TablesDivision from tables: one fact, four sums
Division is not a new set of facts to learn. It is the multiplication table read from the answer backwards. A child who knows that 7 × 8 = 56 already owns four sums: 7 × 8 = 56, 8 × 7 = 56, 56 ÷ 7 = 8 and 56 ÷ 8 = 7. Teachers call this a fact family. This page shows how to use tables for division, including sums that do not come out evenly.
Reading the table backwards
To work out 72 ÷ 9, do not start sharing 72 things. Ask instead: "9 times what is 72?" Run down the table of 9 until you meet 72. It is on the eighth line, so 72 ÷ 9 = 8.
| Multiplication fact | Turn-around | Division facts |
|---|---|---|
| 7 × 8 = 56 | 8 × 7 = 56 | 56 ÷ 7 = 8 and 56 ÷ 8 = 7 |
| 6 × 9 = 54 | 9 × 6 = 54 | 54 ÷ 6 = 9 and 54 ÷ 9 = 6 |
| 4 × 12 = 48 | 12 × 4 = 48 | 48 ÷ 4 = 12 and 48 ÷ 12 = 4 |
| 9 × 9 = 81 | 9 × 9 = 81 | 81 ÷ 9 = 9 and 81 ÷ 9 = 9 |
| 3 × 15 = 45 | 15 × 3 = 45 | 45 ÷ 3 = 15 and 45 ÷ 15 = 3 |
When it does not divide exactly
For 50 ÷ 7, look for the largest answer in the table of 7 that is not more than 50. That is 49, on line 7. So 50 ÷ 7 is 7 with remainder 1, because 50 − 49 = 1. Check: 7 × 7 + 1 = 50.
Three more worked examples:
- 38 ÷ 6: the table of 6 reaches 36 on line 6, so the answer is 6 remainder 2.
- 75 ÷ 8: the table of 8 reaches 72 on line 9, so the answer is 9 remainder 3.
- 100 ÷ 9: the table of 9 reaches 99 on line 11, so the answer is 11 remainder 1.
The remainder is always smaller than the number you divide by. If it is not, the answer was one line too low in the table.
Sharing and grouping
Division answers two kinds of question, and children should meet both.
- Sharing: 24 laddoos shared equally among 6 children. Each gets 24 ÷ 6 = 4.
- Grouping: 24 laddoos packed 6 to a box. You need 24 ÷ 6 = 4 boxes.
The sum is the same, but the meaning of the answer differs. With remainders it matters: 26 children in autos that seat 3 need 9 autos, not 8 remainder 2, because the last two children also need a ride.
Long division uses the same idea
In long division of 952 by 7, each step asks a table question. 7 into 9 goes 1 time, remainder 2. Bring down the 5 to make 25: the table of 7 gives 21, so 3 times, remainder 4. Bring down the 2 to make 42: 7 × 6 = 42, so 6 times, no remainder. The answer is 136. A child who is slow at long division is nearly always slow at table facts, not at the method.
Divisibility checks that come from tables
- A number divides by 2 if it ends in 0, 2, 4, 6 or 8.
- By 5 if it ends in 0 or 5. By 10 if it ends in 0.
- By 3 if its digits add to a multiple of 3. By 9 if they add to a multiple of 9.
- By 4 if its last two digits form a multiple of 4.
Our neighbour site Factors explains these rules and shows the working for factors, HCF and LCM.