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Directed Numbers
A directed number is simply a number with a positive or negative sign in front of it, such as +4 or 2. The sign tells you which direction to count along the number line (right for positive, left for negative). Getting your head around directed numbers can be quite tricky  many European mathematicians refused to acknowledge their existence until well into the 17th Century because they found them so confusing, so if you find them a little difficult, you're in good company! However, they do crop up an awful lot, and are very useful in situations when we have to count past zero (for example, in winter when temperatures drop below freezing).
Adding and Subtracting Directed Numbers
Level 5
You should be able to add and subtract directed (positive and negative) numbers.
First of all, directed numbers can cause confusion because problems involving them can be written in different ways.
First of all, directed numbers can cause confusion because problems involving them can be written in different ways.
If you see a number on its own with no signs, you assume it's a positive amount.
For example, if I tell you it's 5 degrees outside, you assume I mean 5 degrees above zero, or positive 5. If I come rushing in half an hour later and tell you it's now 5 degrees, you know I mean 5 degrees below zero, or minus 5. Conventionally in mathematics we only write directional (e.g. positive and negative) signs when they are important  like when I'm telling you about temperatures and I need to distinguish between temperatures above and below freezing. 
We also assume that numbers on their own are positive amounts. If I tell you that it was 3°C this morning but that the
temperature has risen by 5°C, you quickly work out 3 + 5 = 8, so it must now be 8°C. You automatically treat 3 as "positive 3" and 5 as "positive 5".
However, to confuse things, many maths textbooks start putting direction signs in when you do directed number problems. Suddenly 3 + 5 becomes +3 + +5 and you get very confused, as you're not used to seeing the problem written that way.
The distinction here is between the "+" signs in front of the numbers and the "+" sign in between +3 and +5. The "+" signs in front of the numbers are the ones we don't usually write  the ones that tell us we are dealing with a positive amount. The "+" sign in between +3 and +5 tells us the operation we need to do  i.e. start at +3 and add on +5. The answer to this is still 8...or if we're being really picky, +8.
Now onto the tricky part: how to add and subtract directed numbers. I've put together a little picture story below about a hot air balloon that should help you to understand what happens; have a look at the pictures or download the Powerpoint in full below (it's got animations and everything!).
temperature has risen by 5°C, you quickly work out 3 + 5 = 8, so it must now be 8°C. You automatically treat 3 as "positive 3" and 5 as "positive 5".
However, to confuse things, many maths textbooks start putting direction signs in when you do directed number problems. Suddenly 3 + 5 becomes +3 + +5 and you get very confused, as you're not used to seeing the problem written that way.
The distinction here is between the "+" signs in front of the numbers and the "+" sign in between +3 and +5. The "+" signs in front of the numbers are the ones we don't usually write  the ones that tell us we are dealing with a positive amount. The "+" sign in between +3 and +5 tells us the operation we need to do  i.e. start at +3 and add on +5. The answer to this is still 8...or if we're being really picky, +8.
Now onto the tricky part: how to add and subtract directed numbers. I've put together a little picture story below about a hot air balloon that should help you to understand what happens; have a look at the pictures or download the Powerpoint in full below (it's got animations and everything!).
The picture on the left shows the "rules" for adding and subtracting directed numbers. Notice it's the signs in the middle (the operation and following direction sign) that we're interested in.
I recommend you don't just learn rules like "a plus and a plus makes a minus" without understanding them, because this can get really confusing if you're not sure how to apply it. Download the Powerpoint for future reference!

Weblinks
Still stuck or looking for something more? Try these links below.
Videos 
GamesQuestions to TryLinksMymaths: ChallengesOops, nothing here yet!

Multiplying and Dividing Negative Numbers
Level 6
Because of the relationship between addition and multiplication, the rules for multiplying directed numbers look very similar to those for adding.
Multiplication is just repeated addition; when we write 3 x 2, we're doing "3 lots of 2", or 2 + 2 + 2 (this is how computers do all multiplication, even for very large numbers!).
So, if we do something like 3 x 2, we're actually doing 2 + 2 + 2. Using the work on addition and subtraction above, we know that this is just 2  2  2, which equals 6.
Similarly, 3 x 2 is 2 lots of 3. This is 3 + 3, or just 3  3, which equals 6.
Again, using the work above, it must follow that 2 x 3 = +6.
We can think about this as 2 lots of 3, which is (3 + 3), or (6), or simply +6 (remember, this can be written without the positive sign as just "6").
Because division is the opposite (inverse) of multiplication, the rules work in exactly the same way for dividing directed numbers.
Multiplication is just repeated addition; when we write 3 x 2, we're doing "3 lots of 2", or 2 + 2 + 2 (this is how computers do all multiplication, even for very large numbers!).
So, if we do something like 3 x 2, we're actually doing 2 + 2 + 2. Using the work on addition and subtraction above, we know that this is just 2  2  2, which equals 6.
Similarly, 3 x 2 is 2 lots of 3. This is 3 + 3, or just 3  3, which equals 6.
Again, using the work above, it must follow that 2 x 3 = +6.
We can think about this as 2 lots of 3, which is (3 + 3), or (6), or simply +6 (remember, this can be written without the positive sign as just "6").
Because division is the opposite (inverse) of multiplication, the rules work in exactly the same way for dividing directed numbers.
Download the Powerpoint for future reference!
Weblinks
Still stuck or looking for something more? Try these links below.
Videos 
GamesGrade or No Grade
Connect 4 (2 Players) 60 Sec Challenge: Multiplication 60 Sec Challenge: Division Jeopardy: All Four Operations Questions to TryLinksChallengesOops, nothing here yet!

Quite Interesting Things about Percentages
 Percentages crop up everywhere in everyday life, especially when shopping on the high street, where you'll see percentages in bank windows quoting interest rates and shops showing how much money you get off in their sales. However, one unusual application of percentages is Bakers Percentages; professional bakers use a percentagebased recipe which gives amounts of other ingredients to be used as a percentage proportion of flour used.