In mathematics, the ratio establishes a comparison between two quantities , the coefficient being between two numbers.
The proportion is determined by the equality between two reasons , or even when two reasons have the same result.
Note that the reason is related to the division’s operation. It is worth remembering that two quantities are proportional when they form a proportion.
Although we are not aware of it, we use the concepts of reason and proportion on a daily basis. To prepare a recipe, for example, we use certain proportional measures between the ingredients.
Attention!
For you to find the ratio between two quantities, the units of measurement must be the same.
Examples
From the quantities A and B we have:
Reason :
or A: B, where b ≠ 0
Proportion :
where all the coefficients are ≠ 0
Example 1
What is the ratio between 40 and 20?
Remember that in a fraction , the numerator is the number above and the denominator, the bottom one.
If the denominator is equal to 100, we have a percentage ratio , also called a centesimal ratio.
Furthermore, for the reasons, the coefficient that is located above is called the antecedent (A), while the lower one is called the consequent (B).
Example 2
What is the value of x in the proportion below?
3. 12 = x
x = 36
So, when we have three known values, we can discover the fourth, also called the “proportional fourth”.
In proportion, the elements are called terms. The first fraction is formed by the first terms (A / B), while the second is the second terms (C / D).
In problems where the resolution is made using the rule of three , we use the proportion calculation to find the value sought.
Aspect Ratio Properties
1 . The product of the media is equal to the product of the extremes, for example:
Soon:
A · D = B · C
This property is called cross multiplication .
2 . It is possible to change the extremes and means of place, for example:
is equivalent
Soon,
D. A = C. B
Solved Exercises
1 . Calculate the ratio of the numbers:
a) 120: 20
b) 345: 15
c) 121: 11
d) 2040: 40
Answer:
a) 6
b) 23
c) 11
d) 51
2 . Which of the proportions below are equal to the ratio between 4 and 6?
a) 2 and 3
b) 2 and 4
c) 4 and 12
d) 4 and 8
Answer:
Alternative to: 2 and 3