Multiplication facts and multi-digit multiplication

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Lesson notes

What is Multiplication?

Multiplication is a quick way to add the same number many times. For example, 4 × 3 means 3 + 3 + 3 + 3 = 12.
The × sign is called the multiplication sign. The numbers you multiply are called factors, and the answer is the product.
You can show multiplication with an array – objects arranged in rows and columns. For example, 3 rows of 4 dots is 3 × 4 = 12.
Multiplication can also compare amounts: “4 times as many” means multiply by 4. If you have 5 apples and your friend has 4 times as many, your friend has 5 × 4 = 20 apples.
The order of factors does not change the product. This is the commutative property: 4 × 3 = 3 × 4 = 12.

Multiplication Facts Up to 12 × 12

You should memorize the multiplication table (also called times table) for numbers 1 to 12. It shows all products like 7 × 8 = 56.
The table is symmetric: 7 × 8 = 8 × 7, so you only need to learn half of it.
Multiplying by 0 always gives 0: 0 × 9 = 0.
Multiplying by 1 gives the same number: 1 × 6 = 6. This is the identity property.
Multiplying by 10 is easy: just put a 0 at the end. For example, 4 × 10 = 40.
Practice with flashcards or games to recall facts quickly and correctly.

Multiplying Three Numbers

You can multiply three numbers together, like 2 × 3 × 4.
The order does not matter, so you can group any two first. For example, (2 × 3) × 4 = 6 × 4 = 24, and 2 × (3 × 4) = 2 × 12 = 24.
This is called the associative property of multiplication.
When you see a multiplication with three factors, just multiply two at a time.

Multiplying by 10 and 100

When you multiply a number by 10, each digit moves one place to the left. For example, 35 × 10 = 350.
When you multiply by 100, each digit moves two places to the left. For example, 35 × 100 = 3500.
You can think of it as adding zeros: × 10 adds one zero, × 100 adds two zeros.
This works because our number system is base-ten – each place value is ten times bigger than the one to its right.
Dividing by 10 or 100 moves digits to the right: 350 ÷ 10 = 35, and 3500 ÷ 100 = 35.

Multiplying a Two-Digit or Three-Digit Number by a One-Digit Number

Use the formal written method (also called the column method) to multiply bigger numbers.
Write the one-digit number under the ones place of the bigger number. For example, to do 23 × 4, write 4 under the 3.
Multiply the ones digit first: 3 × 4 = 12. Write 2 in the ones place and carry the 1 to the tens column.
Then multiply the tens digit: 2 × 4 = 8, and add the carried 1 to get 9. So 23 × 4 = 92.
For three-digit numbers, do the same: multiply ones, then tens, then hundreds, carrying as needed. For example, 123 × 3: 3×3=9 (ones), 2×3=6 (tens), 1×3=3 (hundreds), so 123 × 3 = 369.
Always check your answer by estimating or using repeated addition.

Patterns in the Multiplication Table

The multiplication table has patterns that help you memorize facts.
For multiples of 2, 4, 6, and 8, the ones digits follow a repeating pattern. For example, multiples of 2 end in 2, 4, 6, 8, 0.
Multiples of 5 always end in 0 or 5.
Multiples of 9 have a neat trick: the digits add up to 9. For example, 9 × 3 = 27, and 2 + 7 = 9.
Multiples of 10 always end in 0.
You can use these patterns to check your answers or to find a fact you forgot.

Solving Word Problems with Multiplication

Read the problem carefully and look for words like “times”, “each”, “per”, or “product” – they often mean multiply.
If a problem says “4 times as many”, multiply the original amount by 4.
If you have groups of equal size, multiply the number of groups by the size of each group. For example, 5 bags with 6 apples each: 5 × 6 = 30 apples.
Draw a picture or an array to help you see the problem.
Write a number sentence and solve it. Then check that your answer makes sense.

Why Memorize Multiplication Facts?

