Modular Arithmetic Math Worksheet With Answers - Grade 7/8, University Of Waterloo, 2016 Page 9
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134. If Mary’s birthday was on a Thursday in 2014, what day of the week will her birthday
be on next year (2017)?
[(365
2) + 366] (mod 7) = (1
2) (mod 7) + 2 (mod 7) = 2 + 2 (mod 7) = 4
Mary’s birthday would have been on a Monday, since that is 4 days after Thursday.
5. Using a regular deck of 52 cards, I dealt all the cards in the deck to 3 people (including
myself). Were the cards dealt evenly?
52 (mod 3) = 1
No, it wasn’t dealt evenly.
6. A litre of milk is 4 cups, and one cake recipe uses 3 cups. If I have 8 litres of milk,
how many cakes can I make? And how many cups of milk will be leftover, if any?
8
4 (mod 3) = 2
1 (mod 3) = 2
(8 4) 2
32 2
30
=
=
= 10
3
3
3
I will be able to make 10 cakes with 2L of milk leftover.
7. I bought as many mini-erasers as possible at 25 cents each and spent the rest of my
money on paperclips at 3 cents each. How many of each did I buy given that I have
$1.70? Is there anything leftover? (Assume there’s no tax.)
Maximum amount of money I can spend on erasers is $1.50, getting me 6 erasers and
leaving me with $0.20 to buy paper clips.
20 (mod 3) = 2 and since 20 = 3(6) + 2
I can buy 6 erasers and 6 paperclips, and would have 2¢ leftover.
8. I have 5 trays with 6 muffins each that I divided evenly among 4 of my friends, and I
ate the leftovers. How many muffins did each of my friends eat? How many muffins
did I eat?
5
6 = 30 = 7(4) + 2
Each of my friends ate 7 and I ate 2.
9. If Math Circles started on Tuesday, February 2 , 2016, and lasts for 44 days, what
day will it end? (Give the full date.)
Note that 44 us not the number of classes there are, rather it is the number of days
in between the first and last day of Math Circles.
44 + 2 (mod 29) = 15 + 2 (mod 29) = 17 =
So it will fall on the 17 day of March.
44 (mod 7) = 2 =
So it will fall 2 days after Tuesday, ie. it will fall on a Thursday.
The last day will be Thursday, March 17 , 2016.
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