Discover Mathematics P6: Term 1, Unit 1, Lessons 1–2
GoalDivide a 4-digit number by a 2-digit number, estimate first, and say what the remainder means.
New words
long division · dividing a big number one digit at a timequotient · the answer to a divisionremainder · what is left over and is smaller than the divisorestimate · a quick guess that is close to the real answer
Explanation
Long division shares a big number into equal groups, one digit at a time. Before you start, estimate: round the divisor to a friendly number and ask roughly how big the answer should be. Then repeat four steps: divide, multiply, subtract, bring down the next digit. When there are no digits left, the number at the bottom is the remainder. A remainder is always smaller than the divisor. What you do with it depends on the story: sometimes it is simply left over, and sometimes it needs one more group. Always check: quotient × divisor + remainder must give the number you started with.
Amal's school ordered 2,736 notebooks to share equally among 24 classes. Estimate first: 2,700 ÷ 25 is about 108, so expect a little more than 100. Divide: 27 ÷ 24 = 1; 27 − 24 = 3; bring down 3 to make 33; 33 ÷ 24 = 1, left 9; bring down 6 to make 96; 96 ÷ 24 = 4, left 0. Each class gets 114 notebooks. Check: 114 × 24 = 2,736.
A fruit seller packs 1,250 mandarins into boxes of 24. 1,250 ÷ 24 = 52 with remainder 2, because 24 × 52 = 1,248. He fills 52 boxes, and the 2 mandarins that are left over stay out. Here the remainder is simply left over.
1,150 passengers must travel by trains that carry 48 people each. 1,150 ÷ 48 = 23 with remainder 46, because 48 × 23 = 1,104 and 1,150 − 1,104 = 46. The 46 people still need seats, so we need 23 + 1 = 24 trains. Here the remainder means one more group.
Class activity
Estimation race. A grown-up writes a 4-digit number and a 2-digit number on paper. The child has 20 seconds to say an estimate of the quotient, then divides carefully and checks. The closer the estimate was, the more points the child scores. Swap roles after three rounds.
Practice
1
Divide 4,368 ÷ 26. Estimate first.
168. Estimate: 4,400 ÷ 25 is about 176. Check: 26 × 168 = 4,368.
2
Divide 1,875 ÷ 25 and check your answer.
75, because 25 × 75 = 1,875 and nothing is left over.
3
A baker has 1,000 eggs and puts 12 in each carton. How many full cartons are there, and how many eggs are left over?
1,000 ÷ 12 = 83 remainder 4. There are 83 full cartons and 4 eggs left over (12 × 83 = 996).
4
2,350 children go on a school trip. A bus has 40 seats. How many buses are needed?
2,350 ÷ 40 = 58 remainder 30. The 30 children need a bus too, so 59 buses are needed.
5
Hazem says 1,560 ÷ 30 = 520. Use an estimate to show that he is wrong, then find the right answer.
1,500 ÷ 30 = 50, so the answer should be near 50, not 520. The right answer is 52 (30 × 52 = 1,560).
