Remainders

Understanding remainders

Use arrays and practice problems to understand remainders.

Some division problems work out nicely.

start color tealD, 24, end color tealD, divided by, start color purpleC, 8, end color purpleC, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

Explain

Other division problems don't work out nicely.

start color tealD, 25, end color tealD, divided by, start color purpleC, 7, end color purpleC
Oh no! We can't split start color tealD, 25, end color tealD circles into perfect groups of start color purpleC, 7, end color purpleC. We have some circles left over.
How many groups of start color purpleC, 7, end color purpleC can we make?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

Explain
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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

Explain

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

25, divided by, 7, equals, 3, space, w, i, t, h, space, a, space, r, e, m, a, i, n, d, e, r, space, o, f, space, 4
empty space, equals, 3, space, R, space, 4

Practice problems

Practice problem 1
19, divided by, 9, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i
R
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

Explain

Challenge: Try this game

Instructions: Your goal is to figure out the remainder of the division problem shown on the screen. Once you know the answer, rotate the shape so that the edge with the answer is at the bottom.
[But how do I rotate the shape?]
If you have a keyboard, use your left and right arrow keys to rotate the shape.
If you don't have a keyboard, press the arrows shown on screen.
Pro tip: The down arrow speeds things up.