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Abacus · Ages 7+ · Set A
Remainders
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Remember: The remainder is what is over after a fair share. It is always smaller than the number sharing.

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The party cupcakesGran baked fourteen cupcakes for Mia and Ben's party. Four friends were coming, so Ben set out four plates. Mia dealt the cupcakes one at a time, one for each plate. Going all the way round once is one round. After three rounds, every plate had three cupcakes. Mia looked at the tray. Some cupcakes were still there, but there were not enough for a whole round, because four plates need four cupcakes. Cupcakes left over after a fair share have a special name: the remainder.
1
How many cupcakes did each plate get?
2
Four plates with three cupcakes each: cupcakes were handed out.
3
Gran baked 14 cupcakes. 14 take away 12 leaves cupcakes.
4
What do we call the cupcakes left over after a fair share?
the quotientthe remainderthe plates
5
The remainder can be bigger than the number of plates.
TrueFalse

Share and find what is left

6
17 shared among 5 gives 3 each. Which frame shows one share?
A
B
C
7
Sharing among 6 plates. Which remainder can happen?
twosixseven
8
Ben shares 22 sweets among 7 bags. Which is right?
4 each, 1 over3 each, 0 over3 each, 1 over
9
18 grapes shared among 6 plates leaves a remainder of zero.
TrueFalse
10
Join each sharing among five to its answer.
  1. 119 ÷ 5
  2. 220 ÷ 5
  3. 321 ÷ 5
  4. 423 ÷ 5
  • A4 each, 3 over
  • B4 each, 1 over
  • C3 each, 4 over
  • D4 each, 0 over
11
Mia says 17 ÷ 5 is 2 each with 7 over. What is wrong?
The remainder must be 07 is bigger than 5, so she can deal another roundShe should share among 7
12
The frame shows 27 beads. Four piles get six each, which uses 24. The remainder is .
13
Stretch: Gran has 41 cookies for 6 plates. After a fair share, how many are left over?
14
Draw the remainder for 14 ÷ 4 on the empty frame.
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Answer key · Set A
Remainders
13 After three rounds every plate had three cupcakes.
212 Four plates, three each: 3 + 3 + 3 + 3 = 12.
32 Fourteen take away the twelve handed out leaves two.
4the remainder The remainder is what is over after a fair share. The quotient is how many each one gets.
5False If as many as the plates were left, another round could be dealt. The remainder is always smaller than the number sharing.
6C Three beads across on one row show the share. Five is the number of friends and two is what is left.
7two The remainder must be smaller than six. With six or more left, another round could be dealt.
83 each, 1 over Three rounds use 21 sweets (7 × 3). One is over, and seven bags need seven for another round.
9True Six plates with three grapes each use all 18, so nothing is over.
101-C, 2-D, 3-B, 4-A
117 is bigger than 5, so she can deal another round With 7 over there are enough for another round of 5. So it is 3 each, with 2 over.
123 27 take away the 24 handed out leaves 3 beads on the frame, and 3 is smaller than 4.
135 Six rounds use 36 cookies (6 × 6). 41 take away 36 leaves 5, which is smaller than 6.
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