Year 6 Maths: Long Multiplication

What is Long Multiplication?

Long multiplication is a method we use to multiply larger numbers. It helps us to break down the multiplication into smaller, more manageable steps, making it easier to find the answer.

How Do We Do Long Multiplication?

Let’s say we want to multiply 23 by 5. Here’s how we can do it step by step:

1. Write the Numbers: Write the larger number on top (23) and the smaller number below it (5), aligning them to the right. 23 x 5
2. Multiply the Bottom Number by Each Digit of the Top Number:
   • First, multiply 5 by the digit in the ones place of the top number (3).
     • (5 \times 3 = 15)
   • Write down the 5, carry over the 1 (the 10 from 15).
   • Next, multiply 5 by the digit in the tens place of the top number (2).
     • (5 \times 2 = 10) and add the carried-over 1.
     • (10 + 1 = 11)
   Now, write down your answer: 23 x 5 ----- 115

Example with Two-Digit Numbers

Let’s try a bigger example: multiply 34 by 12.

1. Write the Numbers: 34 x 12
2. Multiply the Bottom Right Digit (2) by Each Digit of the Top Number:
   • (2 \times 4 = 8)
   • (2 \times 3 = 6)
   So, we write down 68: 34 x 12 ------ 68 (This is 34 x 2)
3. Now Multiply the Bottom Left Digit (1) by Each Digit of the Top Number:
   • Don’t forget it’s actually 10, so we need to add a zero to the end of this line.
   • (1 \times 4 = 4)
   • (1 \times 3 = 3)
   This gives us: 34 x 12 ------ 68 (This is 34 x 2) 340 (This is 34 x 10)
4. Add the Two Results Together: 68 + 340 ------ 408

So, (34 \times 12 = 408).

Key Rules for Long Multiplication

1. Align Numbers: Always write numbers in a column, aligned to the right.
2. Multiply from Right to Left: Start with the ones place and move to the left.
3. Carry Over: If a multiplication gives you a number greater than 9, carry over the extra to the next digit.
4. Add Carefully: When you add your results, make sure to line them up properly.

Tips and Tricks

• Practice: The more you practice, the easier it will become.
• Use Graph Paper: This can help keep your numbers in line.
• Check Your Work: If you have time, go back and check your multiplication and addition.

Practice Questions

Easy Level Questions

1. (12 \times 3 = ?)
2. (15 \times 4 = ?)
3. (22 \times 2 = ?)
4. (30 \times 1 = ?)
5. (10 \times 5 = ?)
6. (8 \times 9 = ?)
7. (25 \times 2 = ?)
8. (14 \times 3 = ?)
9. (11 \times 4 = ?)
10. (6 \times 7 = ?)
11. (5 \times 10 = ?)
12. (9 \times 5 = ?)
13. (4 \times 6 = ?)
14. (3 \times 8 = ?)
15. (2 \times 11 = ?)
16. (1 \times 13 = ?)
17. (7 \times 5 = ?)
18. (4 \times 9 = ?)
19. (8 \times 3 = ?)
20. (6 \times 4 = ?)

Medium Level Questions

1. (24 \times 3 = ?)
2. (15 \times 12 = ?)
3. (32 \times 5 = ?)
4. (18 \times 6 = ?)
5. (21 \times 7 = ?)
6. (13 \times 11 = ?)
7. (14 \times 9 = ?)
8. (27 \times 4 = ?)
9. (36 \times 3 = ?)
10. (25 \times 6 = ?)
11. (22 \times 5 = ?)
12. (30 \times 8 = ?)
13. (19 \times 7 = ?)
14. (17 \times 6 = ?)
15. (12 \times 15 = ?)
16. (15 \times 14 = ?)
17. (16 \times 9 = ?)
18. (20 \times 11 = ?)
19. (28 \times 2 = ?)
20. (38 \times 3 = ?)

Hard Level Questions

1. (46 \times 24 = ?)
2. (58 \times 32 = ?)
3. (76 \times 19 = ?)
4. (89 \times 11 = ?)
5. (63 \times 24 = ?)
6. (54 \times 36 = ?)
7. (47 \times 25 = ?)
8. (65 \times 43 = ?)
9. (72 \times 29 = ?)
10. (82 \times 12 = ?)
11. (34 \times 56 = ?)
12. (91 \times 14 = ?)
13. (78 \times 19 = ?)
14. (64 \times 33 = ?)
15. (83 \times 22 = ?)
16. (12 \times 144 = ?)
17. (97 \times 15 = ?)
18. (38 \times 27 = ?)
19. (49 \times 36 = ?)
20. (56 \times 48 = ?)

Answers and Explanations

Easy Level Answers

1. (36)
2. (60)
3. (44)
4. (30)
5. (50)
6. (72)
7. (50)
8. (42)
9. (44)
10. (42)
11. (50)
12. (45)
13. (24)
14. (24)
15. (22)
16. (13)
17. (35)
18. (36)
19. (24)
20. (24)

Medium Level Answers

1. (72)
2. (180)
3. (160)
4. (108)
5. (147)
6. (143)
7. (126)
8. (108)
9. (108)
10. (150)
11. (110)
12. (240)
13. (133)
14. (102)
15. (180)
16. (210)
17. (144)
18. (220)
19. (56)
20. (114)

Hard Level Answers

1. (1104)
2. (1856)
3. (1444)
4. (979)
5. (1512)
6. (1944)
7. (1175)
8. (2795)
9. (2088)
10. (984)
11. (1904)
12. (1872)
13. (1482)
14. (2112)
15. (1826)
16. (1728)
17. (1455)
18. (1026)
19. (1764)
20. (2688)

Feel free to ask questions if you have any doubts or need further explanations! Happy multiplying!