Class 4 — Mathematics

Multiplication by 2- and 3-Digit Numbers

Class 4

✓By the end of this lesson students will be able to multiply a 2-digit number by a 2-digit number.
✓By the end of this lesson students will be able to multiply a 3-digit number by a 2-digit number.
✓By the end of this lesson students will be able to multiply a 3-digit number by a 3-digit number.
✓By the end of this lesson students will be able to solve word problems involving multiplication by 2- and 3-digit numbers.

Key concepts

Multiplication by a 2-Digit Number

To multiply a number by a 2-digit number, we break down the multiplier into its ones and tens place values. First, we multiply the multiplicand by the digit in the ones place of the multiplier. This gives us the first partial product. Next, we multiply the multiplicand by the digit in the tens place of the multiplier. Remember to place a zero (0) in the ones place before writing this product, as we are multiplying by tens. This gives us the second partial product. Finally, we add these two partial products to get the final product.

Multiplication by a 3-Digit Number

To multiply a number by a 3-digit number, we extend the method used for 2-digit multipliers. We break down the multiplier into its ones, tens, and hundreds place values. First, multiply the multiplicand by the digit in the ones place. This is the first partial product. Second, multiply the multiplicand by the digit in the tens place. Place a zero (0) in the ones place before writing this product. This is the second partial product. Third, multiply the multiplicand by the digit in the hundreds place. Place two zeros (00) in the ones and tens places before writing this product. This is the third partial product. Finally, add all three partial products to find the final product.

Partial Products

When we multiply by a multi-digit number, we multiply the multiplicand by each digit of the multiplier separately, considering its place value. The results obtained from these individual multiplications are called partial products. These partial products are then added together to get the final product.

Key facts to remember

1Multiplication is a shortcut for repeated addition.
2The product of any number and 0 is 0.
3The product of any number and 1 is the number itself.
4When multiplying by a 2-digit number, first multiply by the ones digit, then by the tens digit (placing a zero in the ones place), and then add the partial products.
5When multiplying by a 3-digit number, first multiply by the ones digit, then by the tens digit (placing one zero), then by the hundreds digit (placing two zeros), and then add all the partial products.
6Correct alignment of digits according to their place value is crucial for accurate multiplication.
7Carrying over is an important step in multi-digit multiplication.

Worked examples

Example 1

Multiply: 45 × 23

IStep 1: Multiply 45 by the ones digit of the multiplier (3).

II 45

III x 3

IV -----

V 135 (First partial product: 45 × 3)

VIStep 2: Multiply 45 by the tens digit of the multiplier (2, which represents 20). Place a zero in the ones place.

VII 45

VIII x 20

9 -----

10 900 (Second partial product: 45 × 20)

11Step 3: Add the partial products.

12 135

13 + 900

14 -----

15 1035

16Therefore, 45 × 23 = 1035.

Answer

1035

Remember to carry over digits when multiplying and adding.

Example 2

Find the product of 234 and 21.

IStep 1: Multiply 234 by the ones digit of the multiplier (1).

II 234

III x 1

IV -----

V 234 (First partial product: 234 × 1)

VIStep 2: Multiply 234 by the tens digit of the multiplier (2, which represents 20). Place a zero in the ones place.

VII 234

VIII x 20

9 -----

10 4680 (Second partial product: 234 × 20)

11Step 3: Add the partial products.

12 234

13 + 4680

14 ------

15 4914

16Thus, 234 × 21 = 4914.

Answer

4914

Always align the digits carefully according to their place values.

Example 3

Multiply: 123 × 105

IStep 1: Multiply 123 by the ones digit of the multiplier (5).

II 123

III x 5

IV -----

V 615 (First partial product: 123 × 5)

VIStep 2: Multiply 123 by the tens digit of the multiplier (0, which represents 00). Place a zero in the ones place.

VII 123

VIII x 00

9 -----

10 000 (Second partial product: 123 × 00)

11Step 3: Multiply 123 by the hundreds digit of the multiplier (1, which represents 100). Place two zeros in the ones and tens places.

12 123

13 x 100

14 -----

15 12300 (Third partial product: 123 × 100)

16Step 4: Add all the partial products.

17 615

18 000

19 + 12300

20 -------

21 12915

22Hence, 123 × 105 = 12915.

Answer

12915

Multiplying by zero in any place value will result in zero for that partial product, but it is important to maintain place value alignment.

Common mistakes

✗Forgetting to place the zero (or zeros) as a placeholder when multiplying by the tens or hundreds digit.
✗Incorrectly carrying over digits during the multiplication steps or when adding the partial products.
✗Making errors in basic multiplication facts (tables).
✗Misaligning the partial products, leading to incorrect addition.
✗Adding the partial products incorrectly, especially when there are many digits.

Exam tips

★Memorise your multiplication tables up to 10 or 12 to perform calculations quickly and accurately.
★Always write digits clearly and align them properly according to their place value to avoid confusion.
★Double-check your basic multiplication facts and the addition of partial products before finalising your answer.
★Practice multi-digit multiplication regularly to improve your speed and accuracy.

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