Basic Division Facts (Divisors 1-10) - Third Grade Mathematics

Fluency with division facts up to 100 allows you to solve multi-step problems, work with fractions, and understand proportional relationships without getting bogged down in arithmetic. In this chapter, you will master division facts for all divisors from 1 through 10 by connecting them directly to your multiplication tables and utilizing targeted mental strategies.

Master Division Strategy: The Multiplication Inversion

Whenever you face a division fact, remember that division is simply asking for a missing factor.

Division Question:              What You Think:
24 ÷ 6 = ?                      6 x [ ? ] = 24
Since 6 x 4 = 24, the answer is 4!

Division Fact Strategies by Divisor

Let us break down strategies for divisors 1 through 10.

Dividing by 1 and 2

  • Divisor 1: Any number divided by 1 is itself (8 ÷ 1 = 8; 25 ÷ 1 = 25).
  • Divisor 2: Dividing by 2 means finding half of an even number (14 ÷ 2 = 7; 18 ÷ 2 = 9).

Dividing by 3 and 4

  • Divisor 3: Skip count by 3s or recall your 3s table (21 ÷ 3 = 7 because 3 x 7 = 21).
  • Divisor 4: Cut the number in half, and then cut it in half again! Example: 28 ÷ 4: Half of 28 is 14; half of 14 is 7. Answer: 7!

Dividing by 5 and 10

  • Divisor 5: Think of nickels or clock minutes. If the dividend ends in 0, the answer is even; if it ends in 5, the answer is odd (35 ÷ 5 = 7; 40 ÷ 5 = 8).
  • Divisor 10: Simply drop the zero from the end of the dividend (70 ÷ 10 = 7; 90 ÷ 10 = 9).

Dividing by 6, 7, 8, and 9

  • Divisor 6: If you divide by 3 and cut that in half, you get the division by 6. Or think of 6 x ? = dividend (42 ÷ 6 = 7).
  • Divisor 7: Recall 7s multiplication milestones: 7 x 5 = 35, 7 x 7 = 49, 7 x 8 = 56 (56 ÷ 7 = 8).
  • Divisor 8: Cut in half three times! Example: 48 ÷ 8: Half of 48 is 24; half of 24 is 12; half of 12 is 6. Answer: 6!
  • Divisor 9: Recall that the digits of multiples of 9 add up to 9. The tens digit of the dividend is 1 less than the quotient! Example: 54 ÷ 9: The tens digit is 5, so the quotient is 5 + 1 = 6!

Master Division Reference Grid

+----------+----+----+----+----+----+----+----+----+----+----+
| Dividend | ÷1 | ÷2 | ÷3 | ÷4 | ÷5 | ÷6 | ÷7 | ÷8 | ÷9 | ÷10|
+----------+----+----+----+----+----+----+----+----+----+----+
|    10    | 10 |  5 |  - |  - |  2 |  - |  - |  - |  - |  1 |
|    12    | 12 |  6 |  4 |  3 |  - |  2 |  - |  - |  - |  - |
|    18    | 18 |  9 |  6 |  - |  - |  3 |  - |  - |  2 |  - |
|    24    | 24 | 12 |  8 |  6 |  - |  4 |  - |  3 |  - |  - |
|    36    | 36 | 18 | 12 |  9 |  - |  6 |  - |  - |  4 |  - |
|    40    | 40 | 20 |  - | 10 |  8 |  - |  - |  5 |  - |  4 |
+----------+----+----+----+----+----+----+----+----+----+----+

Chapter Practice Exercises

  1. Quick-fire division practice: a. 18 ÷ 2 b. 25 ÷ 5 c. 32 ÷ 4 d. 45 ÷ 9 e. 60 ÷ 10
  2. Higher facts: a. 42 ÷ 7 b. 48 ÷ 6 c. 56 ÷ 8 d. 63 ÷ 9 e. 64 ÷ 8
  3. Use the "half and half again" strategy to solve 36 ÷ 4. Show both halving steps.
  4. Solve 72 ÷ 8 and 72 ÷ 9. What do you notice about their relationship?
  5. A farmer collects 48 eggs. She packs them into cartons that hold 6 eggs each. How many cartons can she fill?

Solutions and Step-by-Step Answers

  1. Quick-fire facts: a. 18 ÷ 2 = 9 (half of 18). b. 25 ÷ 5 = 5. c. 32 ÷ 4 = 8 (half of 32 is 16; half of 16 is 8). d. 45 ÷ 9 = 5. e. 60 ÷ 10 = 6.
  2. Higher facts: a. 42 ÷ 7 = 6 (7 x 6 = 42). b. 48 ÷ 6 = 8 (6 x 8 = 48). c. 56 ÷ 8 = 7 (8 x 7 = 56). d. 63 ÷ 9 = 7 (9 x 7 = 63). e. 64 ÷ 8 = 8 (square fact: 8 x 8 = 64).
  3. For 36 ÷ 4:
  4. First half: 36 ÷ 2 = 18.
  5. Second half: 18 ÷ 2 = 9. Answer: 36 ÷ 4 = 9.
  6. 72 ÷ 8 = 9, and 72 ÷ 9 = 8. They belong to the exact same fact family (8 x 9 = 72). When the divisor is 8, the quotient is 9; when the divisor is 9, the quotient is 8!
  7. 48 eggs packed in cartons of 6: 48 ÷ 6 = 8 cartons.