To reduce anything implies making it easy to see or comprehend. Thus, simplifying fractions involves making any fractional number relatively feasible. When one fractional number is written at its most basic terms, its upper, as well as bottom values, can no more be reduced by any whole value accurately or equally (except the integer 1).
We achieve it by dividing both upper and lower values of the fraction through the greatest integer which divides perfectly across both integers. We can also say that we split both upper and lower with the largest integer both share.
It’s worth noting here that the upper, as well as lower parts of any fractional number, are referred to as “terms.” Therefore, when one reduces a fractional number, we decrease it to its simplest way possible.
Proper & Improper Fractions
Proper fractional numbers are those where the value in the lower part of the fraction is greater than its value in the upper part of the fractional number. Improper fractional numbers are those where the value in the lower part of the fraction is lower than its value in the lower part of that fractional number. Mixed fractional numbers are improper fractional number subsets that contain a whole value as well as a fractional value.
Now let us look at a few instances.
- Proper Fractions – 8/9, because the upper part of the provided fractional number is smaller than its lower part amount.
- Improper Fractions – 8/7, because the upper part of the provided fractional number is bigger than its lower part amount.
Decimal Numbers
Throughout math, numbers are categorized into several categories, including real figures, natural figures, whole ones, etc. One of them is decimal numbers. This is one of the most common ways to express both integral as well as non-integer quantities.
Decimal digits are among the forms of number systems in Mathematics that have a whole integer as well as a partial component distinguished through a point. This decimal point is just the dot that appears among the full number as well as the fractional part. 23.7, for instance, is, therefore, a decimal number.
In this case, 23 becomes the whole number half, while 7 becomes the fraction portion. A decimal point is denoted by “.”
How to Simplify Fractions?
Now, how can one simplify fractional numbers? The two main approaches to calculate them are as follows:
- Check & Guess
- The Highest Common Factor (HCF)
Guess and Check Method
If one uses the guess and verify approach, one selects an integer that splits uniformly through both the upper and lower parts of the fraction but isn’t certain whether this is the greatest. As a result, one might need to keep reducing that fractional number as needed.
HCF Method
To demonstrate these common factors, modify both upper as well as lower parts of the fractional numbers. In necessity, convert both these numbers to prime integers. Then reduce via deleting common components utilizing equal parts concept. Finally, the left-out components should be multiplied.
Both approaches seem absolutely appropriate, also it becomes a matter of individual choice on whichever strategy one will choose.
It is obvious that maybe if one’s prediction might be the HCF, then it will simplify the fractional number quickly since the HCF generally yields the smallest feasible drop.
Example to Simplify Fractions
Identify the greatest common factor (GCF) of the upper and lower part of the fraction. Reduce the upper as well as the lower part of that number through GCF.
Example 1: Can you tell me if the fractional number 5/10 is in its simple form?
Solution: Factors of the upper part of fraction 5 = 1, 5
Factors of the lower part of fraction 5 = 1, 2, 5, 10
GCF (Greatest common factor) of 5 & 10 = 5
By multiplying the upper and lower parts of the fraction by 5 (GCF), one obtains
(5 / 5) / ( 10 / 5) = 1/2
Therefore, ½ would be the fractional number’s simple form 5/10.