Why Is the Remainder Smaller Than the Divisor?

📚 What you will learn

• 13 sticks, 4 sticks per square: 3 squares, with 1 stick left over.
• Written as 13 ÷ 4 = 3 R 1: 13 is the dividend, 4 the divisor, 3 the quotient and 1 the remainder.
• If 4 sticks were left, they would make one more square, so the remainder can never be 4 (or more).
• Rule: the remainder is always smaller than the divisor. When dividing by 4, the remainder can only be 1, 2 or 3.
• Check: quotient × divisor + remainder = dividend → 3 × 4 + 1 = 13.

🎙️ What the video says (in Chinese)

1. 分糖果剩下的，为什么总比每份的少？我们用小棒摆一摆！
2. 有 13 根小棒，每 4 根摆一个正方形。
3. 一个，两个，三个！还剩 1 根，不够再摆一个了。
4. 13 ÷ 4 = 3 …… 1
5. 如果剩下的是 4 根呢？4 根又能摆一个正方形！所以不能剩 4 根。
6. 所以：余数一定要比除数小！

✏️ Try it yourself

1. 17 ÷ 5 = ? R ?

   Show answer

   17 ÷ 5 = 3 R 2 (3 × 5 + 2 = 17)

2. When dividing by 6, what is the biggest possible remainder?

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   5, because the remainder must be smaller than 6