you get to solve puzzles!

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Mr Barton’s Maths Notes
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Presentation transcript:

you get to solve puzzles! Algebra is great fun!!!! you get to solve puzzles! https://www.mathsisfun.com/algebra/introduction.html

A Puzzle What is the missing number? − 2 = 4 OK, the answer is 6, right? Because 6 − 2 = 4. Easy stuff. Well, in Algebra we don't use blank boxes, we use a letter (usually an x or y, but any letter is fine). So we write: x – 2 = 4 It is really that simple. The letter (in this case an x) just means "we don't know this yet", and is often called the unknown or the variable.

Why Use a Letter? Because: it is easier to write "x" than drawing empty boxes (and easier to say "x" than "the empty box"). if there are several empty boxes (several "unknowns") we can use a different letter for each one. So x is simply better than having an empty box. We aren't trying to make words with it! And it doesn't have to be x, it could be y or w ... or any letter or symbol we like.

How to Solve Algebra is just like a puzzle where we start with something like "x − 2 = 4" and we want to end up with something like "x = 6". But instead of saying "obviously x = 6", use this neat step-by-step approach: Work out what to remove to get "x = ..." Remove it by doing the opposite (adding is the opposite of subtracting) Do that to both sides

To remove it, do the opposite, in this case add 2 Here is an example: We want to remove the "−2" To remove it, do the opposite, in this case add 2 Do it to both sides Which is ... Solved!

Why did we add 2 to both sides? To "keep the balance"... Add 2 to Left Side Add 2 to Right Side Also In Balance Out of Balance! In Balance Again

Just remember this: To keep the balance, what we do to one side of the "=" we should also do to the other side!

x + 5 = 12 Another Puzzle Solve this one: What we want is an answer like "x = ...", but the +5 is in the way of that! We can cancel out the +5 with a −5 (because 5−5=0) So, let us have a go at subtracting 5 from both sides: x + 5 −5 = 12 −5 A little arithmetic (5 − 5 = 0 and 12 − 5 = 7) becomes: x + 0 = 7 Which is just: x = 7

Exercise Y + 2 = 8 C - 3 = 12 D x 1 = 5 E ÷ 2 = 5 Y + 5 = 7 C – 5 = 7

Exercise 2Y + 3 = 7 4C - 3 = 13 5D x 1 = 5 2E ÷ 2 = 5 2Y + 5 = 7