Finding Remainders

Using Number Properties

Problem: “Joy works out 39 803 ÷ 3 on her calculator and gets 13267.6666. Joy claims the remainder is 2. Is she correct?

(Possible answer: Yes. 0.6666666 derives from 2 ÷ 3 so the remainder is 2.)

Examples: Find the remainders for these divisions:

10 334 ÷ 3
1 347 ÷ 4
233 ÷ 5
12 789 ÷ 2
124 ÷ 3

Problem: “Joy has to pack 5 673 sweets into packets of 34 sweets. How many loose sweets will be left?”

Do 5673 ÷  34 on a calculator. (Answer: 166.8529412.)

Discuss why this means there are 166 packets, which use 166 x 34 = 5 644 sweets. So there are 5 673 – 5 644 = 29 sweets left over.

Examples: Find the remainders for these divisions:
10 334 ÷ 27
11 327 ÷ 67
123 833 ÷ 27
62 789 ÷ 967
345 810 ÷ 1 614

Understanding Number Properties:

For any whole numbers d and b, how do you find the remainder for  d ÷ b? (Answer: Work out d ÷ b on a calculator. Ignore the decimal part to get the quotient.  The remainder is d minus the quotient times b.)