The ratio describes the "relationship" between two or more things.
The ratio connects the given terms and describes how many times greater or smaller a certain magnitude is than another.
Let's see an example from everyday life:
When asked in a class, what is the ratio between boys and girls, it refers to how many girls there are in relation to a certain number of boys.
Or, for example, if in a certain vase there are red and white balls, the ratio between them can describe how many red balls there are in relation to a certain number of white balls or vice versa.
We know that the ratio between apples and oranges in a basket is 2:3. The total amount of fruit in the basket is 25. We are asked to calculate the number of apples and oranges in the basket. We can deduce that the 2 represents the number of apples and the 3 represents the number of oranges. We will denote both fruits with a variable X.
Now let's draw a simple equation:
2X+3X=25
5X=25
X=5
From here we can infer that the number of apples is 10(2X) and the number of oranges is 15(3X). We can always go back and check our result by verifying that the total number of apples and oranges is 25, as shown in the first piece of data we received.
Example 2
In the dishware cabinet, there is a total of 30 utensils that include plates and bowls. The ratio between plates and bowls is 7:3.
We are asked to determine how many plates and bowls are in the cabinet.
According to what we have learned, we can deduce that the 7 represents the number of plates and the 3 the number of bowls.
Let's denote both with a variable X.
Now let's set up a simple equation:
7X+3X=30
10X=30
X=3
From here we can infer that the number of plates is 21(7X) and the number of bowls is 9(3X).
We can always go back and check our result by verifying that the total number of utensils in the cabinet is 30, as seen in the first given data.
Examples and exercises with solutions of Ratio
Exercise #1
There are 18 balls in a box, 32 of which are white.
How many white balls are there in the box?
Video Solution
Answer
12
Exercise #2
In a box there are 28 balls, 41 of which are orange.
How many orange balls are there in the box?
Video Solution
Answer
7
Exercise #3
There are two circles.
One circle has a radius of 4 cm, while the other circle has a radius of 10 cm.
How many times greater is the area of the second circle than the area of the first circle?
Video Solution
Answer
641
Exercise #4
There are two circles.
The length of the radius of circle 1 is 6 cm.
The length of the diameter of circle 2 is 12 cm.
How many times greater is the area of circle 2 than the area of circle 1?
Video Solution
Answer
They are equal.
Exercise #5
There are two circles.
The length of the diameter of circle 1 is 4 cm.
The length of the diameter of circle 2 is 10 cm.
How many times larger is the area of circle 2 than the area of circle 1?
Video Solution
Answer
641
Do you know what the answer is?
Question 1
There are two circles.
The length of the diameter of circle 1 is 4 cm.
The length of the diameter of circle 2 is 10 cm.
How many times larger is the area of circle 2 than the area of circle 1?