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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. Divisibility
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If there is no remainder, we say division is exact. For
example,
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If there is a remainder, we say division is
not exact. For
example,
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If a number is divisible by another number, we can make a multiplication sentence from the division sentence: 18 ÷ 9 = 2 and 2 × 9 = 18. If division is not exact (there is a remainder),
then we cannot make 19 ÷ 9 = 2, R 1 but 2 × 9 19. |
Example problems
1. Follow the example and find if the following numbers are divisible by given numbers.
Is 15 divisible by 5? Yes, because 15 ÷ 5 = 3, R 0. |
Is 22 divisible by 2? Yes/no, because |
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Is 17 divisible by 5? No, because there is a remainder: |
Is 14 divisible by 3? Yes/no, because |
2. If the division is exact, mark the remainder as 0.
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List of numbers that were divisible by 3: _______________________________________________________ Where have you seen that list of numbers before???? |
3. If the division is exact, mark the remainder as 0.
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From this list, numbers that were divisible by 5 are: _______________________________________________________ This was just a partial list of numbers from the multiplication table of __. |
4. Write a list of twelve different numbers that are divisible by 6. Then write twelve different numbers that are NOT divisible by 6.
5. Divide and indicate a remainder if there is any.
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24 ÷ 3 = __, R __ 41 ÷ 6 = __, R __ |
34 ÷ 5 = __, R __ 21 ÷ 2 = __, R __ |
22 ÷ 10 = __, R __ 45 ÷ 8 = __, R __ |
6. Write a division or multiplication sentence for each word problem. Indicate a remainder if there is any.
a) Mom baked 29 rolls for the dinner party. There were 8 guests. How many rolls did each one get if they were divided evenly, and how many were left over?
f) Pat wanted to bake 3 rolls for each guest of the party. She had invited 12 guests. How many rolls did she need to bake?
7. Divide by 10! Discuss with your teacher the patterns you notice.
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0 ÷ 10 = 0, R __ 1 ÷ 10 = 0, R 1 2 ÷ 10 = 0, R 2 3 ÷ 10 = __, R __ 4 ÷ 10 = __, R __ 5 ÷ 10 = __, R __ 6 ÷ 10 = __, R __ 7 ÷ 10 = __, R __ 8 ÷ 10= __, R __ 9 ÷ 10 = __, R __ |
10 ÷ 10 = __, R __ 11 ÷ 10 = __, R __ 12 ÷ 10 = __, R __ 13 ÷ 10 = __, R __ 14 ÷ 10 = __, R __ 15 ÷ 10= __, R __ 16 ÷ 10 = __, R __ 17 ÷ 10 = __, R __ 18 ÷ 10 = __, R __ 19 ÷ 10 = __, R __ |
30 ÷ 10 = __, R __ 31 ÷ 10 = __, R __ 32 ÷ 10 = __, R __ 33 ÷ 10= __, R __ 34 ÷ 10 = __, R __ 35 ÷ 10= __, R __ 36 ÷ 10 = __, R __ 37 ÷ 10 = __, R __ 38 ÷ 10 = __, R __ 39 ÷ 10 = __, R __ |
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Make a list of numbers less than 150 that are divisible by 10: _______________________________________________________ |
8. Did you notice the pattern of reminders in the previous exercise? Based on that you can easily solve:
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41 ÷ 10 = __, R __ 60 ÷ 10 = __, R __ |
77 ÷ 10 = __, R __ 53 ÷ 10 = __, R __ |
99 ÷ 10 = __, R __ 100 ÷ 10 = __, R __ |
9. Make a list of numbers that are divisible by 2. (Hint: think multiplication table of 2!):
_________________________________________________________________________________
Numbers that are divisible by 2 are called even numbers. |
We can continue the table by adding 2 each time. Fill also the division table.
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Now make a LONG list of even numbers! How long a list can you make?
0, 2, _____________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
10. Make a list of numbers that are NOT divisible by 2 and are less than
50. They are called odd numbers.
_________________________________________________________________________________
_________________________________________________________________________________
11. Find all the numbers between 0 and 100 that are divisible by 5. Start out with those that are in the multiplication table of 5. What pattern do you notice?
_________________________________________________________________________________
12. Find all the numbers between 0 and 200 that are divisible by 10. Start out with those that are in the multiplication table of 10. What pattern do you notice?
_________________________________________________________________________________
13. Make a list of numbers that are divisible by 3. (Hint: think multiplication table of 3!):
_________________________________________________________________________________
Continue the multiplication table by adding 3 each time. Fill also the division table.
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Based on the tables above, tell which of these numbers are divisible by 3, and which are not:
43 54 64 34 38 40 50 51 56 58 60
14. Find all the numbers between 0 and 100 that are
divisible by 4. Start with those in the
multiplication table of 4.
_________________________________________________________________________________
15. From the lists you have made, find all the numbers between 0 and 100 that are divisible both by 4 AND 5.
_________________________________________________________________________________
16. a) Find a number between 21 and 30 that is divisible by 2,
3, and 4.
b) Find two numbers between 21 and 30 that are NOT divisible by 2, 3, or 4.
 What are the
mystery numbers? All numbers are less than 50.
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The fast, FUN, and easy way to learn multiplication. Learn the upper times tales in two sittings using mnemonic stories.
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