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1 Integers, powers and roots

Mathematics is about !nding patterns. Key words

How did you !rst learn to add and multiply negative integers?
Perhaps you started with an addition table or a multiplication table Make sure you learn and
understand these key words:
for positive integers and then extended it. "e patterns in the tables

help you to do this. power
index (indices)

+ 3 2 1 0 −1 −2 −3
3 6 5 4 3 2 1 0

2 5 4 3 2 1 0 −1
1 4 3 2 1 0 −1 −2

0 3 2 1 0 −1 −2 −3 This shows
1 + −3 = −2.
−1 2 1 0 −1 −2 −3 −4
You can also subtract.
−2 1 0 −1 −2 −3 −4 −5 −2 − 1 = −3 and
−2 − −3 = 1.
−3 0 −1 −2 −3 −4 −5 −6

× 3 2 1 0 −1 −2 −3 This shows
3 9 6 3 0 −3 −6 −9 2 × −3 = −6.
You can also divide.
2 6 4 2 0 −2 −4 −6
−6 ÷ 2 = −3 and
1 3 2 1 0 −1 −2 −3 −6 ÷ −3 = 2.
0 0 0 0 0 0 0 0

−1 −3 −2 −1 0 1 2 3
−2 −6 −4 −2 0 2 4 6

−3 −9 −6 −3 0 3 6 9

Square numbers show a visual pattern.
1 + 3 = 4 = 2 2
1 + 3 + 5 = 9 = 3 2
1 + 3 + 5 + 7 = 16 = 4 2
Can you continue this pattern?

1 Integers, powers and roots 7