# Understanding Ratios and Solving Word Problems

## Introduction on ratios

Ratios are a way of comparing two quantities or values. They tell us how much of one thing is present in relation to another. It is represented using a colon (:), which separates the two numbers. For example, if we have 5 apples and 3 oranges, the ratio of apples to oranges would be 5:3. Ratios are commonly used in cooking and baking to measure ingredients, in financial statements to show the relationship between expenses and income, and in many other fields. Understanding ratios is an essential skill for solving various problems. In this blog post, we will explore a lesson plan on ratio word problems and how to solve them.

## Understanding Ratio

The first step in solving any ratio problem is to understand what a ratio is. In the lesson plan, the teacher introduces the concept of ratio by showing a custard recipe for eight people. The students learn that ratios express the relationship between different ingredients, such as caster sugar, double cream, and milk, in a recipe.

## Simplifying Ratios

The next step is to simplify the ratio to make it easier to work with. In the example given, the ratio of caster sugar to double cream to milk is 100:200:700. By simplifying this ratio, we get 1:2:7, making it easier to work with.

## Solving Ratio Word Problems

The teacher then moves on to solve a word problem involving ratios. The problem involves finding the total number of horses and hens on a farm, given that the ratio of horses to hens is 3:5 and that there are four more hens than horses. To solve this problem, the teacher demonstrates the four-step problem-solving approach. The first step is to understand and comprehend what the problem is about. In this case, it is a two-step word problem. The second step is to model the diagram. The teacher can draw a bar model, flow chart, or any other diagram that helps the students understand the problem better. The third step is to write down the equations. In this problem, the teacher first finds what one unit is equal to by dividing the total number of animals by the sum of the ratios. The ratio of horses to hens is 3:5, which means that there are 8 units in total. Therefore, 1 unit equals 2 animals, and the total number of animals is 16. The fourth step is to check the answer. This involves working backward to ensure that the answer is correct. In this case, the teacher can work backward by finding the number of each animal and checking if the ratio is the same as that given in the question.

## Conclusion on understanding ratios

Understanding ratios and solving ratio word problems is an essential skill in various fields. The lesson plan introduced in this blog post can help teachers explain the concept of ratios and teach students how to solve ratio word problems. By using the four-step problem-solving approach, students can gain a deeper understanding of ratios and their applications.