Take off ten of the divisor
91 ÷ 7 asks how many 7s make 91. The 7 times table you know by heart does not reach 91, so split 91 into two numbers that 7 divides easily.
Ten 7s make 70, so take 70 off first. The rest is 91 − 70 = 21, and 21 is in the 7 times table too. So 91 = 70 + 21.
84 ÷ 7: 70 comes off as ten sevens, the 14 left is 2 × 7, so the answer is 10 + 2 = 12 exactly
Make N = 91 and split it into 70 and the rest
The whole bar is the number being divided. The gold part is 70, which is ten 7s. Drag the end of the bar to 91: the rest is 21, and it cuts into exactly three 7s.
Share each piece
Now divide each piece by 7. 70 ÷ 7 = 10, because 10 × 7 = 70. And 21 ÷ 7 = 3, because 3 × 7 = 21.
The first jump is 70, which is ten 7s. The second jump is 21, which is three 7s.
Add the answers
Add the two answers: 10 + 3 = 13. There are ten 7s in the 70 and three 7s in the 21, so there are thirteen 7s in 91, and 91 ÷ 7 = 13.
Multiply back to check: 13 × 7 = 70 + 21 = 91.
Choosing the pieces
The first piece does not have to be ten of the divisor. Any piece the divisor divides exactly will do. For 96 ÷ 4, split 96 into 80 + 16: 80 ÷ 4 = 20 and 16 ÷ 4 = 4, so 96 ÷ 4 = 20 + 4 = 24.
Split only the number being divided, never the divisor. 84 ÷ 4 is not 84 ÷ 2 + 84 ÷ 2, which is 84. Sharing 84 among 4 people gives each person less than sharing it among 2.
Worked example: Eggs Packed in Sixes by Splitting the Total
Question A farmer packs 84 eggs into cartons of 6. He packs the first 60 eggs, and then he packs the rest. (a) How many cartons do the first 60 eggs fill? (b) How many cartons does he fill altogether?
1.Ten cartons hold 10 × 6 = 60 eggs. So split 84 into 60 and the rest: 84 = 60 + 24.
Ten cartons hold 60 eggs, so 84 is split into 60 and 24. 2.(a) 60 ÷ 6 = 10, so the first 60 eggs fill 10 cartons.
(a) 60 ÷ 6 = 10 cartons. 3.Divide the rest: 24 ÷ 6 = 4, so the other 24 eggs fill 4 cartons.
The other 24 eggs fill 24 ÷ 6 = 4 cartons. 4.(b) Add the two parts: 10 + 4 = 14 cartons. Check: 14 × 6 = 60 + 24 = 84.
(b) 10 + 4 = 14 cartons altogether.
Answer: (a) 10 cartons; (b) 14 cartons
Common mistakes
- Stopping at 10 cartons. The other 24 eggs still have to be packed, and they fill 4 more cartons.
- Splitting 84 into 80 and 4. Neither 80 nor 4 can be shared into sixes exactly. Choose a first part that is in the 6 times table, such as 60.
More multiplying and dividing in your head problems, worked step by step →