Equations 1 Click mouse

EQUATIONS The important thing to remember about equations is that both sides must balance (both sides must equal each other). e.g. 5 + 2 = 3 + 4 7 7 This means that if you do something to one side of the equation you must also do the same to the other: e.g. 5 + 2 = 3 + 2 e.g. 5 + 2 = 3 + 4 e.g. 5 + 2 = 3 + 4 5 5 If you take 2 away from the first part of the equation YOU MUST ALSO take 2 away from the second part So you can see, the equation is still balanced! Click mouse

Look at this example, and remember the balance! e.g. 6 + 4 = 3 + 7 10 10 Remember, if you do something to one side of the equation you must also do the same to the other: e.g. 6 + 2 = 3 + 3 e.g. 6 + 4 = 3 + 7 e.g. 6 + 2 = 3 + 7 6 6 If you take 4 away from the first part of the equation YOU MUST ALSO take 4 away from the second part So you can see, the equation is still balanced! Click mouse

You can do anything to the equation, IF you do the same to both sides. e.g. 6 + 4 = 3 + 7 10 10 So, if you ADD something to one side of the equation you must also ADD the same to the other: e.g. 6 + 4 + 4 = 3 + 7 + 4 e.g. 6 + 4 = 3 + 7 e.g. 6+ 4 + 4 = 3 + 7 14 14 If you add 4 to the first part of the equation YOU MUST ALSO add 4 to the second part So you can see, the equation is still balanced! Click mouse

You can do anything to the equation, IF you do the same to both sides. e.g. 6 + 4 = 3 + 7 10 10 So, if you DIVIDE one side of the equation by a number you must also DIVIDE the other side by the same: e.g. 6 + 4 = 3 + 7 2 2 e.g. 6 + 4 = 3 + 7 e.g. 6 + 4 = 3 + 7 2 5 5 If you DIVIDE the first part of the equation by 2 YOU MUST ALSO DIVIDE the second part by 2 So you can see, the equation is still balanced! Click mouse

You can do anything to the equation, IF you do the same to both sides. e.g. 6 + 4 = 3 + 7 10 10 So, if you MULTIPY one side of the equation by a number you must also MULTIPLY the other side by the same: e.g. (6 + 4) x 2 = (3 + 7) x2 e.g. 6 + 4 = 3 + 7 e.g. (6 + 4) x 2 = 3 + 7 20 20 If you MULTIPLY the first part of the equation by 2 YOU MUST ALSO MULTIPLY the second part by 2 So you can see, the equation is still balanced! Click mouse

EQUATIONS RULE: Equations must always balance. Whatever you do to one side you must ALSO do to the other. Now that you know these facts they will really help you to solve equations. Click mouse

EQUATIONS MUST ALWAYS BALANCE. This fact will help you to answer the following questions. Have a go at them. The equation is now balanced, because both sides equal 100 1. ….. + 60 = 100 40 What must you add to 60 to make 100 The equation is now balanced, because both sides equal 3 1. ….. - 7 = 3 10 What number take away 7 makes 3 Click mouse

What we really did was to take 60 away from BOTH SIDES Both those sums were very easy and you could work them out in your head. However, if you understand what you are doing it will help you to work out harder sums!! Let’s look again at the first one we did and think about how we did it:- …… + 60 = 100 …… + 60 = 100 …… + 60 = 100 - 60 …… + 60 = 40 Take away 60 Take away 60 What we really did was to take 60 away from BOTH SIDES This left us with the answer we needed! Click mouse

What we really did was to ADD 7 to BOTH SIDES Let’s look again at the second one we did and think about how we did it:- It’s important to remember that this is a MINUS 7 ….. - 7 = 3 …… + 60 = 3 + 7 …… + 60= 3 …… + 60 = 10 ….. - 7 = 3 Add 7 ( to get rid of the –7 ) Add 7 What we really did was to ADD 7 to BOTH SIDES This left us with the answer we needed! Click mouse

Let’s try adding a little algebra! Instead of leaving the gap … we put a letter into the equation. Look at this equation and work it out:- y + 60 = 60 - 40 y + 60 = 20 y + 60 = 60 y + 40 = 60 Find the value of y Take away 40 Take away 40 What we must do is take 40 away from BOTH SIDES to leave the y by itself Click mouse This left us with the answer we needed! y = 20

Now try these – they’re easy!!!! z + 60 = 12 z + 60 = 15 - 3 z + 60 = 15 z + 3 = 15 Find the value of z Take 3 away from BOTH SIDES to leave the z by itself Take away 3 Take away 3 y + 60 = 35 y + 60 = 15 y + 20 = 35 y + 60 = 35 - 20 Find the value of y Take 20 away from BOTH SIDES to leave the y by itself Take away 20 Take away 20 Click mouse

