Review of past work  (Page 5/8)

You can even combine these tips: for example, you can use Tip 1 on $-10+3$ to get $3-10$ and then use Tip 3 to get $-(10-3)=-7$ .

Negative numbers

1. Calculate:

   (a) $(-5)-(-3)$	(b) $(-4)+2$	(c) $(-10)÷(-2)$
   (d) $11-(-9)$	(e) $-16-\left(6\right)$	(f) $-9÷3\times 2$
   (g) $(-1)\times 24÷8\times (-3)$	(h) $(-2)+(-7)$	(i) $1-12$
   (j) $3-64+1$	(k) $-5-5-5$	(l) $-6+25$
   (m) $-9+8-7+6-5+4-3+2-1$

2. Say whether the sign of the answer is $+$ or $-$

   (a) $-5+6$	(b) $-5+1$	(c) $-5÷-5$
   (d) $-5÷5$	(e) $5÷-5$	(f) $5÷5$
   (g) $-5\times -5$	(h) $-5\times 5$	(i) $5\times -5$
   (j) $5\times 5$

Rearranging equations

Now that we have described the basic rules of negative and positive numbers and what to do when you add, subtract, multiply and divide them, we are ready totackle some real mathematics problems!

Earlier in this chapter, we wrote a general equation for calculating how much change ( $x$ ) we can expect if we know how much an item costs ( $y$ ) and how much we have given the cashier ( $z$ ). The equation is:

So, if the price is R10 and you gave the cashier R15, then write R15 instead of $z$ and R10 instead of $y$ .

Now that we have written this equation down, how exactly do we go about finding what the change is? In mathematical terms, this is known as solving an equationfor an unknown ( $x$ in this case). We want to re-arrange the terms in the equation, so that only $x$ is on the left hand side of the $=$ sign and everything else is on the right.

The most important thing to remember is that an equation is like a set of weighing scales. In order to keep the scales balanced, whatever is done to oneside must be done to the other.

Method: rearranging equations

You can add, subtract, multiply or divide both sides of an equation by any number you want, as long as you always do it to both sides.

So for our example we could subtract $y$ from both sides

Now we can see that the change is the price subtracted from the amount paid to the cashier. In the example, the change should be R5. In real life wecan do this in our heads; the human brain is very smart and can do arithmetic without even knowing it.

When you subtract a number from both sides of an equation, it looks like you just moved a positive number from one side and it became a negative on the other,which is exactly what happened. Likewise, if you move a multiplied number from one side to the other, it looks like it changed to a divide. This is because youreally just divided both sides by that number and a number divided by itself is just 1

However, you must be careful when doing this, as it is easy to make mistakes.

The following is the WRONG thing to do

Can you see why it is wrong? It is wrong because we did not divide the $c$ term by $a$ as well. The correct thing to do is

Rearranging equations

1. If $3(2r-5)=27$ , then $2r-5=.....$
2. Find the value for $x$ if $0,5(x-8)=0,2x+11$
3. Solve $9-2n=3(n+2)$
4. Change the formula $P=A+Akt$ to $A=$
5. Solve for $x$ : $\frac{1}{ax}+\frac{1}{bx}=1$