One fraction is a number used to represent installments of an integer value that has been divided into equal parts, that is, if any object is divided, the number that will represent each of the parts obtained in this division will be called a fraction.
One integer any is not meant to represent fractions of objects. For this, the rational numbers.
Rational numbers and the representation of fractions
Any number that belongs to the set of rational numbers is the result of division between two whole numbers. We can represent these numbers in two ways: through decimal numbers or through fractions. If a soda, for example, is shared among five friends, the portion of that soda that will be given to each one will be as follows:
1:5 = 0,2
That division is also very much represented in the following way:
1 = 0,2
5
This representation is what we call the fraction. the number that is Divided is placed on top and is called numerator. the number that divide, in turn, is placed at the bottom and is called denominator.
In the fraction above, the numerator is the number 1, because only a soda was split, and the denominator is the number 5, because the soda was divided to five people.
In addition, the fractions they can also be represented by drawings divided into equal parts. See the image below:
The only two rules for assembling a fraction are:
Numerator and denominator must be whole numbers;
The numerator can never be zero, as it makes no sense to divide something by zero.
Own and inappropriate fractions
O numerator of a fraction it doesn't necessarily have to be 1. Think of the case where a group of six people goes to a pizzeria and orders two pizzas. The fraction that represents the amount of pizza each person will eat, if they eat the same amount, is:
2
6
At fractions whose numerator is smaller than the denominator are called own. One improper fraction has numerator greater than denominator. In the pizza example, this would mean that each person would receive more than one whole pizza. For example, if the same six friends had ordered seven pizzas, we would have the fraction:
7
6
Basic operations involving fractions
→ Addition and subtraction of fractions:
if two fractions have denominators equal, add or subtract the numerators and keep the denominator in the result.
2 + 3 = 2 + 3 = 5
4 4 4 4
Otherwise, if the denominators are not the same, do the least common multiple between the denominators, divide this minimum by the denominator of the first fraction and multiply by your numerator. Do the same with the second fraction. The results found are numerators, and the minimum is the denominator of the fractions that will be added. Look at the example:
2 – 1 = 4 – 3 = 1
3 2 6 6
Note in the example above that 6 is the least common multiple between 3 and 2. Furthermore, (6:3)·2 = 4 and (6:2)·1 = 3, which are the denominators being subtracted in the second step.
More information on adding and subtracting fractions can be found. on here.
Fraction multiplication
For multiply fractions, do the following: multiply numerator by numerator and denominator by denominator. See an example:
2·4 = 2·4 = 8
3 6 3·6 18
fraction division
At division of fractions, we multiply the first by the inverse of the second. Look at the example:
2:4 = 2·6 = 12
3 6 3 4 12
Equivalent Fractions and Simplification of Fractions
equivalent fractionsare those that have the same numerical value, that is, when dividing numerator by denominator, we find the same result.
To find fractionsequivalents, just multiply numerator and denominator by the same number. At fractions next are equivalents, since the second is the result of the product of the numerator and denominator of the first by 2.
2 = 4
7 14
If it is possible to divide the numerator and denominator of a fraction by the same number, the result of this division will also be a fractionequivalent, as in the following example, where the fraction was divided by 3.
18 = 6
24 8
Simplify fractions is to find fractions equivalents by the process of division. When it is no longer possible to find them by this process, the final fraction will be named irreducible fraction.
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