Add 3 to BOTH SIDES to leave the z by itself z - 3 = 15 Now try these with MINUS numbers in them – they’re still easy if you remember the rule!! Find the value of z Remember, this is a MINUS Add 3 to BOTH SIDES to leave the z by itself z - 3 = 15 z + 60 = 15 + 3 z + 60 = 15 z + 60 = 18 ADD 3 ADD 3 to get rid of the -3 y + 60 = 55 y + 60 = 35 + 20 y - 20 = 35 y + 60 = 35 Find the value of y Add 20 ADD 20 to get rid of the -20 Add 20 to BOTH SIDES to leave the y by itself Click mouse

What you are doing is KEEPING THE BALANCE Can you see the pattern? If it is a PLUS on one side of the equation, it becomes a MINUS on the other. This is called INVERSING 2 + 3 = 5 + - 2 + 3 = 5 - 3 SO…….. 2 = 2 If it is a MINUS on one side of the equation, it becomes a PLUS on the other. What you are doing is KEEPING THE BALANCE - + 8 + 3 = 5 + 3 8 - 3 = 5 SO…….. 8 = 8 Click Mouse

Try these. Click the mouse for answer / help Find the value of x x + 8 = 21 Find the value of x x - 19 = 5 - + x - 19 = 5 x = 5 + 19 x = 24 x + 8 = 13 + - x + 8 = 21 x + 8 = 21 - 8 Find the value of y y - 8 = 22 Find the value of b b - 5 = 26 - + y - 8 = 22 y = 22 + 8 y + 8 = 30 b = 31 - + b - 5 = 26 b = 26 + 5 Find the value of z z + 19 = 21 Find the value of a a + 7 = 21 z = 2 z = 21 - 19 + - z + 19 = 21 a = 14 + - a + 7 = 21 a = 21 - 7 Click mouse

The same rules apply – you must keep your equation balanced Now you’ve got the hang of these, let’s try with multiplication and division The same rules apply – you must keep your equation balanced Look at this equation:- 4 x 3 = 12 This is balanced (because 4x3 is 12) To get rid of the x3 we must divide by 3, ON BOTH SIDES OF THE EQUATION Not yet balanced!!! 4 x 3 = 4 4 x 3 = 12 ÷ 3 4 x 3 = 12 4 x 3 = 12 Balanced again! Divide by 3 to get rid of x3 So divide this side by 3 Click mouse

So multiply this side by 2 Keep your equation balanced Look at this equation:- 4 ÷ 2 = 2 This is balanced (because 4 ÷ 2 is 2) To get rid of the ÷ 2 we must multiply by 2, ON BOTH SIDES OF THE EQUATION Not yet balanced!!! 4 x 3 = 2 x 2 4 x 3 = 4 4 x 3 = 2 4 ÷ 2 = 2 Balanced again! Multiply by 2 to get rid of ÷ 2 So multiply this side by 2 Click mouse

So multiply this side by 2 So, now that you can see the same rules apply, let’s try it with algebra Look at this equation:- y ÷ 2 = 8 To get rid of the ÷ 2 we must multiply by 2, ON BOTH SIDES OF THE EQUATION Not yet balanced!!! y x 3 = 16 y x 3 = 8 y ÷ 2 = 8 y x 3 = 8 x 2 Balanced again! Multiply by 2 to get rid of ÷ 2 So multiply this side by 2 Click mouse

Look at this equation:- y x 2 = 8 To get rid of the x 2 we must DIVIDE by 2, ON BOTH SIDES OF THE EQUATION Not yet balanced!!! y x 3 = 4 y x 3 = 8 ÷ 2 y x 3 = 8 y x 2 = 8 Balanced again! Divide by 2 to get rid of x 2 So divide this side by 2 Click mouse

What you are doing is KEEPING THE BALANCE Can you see the pattern? If it is a MULTIPLY on one side of the equation, it becomes a DIVIDE on the other - INVERSING again! x ÷ 2 + 3 = 6 ÷ 3 2 x 3 = 6 SO…….. 2 = 2 If it is a DIVIDE on one side of the equation, it becomes a MULTIPLY on the other. What you are doing is KEEPING THE BALANCE ÷ x 8 + 3 = 4 x 2 8 ÷ 2 = 4 SO…….. 8 = 8 Click Mouse

Try these. Click the mouse for answer / help Find the value of b b x 8 = 24 Find the value of a a x 7 = 49 a = 7 x ÷ a x 7 = 49 a = 49 ÷ 7 b + 8 = 3 x ÷ b x 8 = 24 b + 8 = 24 ÷ 8 Find the value of y y ÷ 4 = 9 Find the value of b b x 5 = 40 y + 8 = 36 ÷ x y ÷ 4 = 9 Y = 9 x 4 b = 40 ÷ 5 x ÷ b x 5 = 40 b = 8 Find the value of z z ÷ 8 = 6 Find the value of a a ÷ 3 = 7 z = 48 z = 6 x 8 ÷ x z ÷ 8 = 6 a = 7 x 3 a = 21 ÷ x a ÷ 3 = 7 Click mouse