Knowing your times tables up to 12 × 12 makes math faster and easier.
It helps you with bigger multiplication, division, fractions, and many real-life problems.
Memorizing facts is like learning a new language – practice a little every day.
Use tricks, songs, or patterns to make memorizing fun.
Once you know the facts, you can solve problems without counting on your fingers.

Slides

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Practice questions

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1.What is 7 × 8?
Easy
- A56
- B54
- C48
- D64
2.Which of these is the same as 9 × 6?
Easy
- A6 × 9
- B9 + 6
- C9 × 9
- D6 × 6
3.The product of any number and 1 is that number itself.
Easy
True or false?
4.What is 23 × 4?
Medium
- A92
- B82
- C102
- D72
5.Which of these is the correct product of 345 × 6?
Medium
- A2070
- B207
- C20700
- D20070
6.Which of the following are equal to 3 × 4 × 2? (select all that apply)
Medium
- A24
- B4 × 3 × 2
- C2 × 4 × 3
- D3 × 4
- E12 × 2
7.Match each multiplication fact to its product.
Easy
- 6 × 7
- 8 × 9
- 5 × 12
- 42
- 72
- 60
8.Put these numbers in order from smallest to largest.
Medium
- 3 × 5
- 4 × 4
- 2 × 9
- 7 × 2

Revision notes

## Multiplication Facts and Multi-Digit Multiplication ### What is Multiplication? Multiplication is a fast way to add the same number many times. For example, 4 × 3 means 3 + 3 + 3 + 3 = 12. It also means an array: 4 rows of 3 dots make 12 dots. And it can mean a comparison: "4 times as many" means multiply by 4. ### Multiplication Facts Up to 12 × 12 You should know your times tables up to 12 × 12 by heart. This helps you solve bigger problems quickly. Remember, order does not matter: 3 × 4 = 4 × 3 = 12. That is called the commutative property. ### Multiplying Three Numbers When you multiply three numbers, you can multiply any two first. For example, 2 × 3 × 4 = (2 × 3) × 4 = 6 × 4 = 24. Or 2 × (3 × 4) = 2 × 12 = 24. The answer is the same. ### Multiplying by 10 and 100 When you multiply by 10, each digit moves one place to the left. For example, 45 × 10 = 450. When you multiply by 100, each digit moves two places to the left. For example, 45 × 100 = 4500. You can also just add zeros: 45 × 10 = 450 (add one zero), 45 × 100 = 4500 (add two zeros). ### Multi-Digit Multiplication (Formal Written Method) To multiply a two-digit or three-digit number by a one-digit number, use the standard algorithm. **Example: 23 × 4** 1. Multiply the ones: 3 × 4 = 12. Write 2 in the ones place, carry 1 to the tens. 2. Multiply the tens: 2 × 4 = 8, then add the carried 1: 8 + 1 = 9. Write 9 in the tens place. 3. Answer: 92. **Example: 145 × 6** 1. Ones: 5 × 6 = 30. Write 0, carry 3. 2. Tens: 4 × 6 = 24, plus 3 = 27. Write 7, carry 2. 3. Hundreds: 1 × 6 = 6, plus 2 = 8. Write 8. 4. Answer: 870. ### Word Problems Read carefully. Look for words like "times", "each", "per", or "as many as". They often mean multiply. **Example:** A box has 6 pencils. How many pencils in 4 boxes? 6 × 4 = 24 pencils. ### Key Points to Remember - Know your times tables up to 12 × 12. - Multiplication is repeated addition, arrays, and comparison. - Order does not change the product. - When multiplying by 10 or 100, digits shift left. - Use the standard algorithm for multi-digit multiplication. - Always check your work!

