Historical Beginnings | The Place Value System | The Branches of Mathematics | Numerical and Literal Numbers | Signs and Symbols in Mathematics | Expressing More Relationships Between Numbers

Pre-Test		Post-test
Q&A	The Basics	Q&A

Numerical and Literal Numbers
CA GR7 AF 1.4

What do numbers mean? Let's take a specific one -- the number 5 -- and see. By itself, the number 5 is meaningless. But if you say 5 inches, 5 feet or 5 miles, the meaning is loud and clear. This is the point of mathematics -- relating our calculations to meaningful quantities.

Now, you know what we mean in using the number 5 feet -- or 100 feet or 560 feet. You are very familiar with the use of numerical numbers (i.e. 1, 2, 3, etc.). There is another kind of number that we also use in math, literal numbers (literal means letter).  X feet is a literal number. How many feet is/are X feet? We don't know. If we did, we would use a numerical number. We use literal numbers to designate quantities we don't know. And we don't have to use X (or Y or Z) to designate any particular unknown number. We can use any letter to designate an unknown quantity of units. Once we decide that a certain letter will represent a number, however, we must continue to use it throughout the calculation of a problem until we can find out what numerical value it really represents.

Thus, we will need to establish how to handle literal numbers in our calculations. We cannot carry out our operations the same way with literal numbers as we can with numerical numbers. For example, we know that 4' + 5' can be expressed more simply as 9'. Can we do the same with A' + B'? Well, it turns out that the simplest way we can express it is A' + B'? We simply cannot do all of the things with literal numbers that we can with numerical numbers. So one thing we have to learn is what we can and cannot do with literal numbers.

Pre-Test		Post-test
Q&A	The Basics	Q&A

Signs and Symbols in Mathematics  (top)
CA GR7 AF 1.4

Now, we will turn our attention to mathematical signs and symbols that will help you to become proficient in doing math. Some of these, of course, you already know, and take for granted. For example, you know that:

• the plus sign (+) means to add, so that 4 + 5 means that 4 is to be added to 5 (to get 9)
   
• the minus sign (-) means to subtract, so that 7 - 2 means to subtract 2 from 7 (to get 5)
   
• the division sign (÷) means to divide, so that 16 ÷ 8 means to divide 16 by 8 (to get 2)
   
• the multiplication sign (x) means to multiply, so that 8 x 6 means to multiply 8 times 6 (to get 48)

You also know that the equal sign (=) means that everything on the left side of it is equal to everything on the right side. Or, to express the above examples in the form of equations, they would look like this:

• 4 + 5 = 9
   
• 7 - 2 = 5
   
• 16 ÷ 8 = 2
   
• 8 x 6 = 48

And, some other symbols that you already know are the apostrophe (') and the quotation mark (") that are used to represent feet and inches and some other things. No doubt you've seen the apostrophe used to designate feet and the quotation mark used to represent inches, so that: 6' 3" means six feet, three inches.

These two symbols have another important meaning in mathematics. Quite often, they are used to signify prime and double prime. For example, the apostrophe (') is referred to as prime and the quotation mark (") is referred to as double prime. If, for example, a straight line is labeled at each end, it can be referred to as line a' a" as follows:

Now, when you want to indicate the reverse of a signed relationship, you can draw a diagonal slash (/) through it:4    5 means 4 does not equal 5. Look at this expression: 5 > 6. This means that 5 is not greater than 6.

Since the above expressions compare two quantities that are not equal, they are called inequalities.

These signs are also used to show the size of angles when we want to show parts of a degree (°). The parts of a degree are minutes (') and seconds ("). And if an angle was 33 degrees, 7 minutes and 16 seconds, it would look like this: 33° 7' 16".

And since the symbol for an angle is ( ), if we had an angle that we labeled angle A, and it had 40 degrees, 17 minutes and 6 seconds, we would represent it like this: A = 40° 17' 6"

Next Page: Expressing More Relationships Between Numbers