1. MULTIPLICATION 5 Multiplicand X 3 Multiplier 15 Product LET’S LEARN
Multiplication is an operation where the result is the total joining of equal groups.
The numbers you multiply are called factors of the product (answer). Refer to the illustration on the top right corner.
Multiplication can be written horizontally or vertically.

2. This means FOUR GROUPS OF TWO stars.
HORIZONTALLY
4 X 2
We say , “Four times two.”
This means FOUR GROUPS OF TWO stars.

3. 4 X 2 4 X 2 = 8 (FOUR GROUPS OF TWO) Let’s count the stars. 1 2 3 4 56 7 8
4 X 2 = 8

4. 3 X 3 HORIZONTALLY We say, “Three times three.”
This means THREE GROUPS OF THREE rabbits.

5. 3 X 3 3 X 3 = 9 (THREE GROUPS OF THREE) Let’s count the rabbits. 1 2 34 5 6 7 8 9
3 X 3 = 9

6. 8 X 1 VERTICALLY We say, “Eight times one.”
This means EIGHT GROUPS OF ONE cube.

7. 8 X 1 8 X1 (EIGHT GROUPS OF ONE) Let’s count the cubes. 1 2 3 4 5 6 7

8. PRACTICE
Complete the following exercises.
7 X 3 =
2 X 10 =
2 X 5 =

9. ANSWER
7 X 3 = 21
2 X 10 = 20
2 X 5 = 10

10. PRACTICE
Complete the following exercises.
3 X 4 =
1 X 9 =
8 X 2 =

11. ANSWER
3 X 4 = 12
1 X 9 = 9
8 X 2 = 16

12. MULTIPLYING BY ZERO IS EASY!
0 X 3 =
ZERO TIMES THREE MEANS ZERO GROUPS OF THREE.
ZERO GROUPS MEANS THERE ARE NO GROUPS. IF THERE ARE NO GROUPS, THEN THERE IS NOTHING. THEREFOR, THE ANSWER IS ZERO.
0 X 3 = 0
ZERO TIMES ANY NUMBER IS ZERO.
0 X = 0

13. 2 X 0 = 0 X 4 = 2 X 0 = 0 0 X 4 = 0 TWO TIMES ZERO OR
TWO GROUPS OF ZERO
0 X 4 =
ZERO TIMES FOUR
ZERO GROUPS OF FOUR
Observe that there is nothing inside the two groups.
2 X 0 = 0
Observe that there is no group to place four objects in.
0 X 4 = 0

14. PRACTICE
Complete the following exercises.
4 X 4 =
0 X 11 =
1 X 12 =

15. ANSWER
4 X 4 = 16
0 X 11 = 0
1 X 12 = 12

16. We can also use graph paper to multiply.

17. 2 X 3 = 3
OF THREE 2
GROUPS

18. Now we count the total amount of boxes enclosed.1 2 3 4 5 6
OF THREE 2
GROUPS
2 X 3 = 6

19. 3 X 4 = 3
GROUPS 4
OF FOUR

20. Now we count the total amount of boxes enclosed.1 2 3 4 5 6 7 8 9 10 11 12 3
GROUPS 4
OF FOUR
3 X 4 = 12

21. 2-DIGIT MULTIPLICATION
LET’S LEARN
When multiplying by two digits, align the last digits of both numbers vertically.
Hundreds
Tens
Ones 4 2 x 3

22. Begin multiplying the ones place value.
Hundreds
Tens
Ones 4 2 x 3 6
Continue multiplying the tens place value.
Hundreds
Tens
Ones 4 2 x 3 1 6 4 X 3 1 2

23. The result is:
Hundreds
Tens
Ones 4 2 x 3 1 6
REMINDER
ALWAYS CHECK YOUR ANSWER!

24. LET’S LEARN
Now we’ll multiply two 2-digit factors.
1st STEP
Hundreds
Tens
Ones 3 5 x 1 6
We begin with the ones place value of the bottom number. We multiply the 6 and ignore the 1 at the moment.

25. Hundreds Tens Ones Hundreds Tens Ones3 5 x 1 6 5 X 6 3
Carry the 3 to the tens place .
Hundreds
Tens
Ones 2 3 5 x 1 6 3 X 6 2 1 18 +3 21
Multiply the 6 to the three and add the 3 we carried.

26. 2nd STEP
Hundreds
Tens
Ones 3 5 x 1 6 2
We finished multiplying with the digit in the ones place. Now we continue multiplying with the digit in the tens place value, the 1. Before we begin, place a zero in the ones place value.
Now we multiply the 1 following the same steps.
Hundreds
Tens
Ones 3 5 x 1 6 2

27. Hundreds
Tens
Ones 3 5 x 1 6 2
Finally, we add the two products together.
Hundreds
Tens
Ones 3 5 x 1 6 2 +
The result is: 560

28. LET’S LEARN
Now we’ll see how to multiply a 3-digit factor by a 2-digit factor following the same steps. 6 3 8 7 4 X 5 9

29. 3 2 6 8 7 4 X 5 9
The final answer is: 3 2 6 8 7 4 X 5 9 + 1 1 1 ,

30. PRACTICE
Find the product. 3 6 X 7 4 8 X 5 2 8 2 X 3 6 5 7 1 X 9 2

31. ANSWER 3 6 X 7 2 5 4 8 X 5 2 9 6 , 8 2 X 3 6 9 5 5 7 1 X 9 2 3 , ,

32. LATTICE MULTIPLICATION
LET’S LEARN
Lattice multiplication is a method of multiplying large numbers using a grid. It is similar to regular long multiplication, but the lattice method breaks the multiplication process into smaller steps, which some students find easier.

33. 36 X 52 =
1st STEP
Draw a grid that has as many rows and columns as the multiplicand and the multiplier. The grid shown here is for multiplying a 2-digit number by a 2-digit number.

34. 36 X 52 =
2nd STEP
Next, draw a diagonal through each box from upper right corner to lower left corner. Continue the line a short way past the grid.

35. 36 X 52 =
3rd STEP
Write one factor across the top and the other down the right side, lining up the digits with the boxes. 5 2

36. 36 X 52 =
4th STEP
Fill in each square of the grid with the product of the digits above and to its right, recording the products so that the tens are in the upper (diagonal) half of the square and the ones are in the lower half.
If the product does not have a tens digit, record a zero in that triangle. 5 2 1 3 5

37. 36 X 52 =
Continue multiplying the other digit 5 2 1 3 5 1 6 2

38. 36 X 52 =
5th STEP
Now add the numbers in the grid along the diagonals, starting from the lower right corner. Carry any tens into the top of the next diagonal. 5 2 1 3 1 5 1 6 2 8 7 2

39. 36 X 52 =
6th STEP
To say the answer, read the digits starting down the left of the grid and continuing across the bottom. 5 2 1 3 1 5 1 6 2 8 7 2
Here, the answer is 1,872.

40. NOW WE ARE READY TO PRACTICE AND ENJOY MULTIPLYING!