Lesson 4: Multiply and Divide by a Double-Digit Number
Lesson 4: Multiply and Divide by a Double-Digit Number
Multiply and divide by two-digit numbers, step by step.
In this lesson you will learn and practice how to multiply any number by a double-digit number vertically.
For example, how to multiply 142 by 32.
You will also learn how to divide any number by a double-digit number using long division. For example, how to divide 345 by 21.
It is important to understand why place value of each digit within each number is important and why it is crucial to follow a certain form when performing operations in order to get the right answer.
In this lesson you will also discover division with a remainder.
A remainder is what is left when two numbers do not divide evenly. For example, 20 does not evenly divide by 9. The closes number to 20 that is divisible by 9 is 18. Thus, 20 ÷ 9 = 2 with remainder 2 (because 18 + 2 = 20).
You will also learn divisibility rules (indicators) and see why they are important. For example, how to tell just by looking at the last digit of a number if it is divisible by 2, 5 or 10, etc.
Key ideas: Multiply and Divide by a Double-Digit Number
To multiply by a two-digit number, multiply by the ones digit, then by the tens digit (put a 0 placeholder first), and add the two results.
Long division by a two-digit number uses the same steps (Divide, Multiply, Subtract, Bring down). Estimating with rounded numbers helps choose each digit of the quotient.
Worked examples
Example 1
Multiply 36 × 24.
- 36 × 4 = 144.
- 36 × 20 = 720.
- 144 + 720 = 864
Example 2
Multiply 47 × 53.
- 47 × 3 = 141 and 47 × 50 = 2350.
- 141 + 2350 = 2491
Example 3
Divide 864 ÷ 24.
- 86 ÷ 24 ≈ 3 (3 × 24 = 72). 86 − 72 = 14. Bring down 4: 144.
- 144 ÷ 24 = 6. Answer: 36
Example 4
Divide 1000 ÷ 32.
- 100 ÷ 32 = 3 (96), remainder 4. Bring down 0: 40 ÷ 32 = 1, remainder 8.
- 31 R8. Check: 31 × 32 + 8 = 1000 ✓
Common mistakes
- Forgetting the 0 placeholder when multiplying by the tens digit.
- Choosing a quotient digit that is too big (the product is larger than the number you are dividing).
Questions students ask
How can I check a division?
Multiply the quotient by the divisor and add the remainder.
Check your understanding
Practise with the Grade 6 quizzes. You’ll see right away if each answer is correct.