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T.3 Divide by 3: quotients up to 12

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What is division by 3?

Division by 3 is the process of separating a total number of items into three equal groups or finding how many groups of three are in a number. It is the inverse operation of multiplication by 3.

Examples:
  • If you have 12 crayons and divide them equally among 3 friends, each friend gets 4 crayons. So, 12 ÷ 3 = 4.
  • If you have 15 stickers and put them into piles of 3, you will make 5 piles. So, 15 ÷ 3 = 5.
Note

Division answers the questions: "How many in each equal group?" or "How many groups of this size can I make?"

Division facts for 3

Memorizing the division facts for 3, up to a quotient of 12, will help you solve problems quickly and accurately.

All Division Facts (3 ÷ 3 to 36 ÷ 3):
  • 3 ÷ 3 = 1
  • 6 ÷ 3 = 2
  • 9 ÷ 3 = 3
  • 12 ÷ 3 = 4
  • 15 ÷ 3 = 5
  • 18 ÷ 3 = 6
  • 21 ÷ 3 = 7
  • 24 ÷ 3 = 8
  • 27 ÷ 3 = 9
  • 30 ÷ 3 = 10
  • 33 ÷ 3 = 11
  • 36 ÷ 3 = 12
Note

Notice the pattern: each dividend (the number being divided) increases by 3, and the quotient increases by 1. These facts are directly related to the 3s multiplication facts.

How to use related multiplication facts

Since division is the opposite of multiplication, you can solve a division problem by thinking of a related multiplication fact.

Steps:
  • For 21 ÷ 3 = ? , ask yourself: "What number times 3 equals 21?"
  • You know that 7 × 3 = 21.
  • Therefore, 21 ÷ 3 = 7.
Note

If you know your 3s multiplication table (3, 6, 9, 12, 15...), you already know the answers to these division problems.

Solving division problems in context

Word problems help us understand how division by 3 is used in real-life situations.

Examples:
  • "Olivia has 24 students. She wants to form 3 equal teams for a project. How many students will be on each team?" (24 ÷ 3 = 8 students)
  • "A baker packs muffins into boxes of 3. If she has 18 muffins, how many full boxes can she make?" (18 ÷ 3 = 6 boxes)
Note

Always identify the total number (dividend) and the number of groups or the group size (divisor). The answer (quotient) tells you the size or number of groups.