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T.7 Divide by 7: quotients up to 12

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What is division?

Division is splitting a total number of items into equal groups. When we divide by 7, we are finding out how many groups of 7 we can make, or how many are in each group if we make 7 groups.

Example:
  • If you have 28 marbles and put them into groups of 7, you can make 4 groups. So, 28 ÷ 7 = 4.
Note

Division is the opposite, or inverse, of multiplication. Knowing your multiplication facts for 7 can help you solve division problems.

Understanding division by 7

To divide by 7 means to repeatedly subtract groups of 7 from a total number until you reach zero, or to share the total equally among 7.

Two ways to think about it:
  • Making Groups: “How many groups of 7 are in 35?” → 35 ÷ 7 = 5
  • Sharing: “If 63 crayons are shared equally by 7 students, how many does each get?” → 63 ÷ 7 = 9
Note

The answer in a division problem is called the quotient. In 42 ÷ 7 = 6, the number 6 is the quotient.

Division facts for 7

Memorizing the division facts for 7 will help you solve problems quickly and accurately. These facts show the quotients when numbers up to 84 are divided by 7.

All division facts for 7 (up to 7 x 12):
  • 7 ÷ 7 = 1
  • 14 ÷ 7 = 2
  • 21 ÷ 7 = 3
  • 28 ÷ 7 = 4
  • 35 ÷ 7 = 5
  • 42 ÷ 7 = 6
  • 49 ÷ 7 = 7
  • 56 ÷ 7 = 8
  • 63 ÷ 7 = 9
  • 70 ÷ 7 = 10
  • 77 ÷ 7 = 11
  • 84 ÷ 7 = 12
Note

Notice the pattern: the quotients (1 through 12) count up by one each time. The dividend (the number being divided) increases by 7 each time.

Using division facts in problems

Once you know the facts, you can use them to solve word problems and check your work using multiplication.

Examples:
  • Problem: A teacher has 56 sheets of paper for 7 projects. How many sheets per project?
    Solution: 56 ÷ 7 = 8 sheets each.
  • Check with multiplication: If 7 projects each get 8 sheets, that's 7 x 8 = 56. It matches!
Note

Always ask yourself: “Does my answer make sense?” If you divide a larger number by 7, the quotient should be smaller than the original number.