Multiplication: A quick way to add the same number many times. For example, 4 × 3 means 3 + 3 + 3 + 3 = 12.
Product: The answer you get when you multiply two or more numbers. For example, the product of 4 and 3 is 12.
Array: An arrangement of objects in rows and columns. For example, 4 rows of 3 dots is an array that shows 4 × 3 = 12.
Commutative property: The rule that says the order of numbers in multiplication does not change the product. For example, 3 × 4 = 4 × 3.
Multi-digit multiplication: Multiplying numbers that have more than one digit, like 23 × 4 or 145 × 6, using a step-by-step method.
Standard algorithm: A step-by-step written method for multiplication. You multiply each digit, carry over extra tens, and add them up.
Place value: The value of a digit based on its position in a number. For example, in 45, the 4 is in the tens place, so it means 40.
Times table: A chart or list that shows the products of numbers, like the 1 to 12 times table. It helps you memorize multiplication facts.

Flashcards

What is 7 × 8?

7 × 8 = 56. You can remember it as 5-6-7-8: 56 = 7 × 8.

What is 6 × 9?

6 × 9 = 54. A trick: 6 × 10 = 60, then subtract 6 to get 54.

What is 12 × 12?

12 × 12 = 144. This is the largest fact in the 12 times table.

What does '4 times as many as' mean? Give an example.

It means multiply by 4. For example, if you have 3 apples and I have 4 times as many, I have 3 × 4 = 12 apples.

How can you write 5 + 5 + 5 as a multiplication?

5 + 5 + 5 = 3 × 5 = 15. Multiplication is repeated addition.

What is the product of 3, 4, and 5?

3 × 4 × 5 = 60. You can multiply in any order: (3 × 4) × 5 = 12 × 5 = 60, or 3 × (4 × 5) = 3 × 20 = 60.

Does the order of multiplication change the product? Give an example.

No. For example, 4 × 7 = 28 and 7 × 4 = 28. This is called the commutative property.

What is 23 × 4? Use the formal written method.

23 × 4 = 92. Write 23 over 4, multiply 4 × 3 = 12 (write 2, carry 1), then 4 × 2 = 8 plus 1 = 9, so 92.

What is 145 × 3? Use the formal written method.

145 × 3 = 435. Multiply 3 × 5 = 15 (write 5, carry 1), 3 × 4 = 12 plus 1 = 13 (write 3, carry 1), 3 × 1 = 3 plus 1 = 4, so 435.

What is 47 × 10?

470. When you multiply by 10, each digit shifts one place to the left, and a zero is added at the end.

What is 63 × 100?

6300. When you multiply by 100, each digit shifts two places to the left, and two zeros are added.

What is 8 × 0?

0. Any number multiplied by 0 equals 0.

What is 9 × 1?

9. Any number multiplied by 1 stays the same.

What is 7 × 6?

42. You can remember it as 6 × 7 = 42, the answer to life, the universe, and everything.

What is 11 × 11?

121. A pattern: 11 × 11 = 121, 11 × 12 = 132, 11 × 13 = 143.

What is 15 × 4?

60. You can break it into 10 × 4 = 40 and 5 × 4 = 20, then add: 40 + 20 = 60.

What is 24 × 5?

120. You can multiply by 10 and halve: 24 × 10 = 240, half is 120.

What is 36 × 3?

108. Break it into 30 × 3 = 90 and 6 × 3 = 18, then add: 90 + 18 = 108.

What is 7 × 9?

63. A trick: 7 × 10 = 70, subtract 7 to get 63.

What is 8 × 8?

64. This is a square number: 8 × 8 = 64.

What is 12 × 8?

96. You can do 12 × 4 = 48, then double it: 48 × 2 = 96.

What is 9 × 12?

108. You can do 9 × 10 = 90 and 9 × 2 = 18, then add: 90 + 18 = 108.

What is 5 × 12?

60. You can do 5 × 10 = 50 and 5 × 2 = 10, then add: 50 + 10 = 60.

What is 3 × 3 × 3?

27. Multiply 3 × 3 = 9, then 9 × 3 = 27.

What is 10 × 10?

100. This is a square number: 10 × 10 = 100.

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