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1.3 B) Simplifying Fractions
1.3 B) Simplifying Fractions
The final example in the video is not relevant for the foundation course.
We always want to have answers to questions in the simplest form and this is because when answers are in their simplest form they are easier to use. We can simplify fractions by finding a common factor in both the numerator and the denominator, and then dividing both the numerator and denominator by that common factor. We can go straight to the simplest fraction by dividing the numerator and the denominator by the highest common factor between the numerator and the denominator; the highest common factor is the highest number that is a factor of both the numerator and the denominator. However, if you cannot see the highest factor straight away, you can divide the numerator and the denominator by any factor of the numerator and the denominator, and then check the answer you obtain to see if there are any more common factors between the numerator and the denominator.
Example 1
Simplify the fraction:
Simplify the fraction:
The numerator for our fraction is 2 and the denominator for the fraction is 10. In order to simplify this fraction, we are looking for the highest common factor between 2 and 10. We can find the highest common factor between these two numbers by writing down the factors of each of the two numbers and then finding the highest factor that goes into both numbers.
- The factors of 2 are 1 and 2.
- The factors of 10 are 1, 2, 5 and 10.
This results in the simplified fraction becoming 1/5.
These two fractions are equivalent to one another. Equivalent fractions are fractions that have the same value despite being written in a different way. You can type 1 ÷ 5 and 2 ÷ 10 into a calculator and they will give you the same answer; in decimal form, both of these fractions are 0.2.
Example 2
Simplify the fraction:
Simplify the fraction:
In order to go straight to the simplified fraction, we are going to divide the numerator and the denominator by the highest common factor between 8 and 20. Let’s suppose that I could not find the highest common factor straight away. If this is the case, we can divide the numerator and the denominator by any common factor and check our answer to see if there are any more common factors between the numerator and the denominator.
Both the numerator and the denominator are even, and this means that they are both multiples of 2. Therefore, I can divide the numerator and denominator by 2.
Both the numerator and the denominator are even, and this means that they are both multiples of 2. Therefore, I can divide the numerator and denominator by 2.
I now need to check whether there are any more factors between the numerator and denominator in the fraction. Both the numerator and the denominator of the fraction are even, and this means that 2 is a factor of both of these numbers. Therefore, I can divide the numerator and the denominator by 2.
There are no more common factors between the numerator (2) and the denominator (5) and this means that the fraction above is in it’s simplest form.
The highest common factor between the numerator and the denominator of the original fraction is 4. Therefore, we could have gone straight to the most simplified answer by dividing the numerator and the denominator of the original fraction by 4. This would give us the same answer as above.
The highest common factor between the numerator and the denominator of the original fraction is 4. Therefore, we could have gone straight to the most simplified answer by dividing the numerator and the denominator of the original fraction by 4. This would give us the same answer as above.