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The ideas in this division lesson are taken from Division 1 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student. Division as repeated subtraction
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Remember how MULTIPLICATION is repeated addition: 5 × 4 = 4 + 4 + 4 + 4 + 4 = 20.
You drew or added __ groups of four. |
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Let's reverse the process. You start out with 20 sticks.
20 − 4 − 4 − 4 − 4 − 4 = 0 This is repeated subtraction. You subtract 4 repeatedly, or many times, till you hit zero. Each subtraction is forming a group of 4. How many groups did you form? How many times did you subtract? That is the answer to the division problem 20 ÷ 4. |
Try it yourself: Separate groups, but in your mind 'move them away' or
subtract.
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DIVISION is repeated subtraction:
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Often, it is handier to actually add instead of subtract:
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Example problems
1. Write a multiplication sentence AND a division sentence that fits the addition/subtraction facts.
5 + 5 + 5 = 15 __ ÷ __ = __ __ ÷ __ = __ |
12 + 12 + 12 + 12 = 48 __ ÷ __ = __ __ ÷ __ = __ |
23 + 23 + 23 = __ __ ÷ __ = __ __ ÷ __ = __ |
40 + 40 = __ __ ÷ __ = __ __ ÷ __ = __ |
2. Write a subtraction sentence for each division sentence.
45 ÷ 15 = __ 45 −
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32 ÷ 8 = __ 32 −
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| Multiplication is repeated addition, and it is like
jumps on the number line.
5 × 4 = 20. Five jumps of 4 gets you to 20. |
| Division is repeated subtraction. You make jumps
of four backwards from 20 till you hit 0:
20 ÷ 4 = 5. 20 − 4 − 4 − 4 − 4 − 4 = 0 |
 
What division is illustrated here? |
2. Draw jumps backwards to illustrate the division sentences.
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4. Solve using repeated subtraction OR adding up to the number being
divided.
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40 ÷ 20 = __ 90 ÷ 30 = __ 30 ÷ 15 = __ |
52 ÷ 13 = __ 34 ÷ 17 = __ 69 ÷ 23 = __ |
45 ÷ 15 = __ 90 ÷ 15 = __ 90 ÷ 18 = __ |
5. If 12 × 2 = 24,
then 13 × 2 is __ How about division? Use the previous
problem to help
you solve the next one.
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a. 26 ÷ 2 = __ 28 ÷ 2 = __ 30 ÷ 2 = __ |
d. 66 ÷ 2 = __ 70 ÷ 2 = __ 78 ÷ 2 = __ |
6. Try the same kind of thing when dividing by 3.
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a. 36 ÷ 3 = __ 39 ÷ 3 = __ |
d. 90 ÷ 3 = __ 99 ÷ 3 = __ |
The fast, FUN, and easy way to learn multiplication. Learn the upper times tales in two sittings using mnemonic stories.
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