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R.5 Multiply three one-digit numbers

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Multiplication of three one-digit numbers

Multiplying three one-digit numbers means taking three numbers from 0 to 9 and finding their total product. You solve it by multiplying two numbers first, then multiplying that result by the third number.

Examples:
  • 2 × 3 × 4 = 24
  • 5 × 1 × 6 = 30
  • 7 × 2 × 2 = 28
Note

This skill helps build a strong foundation for more complex multiplication and problem-solving.

Understanding the order of operations

When multiplying three numbers, the order does not change the final product. You can group the numbers in different ways and still get the same answer.

Examples:
  • (4 × 2) × 3 = 8 × 3 = 24
  • 4 × (2 × 3) = 4 × 6 = 24
  • (3 × 4) × 2 = 12 × 2 = 24
Note

This property is called the Associative Property of Multiplication. It allows you to choose which two numbers to multiply first to make the calculation easier.

Strategies for solving

Use smart grouping strategies to solve problems with three one-digit numbers efficiently. Look for number pairs that are easy to multiply.

Strategy examples:
  • Look for 5 or 10: 2 × 5 × 3 → Multiply 2 × 5 first to get 10, then 10 × 3 = 30.
  • Look for 0 or 1: 9 × 0 × 7 → Any number times 0 is 0, so the answer is 0.
  • Look for doubles: 4 × 2 × 4 → Multiply 4 × 4 first to get 16, then 16 × 2 = 32.
Note

Choosing the easiest pair to multiply first saves time and reduces mistakes. Always scan the numbers before you start calculating.

Special cases to remember

Certain number combinations have quick solutions. Memorizing these patterns makes you a faster problem solver.

Key patterns:
  • Any number × 0 × any number = 0
  • Any number × 1 × any number = product of the other two numbers
  • 5 × 2 × any number = 10 × that number (just add a zero)
  • A number × itself × another number: Find the square first (e.g., 3 × 3 = 9), then multiply by the third number.
Note

Recognizing these patterns helps you solve problems mentally without writing every step.

Applying the skill in word problems

In real-world situations, you often need to multiply three numbers to find a total amount. Read the problem carefully to identify all the numbers you need to multiply.

Example problem:
  • "Ms. Chen's class has 4 rows of desks. Each row has 3 desks. Each desk has 2 drawers. How many drawers are there in total?"
  • Identify the numbers: 4 rows × 3 desks × 2 drawers.
  • Solve: (4 × 3) × 2 = 12 × 2 = 24 drawers.
Note

In word problems, the order of the numbers usually follows the order of the story. However, you can still multiply them in the easiest order.