Fractions are divided into three types of fractions in mathematics. Proper fractions, improper fractions, and mixed fractions. For those who don’t know, fractions are simply the name given to a number that contains a numerator and denominator.
The terminology used to determine the pieces of a whole item are fractions. A pizza, for example, is cut into four pieces, with each piece representing a quarter of the pizza. The numerator is 1 and the denominator is 4. In this article we look into what proper and improper fractions are and how to differentiate them.
What is a proper fraction?
If the numerator is less than the denominator, for example 3/5, the fraction is defined as a proper fraction. A proper fraction’s value is always less than one otherwise it would be a mixed number.
Here is an example of a scenario involving a proper fraction:
Sam bought a chocolate bar and divided it into four equal portions. He kept one half and handed his sister Rachel the rest. We divide Sam’s portion into quarters and Rachel’s into halves. Because the numerator is less than the denominator, both of these fractions are proper fractions.
What is an improper fraction?
An improper fraction is defined as a fraction in which the numerator is greater than the denominator, for example 12/4, 7/3, or 9/2.
There are two pieces to every fraction: the numerator and the denominator. Proper fractions and improper fractions are the two primary forms of fractions in mathematics based on the numerator and denominator values.
How to find the percentage of a fraction?
Difference between proper fractions and improper fractions
The difference between proper fractions and improper fractions is that they are opposite in regards to:
- Their relation to 1;
- The value of the numerator and denominator.
Relation to 1
A major property which defines a proper and improper fraction is its relation to 1. Proper fractions can only ever be smaller than 1. For example 3/9, 12/45, and 70/190. An improper fraction, however, will always be greater than 1 and can be turned into a mixed number.
Numerators and Denominators
The other major property which distinguishes these two types of fractions is the relationship between numerators and denominators. If the numerator is less than the denominator, for example, 2/3, 1/6, or 10/100, then the fraction is a proper fraction. Improper fractions, on the other hand, have a numerator that is either equal to or greater than the denominator. Examples include 5/5, 10/10, 123/54, 7/2.
Step to write improper fractions as mixed numbers
Before learning how to convert an improper fraction into a mixed number, let’s review the definitions of mixed numbers and improper fractions. A mixed fraction has a whole number portion and a proper fraction, and its value is always more than 1. An improper fraction‘s numerator is always greater than or equal to the original denominator. 17/2, 197/3 and 9/5 are examples of improper fractions.
To convert an improper fraction into a mixed number, we must divide the numerator by the denominator. After division, the acquired quotient becomes the whole number, the remainder becomes the new numerator, and the denominator remains the same, resulting in a mixed number.
Here is an example:
Let’s take a look at the fraction 19/6 and see how we can convert it to a mixed number. To begin, we must determine how much of the denominator is transferred to the numerator. We do this by dividing the denominator by the numerator. The numerator will be the new numerator, and the remainder will be the whole number.
There is a leftover of 1 after 6 goes into 19 three times (6 x 3 = 18). As a result, the new numerator is 1 and the entire number is 3 1/6 as we construct our mixed number.
Simplification
A complex fraction, such as 64/12, may be encountered. This appears to be difficult, so we’ll try to simplify the fraction first and then convert it. To find the largest common factor between the two integers and simplify the numerator and denominator, first list the factors of each number:
| 64 | 1, 2, 4, 8, 16, 32, 64 |
| 12 | 1, 2, 3, 4, 6, 12 |
Looking at the factors, we can see that factors 1, 2, and 4 are shared by both. The greatest/highest number is 4. A simplified form of this fraction can be obtained by multiplying the numerator and denominator by four.
64 divided by four equals 16.
12 divided by four equals 3.
As a result, 64/12 can be simplified to 16/3. Converting this to a mixed number will now be much easier:
3 can go into 16 if we multiply it by 5, this leaves a surplus of 1. As a result, 16/3 equals 5 1/3 as a mixed number and simplified fraction.
How to find common multiples of a number?
Converting mixed fractions into improper fractions
Converting a mixed number into an improper fraction is similar to converting a mixed number into an improper fraction but in reverse. You must simply divide the whole number by the denominator before adding the numerator. As a result, we now have a new, incorrect numerator.
Here’s an example:
Make an improper fraction out of 4 7/10. Let’s start by multiplying the numerator (10) by the entire number (4):
40 = 4 x 10
Then, to this answer, add the numerator (7):
47 = 40 + 7
The new numerator is this. As a result, if we expressed 4 7/10 as an improper fraction, we get 47/10.
Simplifying
What if you get a dreaded fraction like 5 84/24? This scary-looking fraction would put off anyone! Do not worry as we can simplify it. At this point, we can ignore the entire number and concentrate solely on the numerator and denominator. Let’s have a look at each of the factors of the numerator and denominator:
The factors of the numerator (84) are composed of the following numbers:
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of the denominator (24) are composed of the following numbers:
1, 2, 3, 4, 6, 8, 12, 24.
The factors 1, 2, 3, 4, 6, and 12 are shared by the numerator and denominator. The largest number is 12, therefore divide the numerator and denominator by this:
84 divided by 12 is 7.
24 divided by 12 is 2.
As a result, 5 84/24 can be simplified to 5 7/2. Let’s convert this considerably less difficult mixed fraction:
2 (denominator) multiplied by 5 (whole number) is 10 (new numerator). Then, if we add the new numerator, 10, with the current numerator, 7, we get 17.
As a result, the mixed fraction of 5 84/24 is expressed as the improper fraction 17/2.
Need more help?
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