _______ 115 (this is 23 multiplied by 5)
3. Move to the Next Digit: Now move to the next digit on the bottom number (4 in this case), but remember it’s actually 40 because it’s in the tens place. So, we treat it as 4 and remember to add a zero at the end.
   • Multiply 4 by 3: $$4 \times 3 = 12$$ . Write down 2 and carry over 1.
   • Multiply 4 by 2: $$4 \times 2 = 8$$ . Add the carried over 1: $$8 + 1 = 9$$ .
   Your work will now look like this: 23 x 45 _______ 115 + 920 (this is 23 multiplied by 40)
4. Add the Results Together: Now, add the two results together.
   • Add 115 and 920:
   115 + 920 _______ 1035

So,

Key Rules

• Always multiply from the right to the left.
• Don’t forget to add a zero for the next digit in the tens place.
• Carry over any extra numbers when multiplying.

Tips and Tricks

• Practice multiplication tables to make multiplying easier.
• Write clearly and neatly to avoid mistakes.
• Double-check your work by estimating the answer before you calculate.

Questions on Long Multiplication

Easy Level (20 Questions)

1. $$12 \times 3$$
2. $$14 \times 2$$
3. $$11 \times 4$$
4. $$15 \times 5$$
5. $$20 \times 6$$
6. $$23 \times 2$$
7. $$30 \times 3$$
8. $$22 \times 2$$
9. $$10 \times 9$$
10. $$18 \times 1$$
11. $$24 \times 3$$
12. $$16 \times 2$$
13. $$13 \times 4$$
14. $$25 \times 4$$
15. $$21 \times 5$$
16. $$12 \times 6$$
17. $$19 \times 2$$
18. $$14 \times 3$$
19. $$15 \times 2$$
20. $$11 \times 5$$

Medium Level (20 Questions)

1. $$23 \times 12$$
2. $$34 \times 13$$
3. $$45 \times 21$$
4. $$56 \times 14$$
5. $$64 \times 15$$
6. $$72 \times 16$$
7. $$81 \times 11$$
8. $$22 \times 19$$
9. $$31 \times 23$$
10. $$40 \times 25$$
11. $$50 \times 18$$
12. $$35 \times 24$$
13. $$27 \times 23$$
14. $$66 \times 12$$
15. $$55 \times 11$$
16. $$41 \times 17$$
17. $$36 \times 15$$
18. $$43 \times 22$$
19. $$12 \times 34$$
20. $$24 \times 31$$

Hard Level (20 Questions)

1. $$123 \times 45$$
2. $$156 \times 32$$
3. $$234 \times 21$$
4. $$345 \times 12$$
5. $$412 \times 24$$
6. $$564 \times 13$$
7. $$678 \times 11$$
8. $$789 \times 15$$
9. $$842 \times 23$$
10. $$1023 \times 34$$
11. $$1234 \times 25$$
12. $$1456 \times 12$$
13. $$2345 \times 14$$
14. $$3456 \times 16$$
15. $$4567 \times 18$$
16. $$5678 \times 21$$
17. $$6789 \times 12$$
18. $$7890 \times 30$$
19. $$8901 \times 25$$
20. $$9012 \times 34$$

Answers and Explanations

Easy Level Answers

1. $$36$$
2. $$28$$
3. $$44$$
4. $$75$$
5. $$120$$
6. $$46$$
7. $$90$$
8. $$44$$
9. $$90$$
10. $$18$$
11. $$72$$
12. $$32$$
13. $$52$$
14. $$100$$
15. $$105$$
16. $$72$$
17. $$38$$
18. $$42$$
19. $$30$$
20. $$55$$

Medium Level Answers

1. $$276$$
2. $$442$$
3. $$945$$
4. $$784$$
5. $$960$$
6. $$1152$$
7. $$891$$
8. $$418$$
9. $$713$$
10. $$1000$$
11. $$900$$
12. $$840$$
13. $$621$$
14. $$792$$
15. $$605$$
16. $$697$$
17. $$612$$
18. $$946$$
19. $$408$$
20. $$744$$

Hard Level Answers

1. $$5535$$
2. $$4992$$
3. $$4914$$
4. $$4140$$
5. $$9908$$
6. $$7356$$
7. $$7467$$
8. $$11835$$
9. $$19366$$
10. $$34882$$
11. $$30850$$
12. $$17472$$
13. $$32830$$
14. $$55296$$
15. $$82326$$
16. $$119934$$
17. $$81468$$
18. $$236730$$
19. $$225025$$
20. $$306408$$

Now that you have learned about long multiplication, try solving the questions and see how well you can multiply! Remember, practice makes perfect!