In the field of mathematics, a division is known as a fraction or fraction, more specifically it is an expression that is used to refer to a quantity that is divided by another quantity , for example, 5/8, which refers to the fact that the number 5 is divided into 8 parts. There are several ways to classify fractions as heterogeneous, homogeneous, unitary, Egyptian, irreducible, and reducible, all based on the relationship between the numerator and the denominator.
Another type is the proper fraction, that is, it expresses a certain number of portions in which the numerator is less than the denominator , and this is represented by an oblique or horizontal bar that separates both numbers.
Examples of Proper Fractions
Proper Fractions Problem
There are some problems in which it is necessary to find out, from the given data, what the corresponding fraction is.
In the fridge there are 13 yogurts, of which 5 are coconut flavored . With what fraction are these data represented?
- 5: this number is the numerator, which is the one that shows the number of parts in which you want to represent the yogurts.
- 13: this number is the denominator, which is the one that shows the number of total parts of yogurt in the fridge.
So the solution to this problem is a proper fraction of 5/13, which is itself an irreducible fraction. This means that it is a division that cannot be simplified by not sharing common factors.
Examples of Proper Fraction Operations
Proper fractions are values , so it is normal that they can participate in mathematical operations such as multiplication, division, addition and subtraction.
Sums of Proper Fractions
An essential requirement for two proper fractions or more to be added is that they have the same divisor , and if they do not have it, it is essential to look for it.
- 1/2 + 1/6
The denominators of these proper fractions are 2 and 6. At the time of addition, it can be seen that 6 is a common multiple for 2 and 6, so the best option is to choose that number as the common denominator for both. To do this, it is necessary to make some adjustments that we will show below.
1/2 + 1/6 = 1(3) + 1/6 = 4/6
Subtraction of proper fractions
- 1/3 – 1/9
In this subtraction, the denominators are 3 and 9, so in order to equal them and be able to carry out said mathematical operation, it is necessary to know that 9 is a common multiple of 9 and 3, so that number is chosen as the common denominator . To do this, it is necessary to make some adjustments that we will show below.
1/3 – 1/9 = 1(3) – 1/9 = 2/9
Multiplication of proper fractions
In this type of fractions, the easiest operation is multiplication because you simply have to multiply the numerator by the numerator and the same happens with the denominators.
5/8 x 10/12 = 5(10) / 8(12) = 50/96
Division of proper fractions
When making the division , you need to do 2 very simple steps ; on the one hand, alter one of the numerators and denominators and, on the other hand, multiply online.
1/3 divided by 5/7 = 1/3 x 7/5 = 1(7) / 3(5) = 7/15