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Course: Arithmetic (all content) > Unit 3

Lesson 14: Remainders
Math
Arithmetic (all content)
Multiplication and division
Remainders
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Understanding remainders

Google Classroom
Use arrays and practice problems to understand remainders.

Some division problems work out nicely.

24÷8=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
An array of 24 circles arranged in 3 rows of 8 circles each.

Other division problems don't work out nicely.

25÷7
An array of 25 circles arranged in 3 rows of 7 circles each and 1 row of 4 circles.
Oh no! We can't split 25 circles into perfect groups of 7. We have some circles left over.
How many groups of 7 can we make?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

How many circles remain? In other words, how many circles are not in a group?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Key idea: We can use a remainder to describe what remains after dividing.

25÷7=3 with a remainder of 4
25÷7=3 R 4

Practice problems

Practice problem 1
19÷9=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
R
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
An array of 19 circles arranged in 2 rows of 9 circles each and 1 row of 1 circle.

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