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O.4 Multiplication sentences up to 12: find the missing factors

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What are multiplication sentences?

A multiplication sentence is a complete mathematical statement that shows a multiplication operation. It has three main parts: the factors and the product, connected by an equal sign.

Example:
  • 4 × 5 = 20
  • 4 and 5 are the factors.
  • 20 is the product.
Note

Think of a multiplication sentence like a complete thought. It must have all its parts to make sense, just like a sentence needs a subject and a verb.

Understanding missing numbers in equations

Sometimes, one number in a multiplication sentence is missing. Your job is to find the missing factor or product that makes the equation true. The equal sign (=) means the value on the left must balance with the value on the right.

Examples with missing numbers:
  • 7 × [] = 42 (The missing factor is 6)
  • 9 × 4 = [] (The missing product is 36)
  • [] × 3 = 24 (The missing factor is 8)
Note

The equal sign is like the center of a scale. Both sides must have the same total value, even if a number is hidden.

Strategies for finding missing factors

When a factor is missing, you can use related division or think of it as a "think multiplication" problem. Ask yourself: "What number multiplied by the known factor gives the known product?"

How to solve:
  • Problem: 5 × [] = 40
  • Think: "5 times what number equals 40?"
  • Strategy 1 (Division): 40 ÷ 5 = 8
  • Strategy 2 (Skip Counting): 5, 10, 15, 20, 25, 30, 35, 40 → Counted 8 times.
  • Answer: The missing number is 8.
Note

Multiplication and division are inverse operations. If you know your division facts, you can use them to find missing factors quickly.

Balancing multiplication sentences on both sides

Some problems show two multiplication expressions that must be equal. First, find the product for the complete side. Then, find the missing factor on the other side that gives the same product.

Example step-by-step:
  • Problem: 12 × 6 = 8 × []
  • Step 1: Solve the complete side. 12 × 6 = 72.
  • Step 2: The equation is now: 72 = 8 × []
  • Step 3: Find the missing factor. "8 times what equals 72?" 72 ÷ 8 = 9.
  • Step 4: Check: 8 × 9 = 72. Both sides are equal.
Note

Always solve the complete side of the equation first. This gives you the target number you need to match on the other side.

Common patterns and tips

Recognizing number patterns and properties of multiplication can help you solve problems faster and check your work.

Helpful patterns:
  • Commutative Property: 3 × 7 is the same as 7 × 3. The order of factors doesn't change the product.
  • Multiplying by 1: Any number times 1 is that same number (e.g., [] × 1 = 9; the missing number is 9).
  • Multiplying by 0: Any number times 0 is 0.
  • Doubles/Halves: If 6 × 4 = 24, then 12 × 2 also equals 24. One factor doubled, the other halved.
Note

After you find a missing number, plug it back into the original sentence. Does it make the equation true? This is the best way to check your answer.