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Multiplication facts and multi-digit multiplication

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Notes de leçon

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.

Diapos

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Questions d'entraînement

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  1. 1.What is 7 × 8?

    Easy
    • A56
    • B54
    • C48
    • D64

  2. 2.Which of these is the same as 9 × 6?

    Easy
    • A6 × 9
    • B9 + 6
    • C9 × 9
    • D6 × 6

  3. 3.The product of any number and 1 is that number itself.

    Easy

    True or false?

  4. 4.What is 23 × 4?

    Medium
    • A92
    • B82
    • C102
    • D72

  5. 5.Which of these is the correct product of 345 × 6?

    Medium
    • A2070
    • B207
    • C20700
    • D20070

  6. 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. 7.Match each multiplication fact to its product.

    Easy
    • 6 × 7
    • 8 × 9
    • 5 × 12
    • 42
    • 72
    • 60

  8. 8.Put these numbers in order from smallest to largest.

    Medium
    • 3 × 5
    • 4 × 4
    • 2 × 9
    • 7 × 2

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