🔢 MathGrade 2Lesson 22
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Relate Division to Multiplication

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What you will learn

  • 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 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 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

Words to know

Multiplication

Joining equal groups to find a total

e.g. 3 × 4 = 12 is multiplication.

Division

Splitting a total into equal groups

e.g. 12 ÷ 3 = 4 is division.

Inverse

An operation that undoes another

e.g. Division is the inverse of multiplication.

Fact family

Three numbers that make four related multiplication and division equations

e.g. 3, 4, and 12 are a fact family.

Dividend

The largest number in a division, the one being split

e.g. In 12 ÷ 3, the dividend is 12.

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!"

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← Lesson 21: Learn Division as SharingLesson 23: Solve Equal Group Word Problems →