🔢 MathGrade 2Lesson 22
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Relate Division to Multiplication

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Learning Objectives

  • 1Match a division equation to its related multiplication fact
  • 2Use a known multiplication fact to solve a related division equation
  • 3List all four equations in a multiplication-division fact family from three numbers
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Mini Lesson

Multiplication and division are inverse operations — they undo each other, just like addition and subtraction do. Every multiplication fact comes with two matching division facts.

The key relationship

  • If 3 x 4 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3.
  • The three numbers (3, 4, 12) form a multiplication-division fact family.
  • The largest number (12) is always the dividend — the number being divided.

How to use multiplication to solve division

  • To solve 12 ÷ 3 = ___, think: "3 times what equals 12?" → 3 x 4 = 12, so the answer is 4.
  • To solve 20 ÷ 4 = ___, think: "4 times what equals 20?" → 4 x 5 = 20, so the answer is 5.

Fact family examples

  • 2, 5, 10 → 2x5=10 | 5x2=10 | 10÷2=5 | 10÷5=2
  • 3, 4, 12 → 3x4=12 | 4x3=12 | 12÷3=4 | 12÷4=3
  • 4, 5, 20 → 4x5=20 | 5x4=20 | 20÷4=5 | 20÷5=4
  • 2, 6, 12 → 2x6=12 | 6x2=12 | 12÷2=6 | 12÷6=2
Multiplication and division fact family for 3, 4, and 12A triangle with 12 at the top, 3 at bottom-left, 4 at bottom-right. Four equations shown below: 3 times 4 equals 12, 4 times 3 equals 12, 12 divided by 3 equals 4, 12 divided by 4 equals 3.Fact Family: 3, 4, 1212343 x 4 = 124 x 3 = 1212 ÷ 3 = 412 ÷ 4 = 3
Fact family triangle for 3, 4, and 12 — two multiplication facts (blue) and two division facts (orange).
Think multiplication to solve division — four worked examplesFour rows. Each row shows a division equation then the think-multiplication strategy and the answer. 12 divided by 3 equals 4; 20 divided by 4 equals 5; 10 divided by 2 equals 5; 12 divided by 6 equals 2.Think Multiplication to Divide12 ÷ 3 = ?Think: 3 x ? = 12 → 3 x 4 = 12 → answer: 420 ÷ 4 = ?Think: 4 x ? = 20 → 4 x 5 = 20 → answer: 510 ÷ 2 = ?Think: 2 x ? = 10 → 2 x 5 = 10 → answer: 512 ÷ 6 = ?Think: 6 x ? = 12 → 6 x 2 = 12 → answer: 2
Four worked examples of the "think multiplication" strategy for solving division.
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Ask yourself: "Which multiplication fact uses these same three numbers? Use it to find the answer!"

Vocabulary
Multiplication
Joining equal groups to find a totale.g. 3 × 4 = 12 is multiplication.
Division
Splitting a total into equal groupse.g. 12 ÷ 3 = 4 is division.
Inverse
An operation that undoes anothere.g. Division is the inverse of multiplication.
Fact family
Three numbers that make four related multiplication and division equationse.g. 3, 4, and 12 are a fact family.
Dividend
The largest number in a division, the one being splite.g. In 12 ÷ 3, the dividend is 12.
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← Lesson 21: Learn Division as SharingLesson 23: Solve Equal Group Word Problems →