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Shape and Space
Statistics and Probability
1/2 means 1 divided by 2. If you try this on a calculator, you will get an answer of 0.5 . 3/6 means 3 divided by 6. Using a calculator, you will find that this too gives an answer of 0.5 . That is because 1/2 = 3/6 = 0.5 . Fractions such as 3/6 can be cancelled. You can divide the top and bottom of the fraction by 3 to get 1/2 .
With fractions, you are allowed to multiply or divide the top and bottom of the
fraction by some number, as long as you multiply (or divide) everything
on the top and everything on the bottom by that number.
Division by Zero
At this point, it is worth mentioning that you are not allowed to divide by zero. Division by zero is undefined. Some people think you can divide by zero and get infinity- you can't. Division by zero is simply not allowed.
Adding and Subtracting Fractions
To add two fractions, the bottom (denominator) of the two fractions must be the same. 1/2 + 3/2 = 4/2 ; 1/10 + 3/10 + 5/10 = 9/10 . If the denominators are not the same, multiply the top and bottom of one (or more) of the fractions by a number to make the denominators the same.
The same is true when subtracting fractions.
This is simple: just multiply the two numerators (top bits) together, and the two denominators together:
If A, B, C and D are any numbers,
These rules work even when the fractions involve algebra.
Fractions, of course, can often be 'cancelled down' to make them simpler. For example, 4/6 = 2/3. You can divide or multiply the top and bottom of any fraction by any number, as long as you do it to both the top and bottom. However, when there is more than one term on the top and/or bottom, to cancel you must divide every term in the top and bottom by that number.
2 + x
Simplify the expression 2x² - 5x + 2