Grade 3Math
Division with RemaindersRemainders, smaller than the divisor, checking, and what to do with the remainder
When you share things out in equal groups, some may be left over. What is left over is called the "remainder." Let's see how to write a division math sentence with a remainder, how to find the answer with the times tables, how to check it, and what to do with the remainder.
The narration and the pictures are in Japanese. You can hear the same words that are used in class at a Japanese school.
- Video
- 2:27（9 scenes）
- Problems
- 3 problems
Open this lesson in Japanese（あまりの ある わり算）
Let's try
Write the math sentence in your notebook first, then open the answer.
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1If you put 26 candies into bags, 4 in each bag, how many bags can you make, and how many candies are left over? Write the math sentence too.
Hint
In the 4 times table, look for the biggest answer that is not more than 26. The number you multiplied 4 by is the answer to the division.
Answer
The math sentence is 26 ÷ 4 = 6 remainder 2. You can make 6 bags, and 2 candies are left over. Check: 4 × 6 = 24, 24 + 2 = 26
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27 people share 30 sheets of colored paper equally. How many sheets does each person get, and how many are left over?
Hint
Use the 7 times table. The remainder will be smaller than 7.
Answer
30 ÷ 7 = 4 remainder 2. Each person gets 4 sheets, and 2 sheets are left over. Check: 7 × 4 = 28, 28 + 2 = 30
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3There are 38 books. You put them on a bookshelf, 5 books on each shelf. How many shelves do you need to put all the books on?
Hint
Think about where to put the books that are left over.
Answer
38 ÷ 5 = 7 remainder 3. The 3 books left over need a place too, so you need one more shelf. 7 + 1 = 8, so you need 8 shelves.
Words in this lesson
- remainder あまり
- The number left over when you share things in equal groups and can't share them all. It is smaller than the divisor.
- divides evenly わりきれる
- In division, there is no remainder.
- does not divide evenly わりきれない
- In division, there is a remainder.
- divisor / dividend わる数・わられる数
- In 14 ÷ 3, 3 is the divisor (the number you divide by), and 14 is the dividend (the number being divided).
For parents and guardians
- The names of lessons and the order of topics differ slightly between textbooks. This page follows the content of Japan's national curriculum guidelines (the Course of Study). The meaning of division without remainders is covered in the 3rd grade unit "Division."
- Children often stumble on answers where the remainder is still larger than the divisor (such as 14 ÷ 3 = 3 remainder 5) and on how to write the checking math sentence. Once your child finds an answer, it helps to build the habit of saying two checks out loud every time: does "divisor × answer + remainder" give back the original number, and is the remainder smaller than the divisor? (Checking only that you get back the original number will miss answers whose remainder is too large.)
- Whether to count the leftover part as one more, as in "How many benches so that everyone can sit?", depends on reading the situation. Try thinking together about "What happens to the remainder?" in everyday situations, such as sharing snacks or counting how many people can ride in a car.