Multiplication facts and multi-digit multiplication

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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.

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Câu hỏi luyện tập

Xem trước miễn phí — 8 trên 63 câu hỏi. Đăng ký để xem tất cả.

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

Thêm câu hỏi

9.Match each multiplication fact to its correct product.
Easy
- 4 × 3
- 5 × 7
- 6 × 8
- 12
- 35
- 48
10.Put these products in order from smallest to largest.
Easy
- 3 × 9
- 4 × 7
- 6 × 6
- 5 × 8
11.The product of 7 and 9 is the same as the product of 9 and 7.
Easy
True or false?
12.What is the product of 3 and 4?
Medium
- A7
- B12
- C34
- D81
13.Which of these is the correct product of 56 × 7?
Medium
- A392
- B342
- C402
- D3920
14.Which of the following are equal to 6 × 8? (select all that apply)
Medium
- A8 × 6
- B6 + 8
- C4 × 12
- D3 × 16
- E2 × 24
15.Match each multiplication to its correct product.
Medium
- 12 × 3
- 15 × 4
- 21 × 2
- 36
- 60
- 42
16.When you multiply any number by 0, the product is 0.
Easy
True or false?
17.What is 34 × 6?
Medium
- A204
- B184
- C214
- D240
18.The product of 6 and 8 is the same as the product of 4 and 12.
Medium
True or false?
19.Which of the following are equal to 7 × 8? (select all that apply)
Medium
- A8 × 7
- B14 × 4
- C16 × 3.5
- D2 × 28
- E4 × 14
20.What is 123 × 4?
Medium
- A492
- B482
- C412
- D4920
21.Multiplying a number by 10 makes the number ten times bigger.
Medium
True or false?
22.What is 45 × 3?
Medium
- A135
- B125
- C145
- D1350
23.The product of 5 and 6 is greater than the product of 4 and 7.
Easy
True or false?
24.Which of the following are equal to 9 × 4? (select all that apply)
Medium
- A4 × 9
- B6 × 6
- C3 × 12
- D2 × 18
- E5 × 8
25.What is 67 × 5?
Medium
- A335
- B325
- C345
- D3350
26.Multiplying a number by 100 makes the number one hundred times bigger.
Medium
True or false?
27.What is 6 × 7?
Easy
- A42
- B36
- C48
- D40
28.What is 8 × 9?
Easy
- A72
- B64
- C81
- D70
29.What is 12 × 6?
Medium
- A72
- B60
- C66
- D78
30.What is 15 × 4?
Medium
- A60
- B45
- C50
- D75
31.What is 23 × 5?
Medium
- A115
- B105
- C125
- D110
32.The product of 4 and 9 is the same as the product of 9 and 4.
Easy
True or false?
33.Multiplying a number by 10 always gives a product that ends with a zero.
Easy
True or false?
34.A school orders 5 boxes of pencils. Each box has 12 packs, and each pack has 8 pencils. How many pencils does the school order in total?
Medium
- A480
- B580
- C400
- D96
35.The product of 0 and any number is always 0.
Easy
True or false?
36.A rectangle is 15 cm long and 6 cm wide. What is its area?
Medium
- A90 cm²
- B21 cm²
- C45 cm²
- D60 cm²
37.Which of the following are equal to 3 × 4 × 5? (select all that apply)
Medium
- A12 × 5
- B3 × 20
- C15 × 4
- D7 × 5
- E60
38.What is 4 × 6?
Easy
- A24
- B20
- C18
- D28
39.The multiplication table is symmetric, meaning 3 × 4 is the same as 4 × 3.
Easy
True or false?
40.What is 56 × 7?
Easy
- A392
- B362
- C402
- D372
41.A box has 4 rows of apples. Each row has 6 apples. How many apples are there in total?
Easy
42.Complete the multiplication fact.
Easy
8 × ____ = 72
43.What is 47 × 10?
Medium
44.What is 560 ÷ 100?
Medium
45.A farmer plants 4 rows of apple trees. Each row has 23 trees. How many apple trees does the farmer plant in total?
Medium
46.Complete the multiplication sentence.
Medium
6 × 7 = ____
47.What is 9 × 8?
Medium
48.A book has 12 chapters. Each chapter has 15 pages. How many pages are in the book?
Hard
49.A school has 5 grades. Each grade has 4 classes. Each class has 23 students. How many students are in the school?
Hard
50.What is 12 × 11?
Medium
51.A shop sells packs of 8 stickers. A customer buys 15 packs. How many stickers does the customer buy?
Hard
52.What is 9 × 7?
Medium
53.Explain why 3 × 7 is the same as 7 × 3. Use the idea of arrays or repeated addition.
Medium
54.Explain how to find the product of 13 and 5 using repeated addition.
Medium
55.Explain how to find the product of 24 and 5 using the distributive property.
Hard
56.A rectangle is 12 cm long and 8 cm wide. Explain how to find its area using multiplication.
Hard
57.A box has 4 rows of apples. Each row has 6 apples. How many apples are there in total?
Easy
- A26
- B22
- C24
- D28
58.What is 47 × 10?
Medium
- A517
- B423
- C564
- D470
59.What is 560 ÷ 100?
Medium
- A6.6
- B5.6
- C4.6
- D7.6
60.A farmer plants 4 rows of apple trees. Each row has 23 trees. How many apple trees does the farmer plant in total?
Medium
- A101
- B110
- C92
- D83
61.A book has 12 chapters. Each chapter has 15 pages. How many pages are in the book?
Hard
- A198
- B216
- C162
- D180
62.A school has 5 grades. Each grade has 4 classes. Each class has 23 students. How many students are in the school?
Hard
- A506
- B414
- C552
- D460
63.A shop sells packs of 8 stickers. A customer buys 15 packs. How many stickers does the customer buy?
Hard
- A144
- B108
- C120
- D132

Ghi chú ôn tập

## 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.

Thẻ ghi nhớ

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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