Subtraction II - Fraction minus Fraction
When boiling water, it slowly evaporates. Let's do a thought experiment on this:
In a pot there is boiling 3/4 litres of water. After half an hour, 1/3 litres of water evaporated. How much water is left in the pot?
Finding out the task here is easy. It's just this one:
Common mistake when subtracting Fractions
Often the mistake is made that the two numerators and the two denominators are subtracted from each other:
Unfortunately, it's not that easy. This is only works when multiplying fractions. Let's see if this makes any sense:
If the water is filled into glasses with a volume of 1/4 litre each, exactly 3 glasses can be filled. 1 glass of it is to be taken away. But: this glass should contain 1/3 litre!
And that is exactly when it comes to a problem! A glass of 1/4 litre water could be easily removed, but 1/4 litre is not equal to 1/3 litre...
Even if the (wrong) result 2/1 litre is illustrated, it doesn't fit anymore: As a result, there should be 2 glasses each with a size of one litre? This is obviously more than the 3/4 liters you had before subtracting.
Problems of the type Fraction minus Fraction can only be solved if the denominators (or the glasses) are equal.
Formula: Subtracting Fractions having Common Denominators
Two fractions having the same denominators or common denominators are subtracted by subtracting the numerator. The denominator remains unchanged.
The result often can be simplified / reduced:
Formula: Subtracting Fractions NOT having Common Denominators
Two fractions that don't have the same denominators or common denominators cannot be subtracted directly! Instead:
Coming back to our "hot-water" problem:
Unfortunately, the denominators are not the same, so we cannot subtract the two fractions directly.
In order to get a common denominator, expand the first fraction by 3 and expand the second fraction by 4. Afterwards, the numerators can be subtracted:
There are still 5/12 litres of water in the pot.
Online Practice: Subtracting Fractions
Here you can practice subtracting fractions online: Subtracting Fractions.
If you have any problems with the exercise, please have a look at the hint and the sample solution first.
Congratulations! Step 4 is done!
Great! On the last pages you have learned, to calculate with fractions: Addition und Subtraction.
It's essential that you know:
- only fractions having the same denominator can be added/subtracted directly by adding/subtracting their numerators and remaining the denominator unchanged
- fractions having different denominators need to have a Common Denominator before adding/subtracting
Always check, whether fractions can be simplified/reduced, especially the result! Is the result is an improper fraction (the numerator is greater than the denominator): convert into a mixed number.
To complete Step 4, please take a minute to answer the comprehension questions: