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Sometimes you will see a multiplication of letters as a dot or without any symbol. Don't worry, its exactly the same thing. Mathematicians areefficient and like to write things in the shortest, neatest way possible.
It is usually neater to write known numbers to the left, and letters to the right. So although $4x$ and $x4$ are the same thing, it looks better to write $4x$ . In this case, the “4” is a constant that is referred to as the coefficient of $x$ .
The fact that $ab=ba$ is known as the commutative property of multiplication. Therefore, both addition and multiplication are described as commutative operations.
Brackets Sometimes people say “parentheses” instead of “brackets”. in mathematics are used to show the order in which you must do things. This is important as you can get different answers depending on the order in which youdo things. For example:
whereas
If there are no brackets, you should always do multiplications and divisions first and then additions and subtractions Multiplying and dividing can be performed in any order as it doesn't matter. Likewise itdoesn't matter which order you do addition and subtraction. Just as long as you do any $\times \xf7$ before any $+-$ . . You can always put your own brackets into equations using this rule to make things easier for yourself, for example:
If you see a multiplication outside a bracket like this
then it means you have to multiply each part inside the bracket by the number outside
unless you can simplify everything inside the bracket into a single term. In fact, in the above example, it would have been smarter to have done this
It can happen with letters too
The fact that $a(b+c)=ab+ac$ is known as the distributive property.
If there are two brackets multiplied by each other, then you can do it one stepat a time:
Negative numbers can be very confusing to begin with, but there is nothing to be afraid of. The numbers that are used most often are greater than zero. Thesenumbers are known as positive numbers .
A negative number is a number that is less than zero. So, if we were to take a positive number $a$ and subtract it from zero, the answer would be the negative of $a$ .
On a number line, a negative number appears to the left of zero and a positive number appears to the right of zero.
When you are adding a negative number, it is the same as subtracting that number if it were positive. Likewise, if you subtract a negative number, it is the sameas adding the number if it were positive. Numbers are either positive or negative and we call this their s ign. A positive number has a positive sign ( $+$ ) and a negative number has a negative sign ( $-$ ).
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