This article aims to find the ratio between two numbers. The article uses the simple concept of ratio. In mathematics, a ratio shows how many times one number contains another. For example, if there are eight pears and six lemons in a bowl of fruit, then ratio of pears to lemons is eight to six (i.e. $8:6$, which corresponds to a ratio of $4:3$). Similarly, the ratio of lemons to pears is $6:8$ (or $3:4$), and the ratio of oranges to total fruit is $ 8:14 $ (or $4:7$).
A ratio may be written by giving both constituting numbers written as $”\dfrac {a }{ b}”$ or “$a:b$”.
Expert Answer
A ratio is comparison between two (or more) different amounts of the same unit. The ratio does not tell us how many there are together, but only how their numbers compare. For example, if the number of boys to girls at a hockey game is $ 2 : 1 $, we know following information:
– There are more number of boys than the girls.
– There are $ 2 $ boys for every girl in the team.
– The number of boys is twice the number of girls, which is the same as saying that there are half as many girls as boys.
-We don’t know the total number of people at the match, but we know it’s a multiple of $ 3 $.
– $ \dfrac { 2 } { 3 } $ from the group are boys and $ \dfrac { 1 } { 3 } $ are girls.
If we know that there are $ 720 $ people at match, we will know that there are $ 480 $ boys and $ 240 $ girls.
\[ \dfrac { 2 } { 3 } \times 720 = 480 \: boys \: and \: \dfrac { 1 } { 3 } \times 720 = 240 \: girls \]
Numerical Result
The ratio is a comparison between two different quantities of the same unit.
Example
What does a $ 3 : 1 $ ratio mean?
Solution
A ratio is comparison between two (or more) different amounts of the same unit. The ratio does not tell us how many there are together, but only how their numbers compare. For example, if the number of oranges to apple at a basket is $ 3 : 1 $, we know the following information:
– There are more oranges than apples.
– There are $ 3 $ oranges for every apple.
– The number of oranges is three times the number of apples.
-We don’t know the total number of fruits in the basket, but we know it’s a multiple of $ 4 $.
– $ \dfrac { 3 } { 4 } $ from the oranges and $ \dfrac { 1 } { 4 } $ are apples.
If we are told that there are $ 20 $ fruits in the basket, we will know that there are $ 15 $ oranges and $ 5 $ apples.
\[ \dfrac { 3 } { 4 } \times 20 = 15 \: oranges \: and \: \dfrac { 1 } { 4 } \times 20 = 5 \: apples \]