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The ideas in this lesson are taken from Division 2 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student. Remainder in long division
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Do you remember?
The remainder is always LESS than the divisor. Otherwise we could divide some more. For example, if in the banana situation the remainder was more than 3, we could continue dividing the remaining bananas between 3 people. How do we check the division if it is not exact? Look at the pictures above. If we end up with 3 people each having 4 bananas and 2 bananas left over, then the total amount of bananas is 3 × 4 + 2 = 14. Or if 5 people have 2 carrots each and there are 4 carrots left over, then all together we have 5 × 2 + 4 = 14 carrots. So to check the division that was not exact, multiply your result by the divisor as normal, and then ADD THE REMAINDER. You should get the original dividend. |
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When using long division, the division is not always exact either.
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Example problems
1. Do these problems in your notebook. Write down here the result and the remainder. Check each division by multiplying and then adding the remainder.
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321 ÷ 2 = 532 ÷ 9 = |
221 ÷ 3 = 922 ÷ 6 = |
490 ÷ 4 = 324 ÷ 6 = |
2. Do the word problems in your notebook.
| a. While playing with matches, Annie had 204 matches. She divided them into piles of 8 matches. How many piles dud she make? How many matches were left over? |
| b. If she divides them into piles of 20, how many piles does she get now? Don't use long division but just think (or use real matches to help). |
3. Remember? Multiply by 10, and make a division sentence.
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10 × 21 = ___ ÷ 10 = 21 |
10 × 90 = ___ ÷ 10 = ___ |
10 × 87 = ___ ÷ 10 = ___ |
4. Based on the previous exercise, divide the following numbers by 10.
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780 ÷ 10 = ___ 150 ÷ 10 = ___ |
450 ÷ 10 = ___ 120 ÷ 10 = ___ |
460 ÷ 10 = ___ 440 ÷ 10 = ___ |
5. Based on the previous exercise, divide the following numbers by 10 and indicate the remainder.
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787 ÷ 10 = 151 ÷ 10 = |
452 ÷ 10 = 126 ÷ 10 = |
463 ÷ 10 = 982 ÷ 10 = |
The fast, FUN, and easy way to learn multiplication. Learn the upper times tales in two sittings using mnemonic stories.
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