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T.11 Divide by 11: quotients up to 12

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Dividing by eleven: the basic rule

Division by 11 is the process of splitting a whole number into 11 equal groups, or finding how many groups of 11 are in a number. The answer is called the quotient.

Example:
  • 33 ÷ 11 = 3
  • This means 33 split into 11 equal groups gives you 3 in each group, OR that there are 3 groups of 11 in 33.
Note

Division is the inverse, or opposite, operation of multiplication. If you know 11 × 4 = 44, then you also know 44 ÷ 11 = 4.

Master the division facts for 11

Memorizing the basic division facts for 11, with quotients up to 12, builds speed and accuracy for solving more complex problems.

Division facts table (11 ÷ 11 to 132 ÷ 11):
  • 11 ÷ 11 = 1
  • 22 ÷ 11 = 2
  • 33 ÷ 11 = 3
  • 44 ÷ 11 = 4
  • 55 ÷ 11 = 5
  • 66 ÷ 11 = 6
  • 77 ÷ 11 = 7
  • 88 ÷ 11 = 8
  • 99 ÷ 11 = 9
  • 110 ÷ 11 = 10
  • 121 ÷ 11 = 11
  • 132 ÷ 11 = 12
Note

Notice the pattern: the dividend (the number being divided) increases by 11 each time, and the quotient increases by 1. This pattern helps with memorization.

Using patterns and related multiplication

You can solve any division by 11 problem by thinking of its related multiplication fact. Ask yourself: "What number times 11 equals the dividend?"

Examples:
  • To solve 88 ÷ 11, think: 11 × ? = 88. Since 11 × 8 = 88, the quotient is 8.
  • To solve 110 ÷ 11, think: 11 × 10 = 110, so the quotient is 10.
Note

For quotients of 10, 11, and 12, remember that 11 × 10 = 110, 11 × 11 = 121, and 11 × 12 = 132. These are extensions of the basic facts.

Applying division by 11 to word problems

Real-world problems often involve dividing items into equal groups. Identifying when to divide by 11 is a key skill.

Example Problem:
  • "A teacher has 121 pencils. She wants to put them equally into 11 supply boxes. How many pencils go in each box?"
  • Solution: The phrase "equally into 11 boxes" signals division. 121 ÷ 11 = 11. Each box gets 11 pencils.
Note

In word problems, look for clues like "split equally," "shared evenly," or "divided into ___ groups" to know when to divide.

Checking your work for accuracy

You can verify any division answer by using multiplication. Multiply the quotient you found by 11. The product should equal the original dividend.

Example:
  • Problem: 77 ÷ 11 = 7
  • Check: 7 × 11 = 77. Since this is true, the answer is correct.
  • Problem: 132 ÷ 11 = 12
  • Check: 12 × 11 = 132. This confirms the answer.
Note

Always take a moment to check your work. This habit helps catch mistakes and strengthens your understanding of the relationship between multiplication and division.