Division with remainders

Quotient and remainder

If you share 17 candies equally among 5 children, each child gets 3 and 2 are left over. The 3 is called the Quotient and the 2 left over is the Remainder. It is often written as 17 ÷ 5 = 3 R 2.

The remainder must always be smaller than the number you divide by. If the remainder were 5 or more, you could give each child one more.

Why children find it hard

• Division uses the times tables in reverse, so if a fact does not come to mind quickly, finding the quotient takes a long time.
• Finding “the largest product that does not go over the number being divided” is an unfamiliar process.
• There are two answers, the quotient and the remainder, so children mix up which is which.

Steps

1. Think of the times table for the number you divide by. For 17 ÷ 5, that is the 5 table.
2. Find the largest product that does not go over the number being divided. 5 × 3 = 15 is less than 17, and 5 × 4 = 20 is more than 17, so the quotient is 3.
3. Work out what is left. 17 − 15 = 2, so the remainder is 2.
4. Check that the remainder is smaller than the number you divide by. 2 is smaller than 5, so it is right.
5. Check the answer. The number you divide by × the quotient + the remainder should give the number being divided: 5 × 3 + 2 = 17.

Common mistakes

• Choosing a quotient that is too small, so the remainder is too big. For example, 29 ÷ 4 = 6 R 5. A remainder bigger than the divisor 4 means you can divide once more. The correct answer is quotient 7, remainder 1.
• Choosing a quotient that is too big, so you cannot subtract. In 38 ÷ 6, if the quotient is taken as 7, then 6 × 7 = 42 is more than 38 and cannot be subtracted. If the product goes over the number being divided, make the quotient 1 smaller.
• Swapping the quotient and remainder. For example, 17 ÷ 5 = 2 R 3, with the boxes swapped. Have your child use the check 5 × 3 + 2 = 17 to see which one is the quotient.

10 practice problems

Same format as this unit in the app (dividing by 2 to 9, one-digit quotient). 8 problems have a remainder and 2 do not. Tap to see each answer.

1. 17 ÷ 5 = ?
   Answer

   Quotient 3, remainder 2

2. 29 ÷ 4 = ?
   Answer

   Quotient 7, remainder 1

3. 38 ÷ 6 = ?
   Answer

   Quotient 6, remainder 2

4. 50 ÷ 7 = ?
   Answer

   Quotient 7, remainder 1

5. 44 ÷ 9 = ?
   Answer

   Quotient 4, remainder 8

6. 23 ÷ 3 = ?
   Answer

   Quotient 7, remainder 2

7. 65 ÷ 8 = ?
   Answer

   Quotient 8, remainder 1

8. 13 ÷ 2 = ?
   Answer

   Quotient 6, remainder 1

9. 42 ÷ 6 = ?
   Answer

   7 (no remainder)

10. 36 ÷ 4 = ?
    Answer

    9 (no remainder)

Practicing this unit in the app

1. Open the Create tab at the bottom of the app. If you have not added your child yet, add them in the Children tab first.
2. Under 📚 Select Level, tap Lv.7 (Ages 9-10), then under 📖 Select Unit choose “Division basics · Remainders”. If times tables are still slow, you can also choose “Multiplication tables” to mix the two.
3. Set the number of problems with the − and + buttons on the unit card, or tap ✏️ to type a number. 5 to 10 problems is an easy start.
4. Choose your child under 👶 For whom? and create the problems. Your child can solve them on their own device, or tap Solve on this phone now right after creating to solve on your phone. For problems with a remainder, the quotient and remainder go in separate boxes.
5. When your child submits, open the worksheet and tap ✅ Grade Now. The correct answer and your child's answer are shown for each problem.
6. If any answers are wrong, tap ❌ Retry Wrong Answers on the results in your child's screen. The correct answers are shown only after they submit again.
7. Check the accuracy for each unit in the Progress tab. 90% or higher is shown as Good, 70-89% as Average, and below 70% as Weak.