Maths Ratio Problems: Step-by-Step Solutions

Maths Ratio and Proportion: Solving Ratio Problems

Maths ratio and proportion is a fundamental concept in mathematics that deals with the relationship between quantities or ratios of quantities. Ratio problems involve determining the value of unknown quantities based on known ratios or proportions. In this article, we will learn how to solve ratio problems using a step-by-step approach.

Step 1: Understand the Problem

The first step in solving a ratio problem is to understand the problem and identify the known and unknown quantities. For example, if we are given a ratio of 2:3 for the number of apples and oranges, we know that there are twice as many apples as oranges.

Step 2: Determine the Relative Size of the Parts

In the given ratio, the first term represents the first part, and the second term represents the second part. In our example, the first term represents the number of apples, and the second term represents the number of oranges. The ratio of 2:3 tells us that for every 2 apples, there are 3 oranges. This means that the relative size of the parts in the ratio is 2:3.

Step 3: Determine the Total Parts

To determine the total parts, we add the parts in the ratio. In our example, the total parts are 2 (apples) + 3 (oranges) = 5.

Step 4: Determine the Value of the Unknown Quantity

To find the value of the unknown quantity, we use the given ratio and the total parts. We can set up a proportion using the known ratio and the total parts:

$$ \frac{\text{Known quantity}}{\text{Unknown quantity}} = \frac{\text{First part}}{\text{Second part}} $$

In our example, we want to find the number of oranges. We can set up the proportion as follows:

$$ \frac{\text{Known quantity}}{\text{Number of oranges}} = \frac{2}{\text{Total parts} - 2} $$

Substituting the known values, we get:

$$ \frac{2}{\text{Number of oranges}} = \frac{2}{5 - 2} $$

Solving the proportion, we get:

$$ \text{Number of oranges} = \frac{2}{1} \times \frac{5 - 2}{2} = 3 $$

Thus, there are 3 oranges.

Step 5: Check Your Answer

After solving the ratio problem, it's essential to check your answer to ensure that it makes sense in the context of the problem. In our example, we have 2 apples and 3 oranges, which is in the ratio of 2:3.

In conclusion, solving ratio problems involves understanding the problem, determining the relative size of the parts, calculating the total parts, finding the value of the unknown quantity, and finally checking your answer. By following this step-by-step approach, you can confidently solve any ratio problem.