What to do with the remainder
Tonight's idea
Six does not go into 50 exactly. Eight sixes make 48, and 2 are left over. The left-over part is called the remainder. We write \(50 \div 6 = 8\) remainder 2.
What you do next depends on the question.
- 50 eggs go into boxes of 6. How many full boxes? 8. Drop the remainder.
- 50 children ride in cars that seat 6. How many cars? 9. Two children still need a car, so round up.
- 50 marbles are shared among 6 friends. Each gets 8, with 2 left over. You cannot cut a marble.
- 50 metres of ribbon are cut into 6 equal lengths. Each is \(8\tfrac13\) metres. Ribbon can be cut, so the last 2 metres are shared too: \(\tfrac26 = \tfrac13\) of a metre each.
One division, four answers. The story decides what the remainder means.
Watch one: \(30 \div 4\)
Seven fours make 28, so \(30 \div 4 = 7\) remainder 2.
30 campers sleep in tents for 4. They need 8 tents, since 7 tents leave 2 campers outside.
30 wheels are fitted to cars, 4 each. That makes 7 cars, with 2 wheels spare.
4 people share 30 dollars. Each gets 7 dollars, and the last 2 dollars split into 50 cents each. So each gets $7.50.
Your turn
- Divide, and give the remainder. (a) \(23 \div 5\) (b) \(47 \div 6\) (c) \(62 \div 8\) (d) \(100 \div 7\)
- \(75 \div 8 = 9\) remainder 3. Use it to answer each question. (a) 75 people sit at tables for 8. How many tables are needed? (b) A 75 cm wire is cut into 8 cm pieces. How many pieces, and how much wire is left? (c) 75 stickers are shared equally among 8 children. How many does each child get?
- (a) Four friends share 26 marbles equally. What happens? (b) Four friends share 26 dollars equally. How much does each get? (c) Why are the two answers different, when both are \(26 \div 4\)?
- Today is Monday. (a) What day of the week will it be in 50 days? (b) What day will it be in 100 days? (c) Which part of the division did you need this time?
Stretch: a mystery number
A number is between 50 and 100. Divide it by 6 and the remainder is 5. Divide it by 7 and the remainder is 6. What is the number? Hint: think about the number that is one bigger.
Answers
- (a) 4 remainder 3. (b) 7 remainder 5. (c) 7 remainder 6. (d) 14 remainder 2.
- (a) 10 tables. Nine tables seat 72, and the other 3 people need a table too. (b) 9 pieces, with 3 cm left. (c) 9 each, and 3 stickers are left over.
- (a) Each gets 6 marbles and 2 are left over. (b) $6.50 each. (c) A dollar can be split into cents, so the remainder can be shared. A marble cannot be split.
- (a) \(50 \div 7 = 7\) remainder 1. Seven whole weeks bring you back to Monday, and one more day is Tuesday. (b) \(100 \div 7 = 14\) remainder 2, so Wednesday. (c) Only the remainder. The number of whole weeks does not matter.
Stretch. 83. The number that is one bigger leaves no remainder when divided by 6 or by 7. So it is in both times tables, and the first such number is 42. The next is 84, so the mystery number is 83. Check: \(83 = 13 \times 6 + 5\) and \(83 = 11 \times 7 + 6\).