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# Understanding remainders

Use arrays and practice problems to understand remainders.

## Some division problems work out nicely.

start color #01a995, 24, end color #01a995, divided by, start color #aa87ff, 8, end color #aa87ff, equals
An array of 24 circles arranged in 3 rows of 8 circles each.

## Other division problems don't work out nicely.

start color #01a995, 25, end color #01a995, divided by, start color #aa87ff, 7, end color #aa87ff
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 start color #01a995, 25, end color #01a995 circles into perfect groups of start color #aa87ff, 7, end color #aa87ff. We have some circles left over.
How many groups of start color #aa87ff, 7, end color #aa87ff can we make?

How many circles remain? In other words, how many circles are not in a group?

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

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

## Practice problems

Practice problem 1
19, divided by, 9, equals
start text, R, end text
An array of 19 circles arranged in 2 rows of 9 circles each and 1 row of 1 circle.

## Want to join the conversation?

• When you have a remanier it can't be bigger than the other numbers right?
• if it greater than the divisor its wrong
• I got all right just from being with my amazing math teacher
• I know right?
• Bruh remainders are awful. I wish we could keep doing decimals..
• at how long can a division equation be
• as long as infinity
(1 vote)
• What is a tip for the remainder game?