A ratio is a fraction used to compare between two quantities of same unit.
For example, 8 parts of a chocolate cake is chocolate and 2 parts are cream. We can say that the ratio of chocolate to cream in a chocolate cake is = 8 : 2 or = 4 : 1.
We can see that “ : ” is the symbol of ratio or comparison between the quantities by division.
For example, if the number of apples in a basket is 5 and the number of apples in another basket is 6. Thus the ratio of apples in both baskets are= 5 : 6 or = 6 : 5.
Ratios are always between same quantities. For example, it is completely impossible to compare the grade of a student to his number of pencils. Comparison should always be between same objects. Hence, grade of a student can only be compared to the grade of another student.
How can we be sure that we can compare two objects in a ratio?
It’s simple. The units of both objects need to be same. If we want to compare the age of two children, we need to compare them in the same unit. If we take the age of one child in years then the age of the other child should also be taken in years and not in months or weeks.
For example, Akib is 5 years and 2 months old. Farhad is 4 years and 11 months old.
To compare both of their ages, we need to convert their ages into months to get the exact age.
Thus, age of Akib is (5 x 12) + 2 = 60 + 2 = 62 months.
Age of Farhad is (4×12) + 11 = 48 + 11 = 59 months.
So, ratio of Akib’s age to Farhad’s age is 62 : 59.
Different types of ratios:
Simple Ratio – The ratio of two quantities is called Simple Ratio.
The first part of a simple ratio is called antecedent and the last part is subsequent.
In the ratio of 4:1, 4 is an antecedent and 1 is a subsequent.
Unit Ratio – The ratio in which the antecedent and the subsequent are equal are called unit ratios. In other words, after division the ratio will be 1:1.
For example, suppose, Tania bought a Doremon toy with 200 TK and also a Batman comic book with 200 TK. The ratio of their prices is 200 : 200 = 1 : 1.
Inverse Ratio – The ratio formed by interchanging the antecedent and subsequent of a ratio is called Inverse Ratio.
For example, 20 : 3 is the inverse ratio of 3 : 20.
Mixed / Compound Ratio – The ratio whose antecedents and subsequent are obtained by multiplying the antecedents and subsequent of more than one simple ratio is called Mixed or Compound Ratio.
For example, the Mixed Ratio of 2 : 1 and 3 : 2 is (2 x 3) : (1 x2) = 6 : 2 = 3 : 1.
Ratio of Less Inequality – The ratio whose antecedent is smaller than its subsequent is called the Ratio of Less Inequality. For example, 1 : 5 and 12 : 31 are Ratios of Less Inequality.
Ratio of Greater Inequality – The ratio whose antecedent is greater than it’s subsequent is called the Ratio of Greater Inequality. For example, 14 : 3 and 51 : 42 are examples of Ratio of Greater Inequality.
Examples of Ratio Problems:
The ratio of the weight of Tara’s cat to the weight of Apon’s cat is 5: 7. Tara’s cat weighs 20 kg. How much more does Apon’s cat weigh?
Solution: If Tara’s cat weighs 20 kg then the ratio will be (5 : 7) x 4 = (20 : 28). If we divide 20 by 5 we get 4. So we multiply the ratio with 4 to get the answer. So the real weight of Apon’s cat is 28 kg. Thus, Apon’s cat has (28 – 20) = 8 kgs more weight than Tara’s cat.
2. What is the ratio of 6 minutes to 8 hours?
Solution: First, we change the hours to minutes:
8 hours = 8 × 60 = 480 minutes
Write the ratio as a fraction and simplify:
We found that the ratio of 6 minutes to 8 hours is 1:80.
- A donut shop made 6 donuts with frosting and 44 donuts without frosting. What is the ratio of the number of donuts without frosting to the number of donuts with frosting?
- The ratio of boys to girls at a basketball game is 8:5. There are 30 girls. How many more boys are there?
- There are 3 packs of pastels available for every 5 students in the art class. How many students can share 15 packs of pastels?
- Bob the builder mixed 3 pints of green paint with 4 pints of yellow pint to make the color blue. He used 27 pints of green paint. How many pints of yellow paint does he need?