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HOW TO THINK ABOUT. ALGEBRA 2. JW Hick. REVISION OF ALGEBRA 1 Whenever we are adding or subtracting we need like terms. You can only add or subtract if the letters are exactly the same as each other. This is not the case when we multiply or divide. We do not need the letters to be the same.
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HOW TO THINK ABOUT ALGEBRA 2 JW Hick
REVISION OF ALGEBRA 1 Whenever we are adding or subtracting we need like terms. You can only add or subtract if the letters are exactly the same as each other. This is not the case when we multiply or divide. We do not need the letters to be the same
INTRODUCTION When we multiply things, it looks like this 7 x 7 What if we wanted to have heaps of 7’s though? Is there an easier way to write it, so we don’t have to write them all, one after another?
Say, we have 10 lots of 7’s being multiplied, one after another 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 An easier way to write this is 7 10 The little number above the 7 tells us “how many 7’s are being multiplied together”. This is called the index
MAIN IDEA “The little number tells us how many are being multiplied together” 4 EG 6 Means 6 x 6 x 6 x 6, we have four sixes
THE LAW OF MULTIPLICATION So we know the index tells us how many are being multiplied, but what about if we had, 4 x 4 3 6 How many 4’s are now being multiplied together? How can we write this using index notation?
Well, we have (4 x 4 x 4) x (4 x 4 x 4 x 4 x 4 x 4) So isn’t this just the same as nine 4’s being multiplied together? 3 6 9 4 x 4 = 4
MAIN IDEA “When we multiply numbers together, we just add the little numbers (indices) together”
Lets try the exact same thing again, but this time use letters to represent numbers, as that is what algebra is all about. QUESTIONS
MAIN IDEA “When we multiply numbers together, we just add the little numbers (indices) together – EVEN IF WE USE A LETTER TO REPRESENT A NUMBER” It is the exact same idea, except now you have a letter instead of a number.
HARDER MULTIPLICATION What happens if there are numbers and letters involved at the same time? EXAMPLE Well we can rewrite this as
MAIN IDEA When there are numbers and letters all being multiplied together • Multiply the numbers separately to see what number you will have out the front • Add the indices to see “how many of each letter you have”
ALGEBRAIC DIVISION When we multiply algebraically we • Multiply the numbers together • Add the indices
ALGEBRAIC DIVISION When we divide algebraically we • Divide the numbers separately • SUBTRACT the indices Algebraic division is the opposite of algebraic multiplication. If you understand multiplication then you can do division
