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, $$23 \times 45 = 1035$$!

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!