Download Unit 3: Integers

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Unit 3: Integers
Worksheet #5: Ring Subtraction
Now that you are able to simplify expressions involving exponents and negative integers, we
can work with more complicated numerical expressions.
Evaluate each expression below. Your answer will be an integer. Show lots of steps!
1) -2(-3) + (-5)3
4) (4 – 5)3 – (6 – 8)2
2) 10 – 5(4 – 5 + 3)
5) 7 – 3( -4) + -42
3) 14 × 23 × 32
6) -23 + (-1)3 + (-2)2 + -14
7) A very curious thing happens when you subtract four numbers in a ring. Here is an
example; we will also show one in class. Please do as instructed in this example.
Start with these four numbers: 10
3
7
9
Find the positive difference between the first two by subtracting 3 from 10. Write the
answer, 7, under the 10. Then do the same for 3 and 7 and write 4 under the 3. Then the same for 7
and 9, write 2 under the 7, and finally find the positive difference between 9 (the last number) and
10 (the first). Write this answer, 1, under the 9.
Now start with this second row, which should read 7 4 2 1 as you have written above. Do
the same work with these four numbers to find the positive differences between each pair of
numbers in order. Show your answers as a third row. Each row will always have four numbers in
it. Then repeat this again. Before you get seven rows, you will know when to stop.
Use the process with these numbers: (No calculators please!)
8)
23
14
85
17
9)
22
76
66
89
10) Construct the seventh row of a prime triangle, as we did in class. That is, the 7th row should
have the integers 1 – 7 arranged in such a way that the sum of any two consecutive numbers
is a prime.
11) *Construct the eighth row of a prime triangle.
12) *Pick any four of your own numbers to see if they confirm what you have experienced in
problems 7 through 9 above. You may want to attach a sheet for this.