🔢 MathGrade 3Lesson 13
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Relate Multiplication and Division

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Learning Objectives

  • 1Identify the multiplication and division facts within a given fact family
  • 2Write the two multiplication and two division facts for any fact family
  • 3Use a known multiplication fact to solve a related division problem
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Mini Lesson

Multiplication and division are inverse operations — they undo each other. A fact family is a set of three numbers that can be written as two multiplication facts and two division facts. Knowing one fact lets you work out the other three quickly.

What is a Fact Family?

  • Choose three numbers that are related, e.g. 3, 4, and 12.
  • Write two multiplication facts: 3 × 4 = 12 and 4 × 3 = 12.
  • Write two division facts: 12 ÷ 4 = 3 and 12 ÷ 3 = 4.

Using Multiplication to Solve Division

  • If you need to solve 28 ÷ 4, think: "4 × ? = 28".
  • From your ×4 table you know 4 × 7 = 28, so 28 ÷ 4 = 7.
  • Multiplication tables are the key to solving division quickly.
Fact Family Triangle for 4, 6, and 24A triangle with 24 at the top, 4 at bottom-left, and 6 at bottom-right. Four equations around the triangle: 4 times 6 equals 24, 6 times 4 equals 24, 24 divided by 4 equals 6, 24 divided by 6 equals 4.Fact Family Triangle24464 \u00d7 6 = 24 \u00a0\u00a0 6 \u00d7 4 = 2424 \u00f7 4 = 6 \u00a0\u00a0 24 \u00f7 6 = 4
Fact family examples for 3,4,12 and 5,6,30Two box panels showing complete fact families. Left panel: 3 times 4 equals 12, 4 times 3 equals 12, 12 divided by 4 equals 3, 12 divided by 3 equals 4. Right panel: 5 times 6 equals 30, 6 times 5 equals 30, 30 divided by 6 equals 5, 30 divided by 5 equals 6.Fact Family Examples3 \u00b7 4 \u00b7 123 × 4 = 124 × 3 = 1212 ÷ 4 = 312 ÷ 3 = 45 \u00b7 6 \u00b7 305 × 6 = 306 × 5 = 3030 ÷ 6 = 530 ÷ 5 = 6
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Picture a triangle with the three fact-family numbers. Multiply the two bottom corners to get the top; divide the top by either bottom corner to get the other.

Vocabulary
Fact family
A group of math facts that use the same numberse.g. 4 × 3 = 12, 3 × 4 = 12, 12 ÷ 3 = 4, 12 ÷ 4 = 3 is a fact family.
Inverse operation
A math operation that undoes anothere.g. Division is the inverse of multiplication.
Multiplication
A fast way to add the same number many timese.g. 4 × 3 = 12 is a multiplication fact.
Division
Splitting a number into equal groupse.g. 12 ÷ 3 = 4 is a division fact.
Product
The answer to a multiplication probleme.g. 12 is the product of 4 × 3.
Quotient
The answer to a division probleme.g. 4 is the quotient of 12 ÷ 3.
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