Multiplying and dividing by two digits; divisibility · Usually met around P4
Long division (by two digits)
Round the divisor to a ten, then adjust.
How to do it
Method
Round the divisor to a ten, then adjust
158 ÷ 23: 23 × 6 = 138, 158 − 138 = 20 → 6 … 20
Another way
Written division
158 ÷ 23 = 6 … 20
In full
To divide by a two-digit number, round the divisor to the nearest ten to guess the quotient. Then multiply back and adjust. 158 ÷ 23: think of 23 as 20. 20 × 7 = 140, so try 7. But 23 × 7 = 161, which is more than 158. That's too big, so try 6: 23 × 6 = 138, 158 − 138 = 20. 20 is less than 23, so the quotient is 6 and the remainder is 20. A two-digit number times a one-digit number splits easily: 23 × 6 = 20 × 6 + 3 × 6 = 120 + 18 = 138. If the quotient has two digits, try the tens first. 936 ÷ 12: 12 × 70 = 840, 936 − 840 = 96, 12 × 8 = 96, 70 + 8 = 78, so the quotient is 78. Another way is written division. Start from the highest place, guess a quotient, multiply back and take away. Each question tells you whether it wants the quotient or the remainder. If it divides exactly, it wants the quotient.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
42 ÷ 21 = ?
Show the answer and working
Answer: 42 ÷ 21 = 2
42 ÷ 21: think of 21 as 20 to try a quotient, 20 × 2 = 40, so try 2; 21 × 2 = 42, 42 − 42 = 0; so the quotient is 2
Example 2
97 ÷ 22 = 4 … ?
Show the answer and working
Answer: 97 ÷ 22 = 4 … 9
97 ÷ 22: think of 22 as 20 to try a quotient, 20 × 4 = 80, so try 4; 22 × 4 = 88, 97 − 88 = 9, and 9 is less than 22; so the quotient is 4 and the remainder 9
Example 3
99 ÷ 38 = ? … 23
Show the answer and working
Answer: 99 ÷ 38 = 2 … 23
99 ÷ 38: think of 38 as 40 to try a quotient, 40 × 2 = 80, so try 2; 38 × 2 = 76, 99 − 76 = 23, and 23 is less than 38; so the quotient is 2 and the remainder 23