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W.2 Multiplication and division facts up to 12: true or false

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Understanding multiplication and division facts

Multiplication facts show the total when you combine equal groups. Division facts show how to separate a total into equal groups. Facts up to 12 involve numbers from 1 through 12.

Examples:
  • Multiplication: 6 groups of 4 → 6 × 4 = 24
  • Division: 24 split into 6 equal groups → 24 ÷ 6 = 4
Note

Multiplication and division are inverse operations. This means they undo each other. If 7 × 8 = 56 is true, then 56 ÷ 8 = 7 must also be true.

Determining if a fact is true or false

To verify a fact, you can use strategies like repeated addition for multiplication, repeated subtraction for division, or recall from memory. A fact is true only if both sides of the equation represent the same amount.

Steps to check:
  • For 9 × 3 = 27: Think 9 + 9 + 9 = 27. This is true.
  • For 42 ÷ 7 = 5: Think 7 × 5 = 35, not 42. This is false; the correct answer is 6.
Note

Always relate the fact back to what you know. Use a fact you are sure of, like 5 × 5 = 25, to help figure out nearby facts like 5 × 6 = 30.

Common patterns and key facts

Recognizing patterns can help you quickly identify true and false statements without calculating every time.

Pattern Examples:
  • Any number multiplied by 1 stays the same (e.g., 12 × 1 = 12).
  • Any number multiplied by 0 equals 0 (e.g., 8 × 0 = 0).
  • In division, the dividend (first number) cannot be smaller than the divisor (second number) unless the divisor is 1. (e.g., 4 ÷ 8 = 2 is false).
Note

Watch for tricky false facts that swap numbers. The order matters in division (56 ÷ 7 is not the same as 7 ÷ 56), but it does not matter in multiplication (7 × 8 equals 8 × 7).

Applying facts in different situations

True or false questions can be written as direct equations or hidden within simple word problems. Your task is to identify the core fact and check it.

Examples in context:
  • “If 11 children each have 4 markers, there are 44 markers in total.” → Check: 11 × 4 = 44? True.
  • “Sharing 48 marbles equally among 6 friends gives each friend 7 marbles.” → Check: 48 ÷ 6 = 7? False (48 ÷ 6 = 8).
Note

When solving, first find the numbers and the operation (multiplication or division). Write the fact as a simple number sentence before deciding if it is true or false.

Strategies for mastering all facts up to 12

Building fluency means knowing facts from memory, but you can use reliable tools to get there.

Helpful strategies:
  • Use fact families: If 8 × 9 = 72, then you also know 9 × 8 = 72, 72 ÷ 9 = 8, and 72 ÷ 8 = 9.
  • Break apart harder facts: 12 × 4 = (10 × 4) + (2 × 4) = 40 + 8 = 48.
  • Look for square numbers as anchors: 7 × 7 = 49, 6 × 6 = 36.
Note

Accuracy is more important than speed at first. Take your time to verify each fact. With practice, your recall will become fast and automatic.