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T.9 Divide by 9: quotients up to 12

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Understanding division by 9

Division is splitting a total amount into equal groups. When we divide by 9, we are finding how many equal groups of 9 we can make, or how many are in each group if we make 9 equal groups.

Example:
  • If you have 27 stickers and put them into 9 equal piles, you are calculating 27 ÷ 9.
  • Each pile would have 3 stickers, so 27 ÷ 9 = 3.
Note

Division is the inverse, or opposite, operation of multiplication. Knowing your multiplication facts for 9 will help you divide by 9 quickly.

Division facts for 9

These are the basic division facts you should know when the divisor is 9, with quotients up to 12. The quotient is the answer to a division problem.

Division facts table (÷ 9):
  • 9 ÷ 9 = 1
  • 18 ÷ 9 = 2
  • 27 ÷ 9 = 3
  • 36 ÷ 9 = 4
  • 45 ÷ 9 = 5
  • 54 ÷ 9 = 6
  • 63 ÷ 9 = 7
  • 72 ÷ 9 = 8
  • 81 ÷ 9 = 9
  • 90 ÷ 9 = 10
  • 99 ÷ 9 = 11
  • 108 ÷ 9 = 12
Note

Notice the pattern: the dividend (the number being divided) increases by 9 each time, and the quotient increases by 1. This pattern can help you memorize the facts.

How to use related multiplication facts

Since multiplication and division are related, you can think of a division fact as a missing-factor multiplication problem. To solve 63 ÷ 9, ask yourself: "9 times what number equals 63?"

Example:
  • Problem: 72 ÷ 9 = ?
  • Think: 9 × ? = 72
  • Since 9 × 8 = 72, then 72 ÷ 9 = 8.
Note

This strategy is very helpful for checking your work. If you know the multiplication fact, you already know the related division fact.

Solving real-world problems

We use division by 9 to solve everyday problems that involve sharing, grouping, or organizing items into equal sets of 9.

Examples:
  • "A baker has 108 muffins. She packs them into boxes that hold 9 muffins each. How many boxes does she need?" (108 ÷ 9 = 12 boxes)
  • "There are 45 students. They need to form 9 equal teams for a game. How many students are on each team?" (45 ÷ 9 = 5 students)
Note

Always read the word problem carefully to determine what is being divided (the total) and what you are dividing by (the size or number of groups). The quotient is your answer.