## Ratios and Proportion Worksheets

What are Ratios?
To compare values, we use the concept of ratios. When we use the term, "to," write two numbers as a fraction, or with a colon between them, we are representing a ratio. It is a comparison of the quantities of two things. It is a measure of how much of thing is there, in comparison to another thing.
A ratio can be used to represent a comparison between two things, and we call it part-to-part ratios. There are cases when you have to compare a part to a whole lot, and we call these ratios part-to-whole. The concept of ratios is very commonly used in writing down recipes.
Example: A delegation comprising of five pupils was sent to XYZ college to represent a school. Out of these five, three were female, and two were male pupils.
We can represent this information in the form of two ratios; part-to-part and whole-to-part.
**Part-to-Part:** - The ratio of females to male can be written as 3:2 or 3/2 The ratio of males to females can be written as 2:3 or 2/3
**Whole-to-Part:** - The ratio of females to the whole delegation can be written as 3:5 or 3/5 The ratio of males to the whole delegation can be written as 2:5 or 2/5
This really gets hot right around the middle grade levels. These skills are used endless throughout life, so it is important for students to grasp this.

- Equivalent Ratios - We show you not only how recognize them, but also to generate them.
- Graphs of Proportional Relationships - We begin to show students how to distinguish trends on graphs.
- Gratuities and Commissions, Fees, and Tax - Students learn how to determine many real-world finance issues.
- Markups and Markdowns Word Problems - Students begin to understand how this skews pricing and we hint to the concept of margins.
- Multistep Ratio and Percent Word Problems - Hope you brushed up on your cross multiplication.
- Percentage as a Rate per Hundred - You basically just drop the percentage value over a fraction of one hundred.
- Percent Error and Percent Increase - This helps us gauge how fast the value is jumping up and falling.
- Proportional Relationships Word Problems - We help make sense of data you will find in these problems.
- Ratio and Rates Word Problems - We start to see how ratios relate to rates of change and how fast they accelerate.
- Ratios and Units of Measurement - We often forget that units of measure are just as important as the values that they represent.
- Recognizing Proportional Relationships - How to spot them and interpret what that means to you.
- Tape Diagrams / Bar Models - We introduce you a method you can use to visualize a ratio.
- What is a Ratio? - The most general introduction to the topic.
- The Constant of Proportionality - This is the ratio value that exists between two directly proportional values.
- Unit Rates and Ratios of Fractions - We show you how the two interconnect and can be used to your advantage.
- Unit Rates and Ratios : The Relationship - A slight better way to visualize and make sense of the topic.
- Unit Rates with Speed and Price Word Problems - The unit price truly indicates if you are getting a deal comparatively.

### What is The Difference Between a Ratio and a Proportion?

Ratios are used to compare two quantities. This comparison is made by using the division operation. They are written in form a/b. Proportions are equations that we use to explain that two ratios are equal or equivalent. They are presented in the form: a/b = c/d. The division operator is sometimes removed or replaced with the symbol (:). Proportions are often given with unknown values. These unknown or missing values are easy to calculate by working off of the other three values that you are given. The unknown value would just need to satisfy the equivalence of proportions. They each serve their own based on what measures you working with and the nature of the data that you are exploring. Ratios are often given to explain unit rates and a wide variety of measures. Proportions are often used to compare the overall value of these unit rates and measures. Both of these have a wide array of applications, but you will use both any time you go grocery shopping.