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Scratching-out
When scratching-out, you divide the whole numerator and the whole denominator by the same value. Everybody calls it like that.
Example 1
In a simple fraction everything is clear
because you can divide the numerator and denominator by 2. Another method, that better shows what happens is
Example 2
It becomes more difficult if there are two terms in the numerator. We're going to do it wrong, and scratch-out only a part of the numerator
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We have clearly not taken the whole numerator. Here is the correct approach
An alternative explanation is clearer
There is another possible explanation, which of course also yields the same answer
If you calculate the fraction otherwise you can clearly see why you must do it like that. You could have written this as
Example 3
Now we dare to tackle larger fractions. Step by step you will see
Here you look at it, and then you can see that it is true. You have to write that this solution only applies for x ≠ 2, because you cannot divide by zero. The alternative explanation is even better
Example 4
Finally, an extra fraction, where you can scratch-out as you like it
A check with the alternative explanation gives
And that looks pretty clear.
Example 5
We want to write this as one fraction
Step by step we continue
( ×10 ∕ ×10) = etc... 034.gif){kind=small}
We guess that the denominator must be 50a, and get
It is striking that we can scratch out 10 in the numerator and denominator, and write
Example 6
Now it gets more difficult
That looks strange, but we will make the denominators equal
That was not difficult. We put it all together in one fraction
Now we calculate the numerator
and remove the brackets in the numerator
That is nice. Now we can use brackets again in the numerator
In the numerator and the denominator we delete x – 2
You must write here that this result is only valid for x ≠ 2, as dividing by zero is not allowed.
Example 7
We take the fraction
You must first make the denominators equal
That is correct. You will understand that a × b is the same as b × a, because 2 × 3 is, after all, just as much as 3 × 2. In alphabetical order the answer is