Table Of Contents
What are Ratios?
A ratio can be defined as an expression that is used to compare two quantities. The ratio of any two numbers is used for comparison only if they have the same unit. Ratios are also used to determine the unit rate of a product.
A ratio is written in the form of p : q, which is read as p to q. Here, the value of the ratio p : q is \(\frac{p}{q}\)
What are Ratio Tables?
Ratio tables are a structured set of equivalent ratios. They help comprehend the relationships between various ratios and numbers.
We can create a ratio table by,
- Adding values to equivalent ratios
- Subtracting values from equivalent ratios
- Multiplying or dividing each number in a ratio by the same value
Solved Examples
Example 1:
Find the missing values to complete the ratio table:
Solution:
In the given ratio table, the original ratio is 0.4 gallons to 0.75 days.
The first number in the second ratio is 1.2, which is 3 times 0.4 and the first number in the third ratio is 3.6 which is 3 times 1.2.
Hence, repeatedly multiply each number in the ratios by 3:
Hence, the missing values are 2.25 and 6.75.
Example: 2
The ratio table shows the distance traveled by Joseph and the time taken. Find the following:
- The distance covered in 16 hours
- Time taken to cover 5 kilometers.
Solution:
The kilometers covered in 16 hours corresponds to the first number in the second ratio and the hours to travel 5 kilometers corresponds to the second number in the third ratio.
So, we need to find the missing values in the ratio table.
Here, the original ratio is 52 kilometers to 4 hours.
The second number in the second ratio is 16, which is 4 times 4.
Hence, the missing value in the second ratio will be 4 times \(\frac{5}{2}\)
that is, \(\frac{5}{2}\times 4=10\)
The first number in the first ratio is \(\frac{5}{2},\) which is 2 times 5.
Hence, the missing value in the third ratio will be, 2 times 4, that is, \(4 \times 2 = 8\)
Therefore, the missing values are 10 and 8 and the equivalent ratios are \(\frac{5}{2} : 4, 10 : 16 \text{ }and\text{ }5 : 8\)
Hence,
- Distance covered in 16 hours is 10 kilometers
- Time taken to cover 5 kilometers is 8 hours.
Example 3:
Find the ratio represented by the tape diagram:
Solution:
From the diagram we can say that Quantity 1 is represented by 2 boxes and Quantity 2 is represented by 3 boxes.
The ratio can be written as 2 boxes to 3 boxes.
Hence, the ratio represented by the tape diagram is 2 : 3.
Ratios are used in many instances like distance traveled per unit time, unit rate of commodities, comparing prices or scores of participants in a competition and many other instances.
Ratio tables organize equivalent ratios in tabular form and aid in visualizing the relationship between ratios and numbers.
Ratios are written by separating two quantities with the help of the symbol ‘:’. For example, ‘a:b’, which is read as ‘a to b’. The value of a ratio is represented by a fraction with a as the numerator and b as the denominator.
Ratios that can be simplified to the same value are said to be equivalent ratios. If one ratio can be written as a multiple of the other, then they are said to be equivalent ratios.