# Ratio and Rates Word Problems Worksheets

When we are working with these types of word problems, we take a slightly different approach to how we are solving these types of problems. With your average everyday ordinary word problems, you spend a good deal of time determining which type of mathematical operation is used to satisfy the question. These types of problems are stated entirely differently they exhibit a relationship between two values. We then are asked to examine this relation in a specific situation. This is something that is a very helpful strategy to learn because ratio and rate word problems are found often in the real world. Many very substantial career paths are built on the back of this technique. Anyone who is in charge of purchasing items and cutting costs for their companies would need to be very good at this skill. These worksheets and lessons will help students become very comfortable tackling word problems that are built off of a rate or ratio.

### Aligned Standard: Grade 6 Proportional Relationships - 6.RP.A.3a

- On the Hunt Step-by-step Lesson- I use the subtle words "catching" rather than "hunting" just in case younger students are very advanced.
- Guided Lesson - Hello ratio tables! We meet again! We also look into equivalent ratios.
- Guided Lesson Explanation - Ratio tables seem to help out in all of these problems.
- Practice Worksheet - A three pronged approach. Ratio tables, word problems, and we get the tri-fecta with equivalent proportions.
- Ratio Word Problems 5 Pack - Relatively straight lined questions are found in this pack.
- Ratio Word Problem Five Pack (Harder) - Slightly more difficult problems in this pack.
- Matching Worksheet - We match equivalent ratios.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Complete with word problems, ratio tables, and numeric fixed ratios.

- Homework 1 - Liam and Noah went for a tour. On the first day Liam ate 3 burgers and Noah ate 5 slices of pizza. One the second day Liam ate 4 burgers and Noah ate 3 slices of pizza. One which day of the tour did Liam and Noah eat a higher ratio of burgers to pizza?
- Homework 2 - Complete the ratio tables in section b.
- Homework 3 - Circle the two ratios that are equal. We can see that the numbers can easily be reduced. Let's reduce them all to see which pair is equal.

### Practice Worksheets

I focus this section on getting students to master the use of cross multiplication.

- Practice 1 - Are these ratios equivalent? You will review a number of different scenarios.
- Practice 2 - Find the equal ratios. You will have to choose between four groups.
- Practice 3 - Complete the ratio tables. You have three given values that leads you to determine the missing value.

### Math Skill Quizzes

We test all forms of the skill to give students a complete picture of where they are at.

- Quiz 1 - Are these ratios equivalent? It is a simple Yes or No activity for you. 9 boxes to 9 students 12 boxes to 24 students
- Quiz 2 - Complete the missing values for each ratio table. This one has the value jump around.
- Quiz 3 - A mixed review. This will have you determine the unit rate to complete the remainder of the exercise.

### What Is the Difference Between a Ratio and a Rate?

It is mathematics where we learn the concept of 'ratio' or 'rate'. This term is very common in statistics and business too. While both the terms specify the relationship between two or more quantities, they are far apart from each other in their actual meaning and usage. Let's discuss both of these in detail to identify the difference between the two.

"Rate" - used to express amount, quantity or frequency with which a certain event occurs or happen. It is commonly expressed as the number of times it has happened for every thousands of the total population. It compares two measurements of different units and signifies how much time it takes to accomplish something. For example, the distance per unit time; 40 miles/hour.

"Ratio," on the other hand, is the relationship or a connection between quantities such as their number, amount, size, or the extent or degree of those two or more similar quantities. It is the proportion of one thing in comparison with the other. A ratio explains the correlation of one thing with another, things, people or units.

Consider this example: "Emma has five apples while Tom has ten."

The ratio of Emma's apples to Tom's is 5:10. It can also be expressed as 2:1. This rate can be applied to future situations and help you predict future outcomes.

### Example Problem from This Section

A farmer can harvest 4 acres of corn in 5 hours with his corn harvester tractor. If he has 160 acres of corn to farm, how long will it take him to harvest all that corn?

Solution: There is a ratio of acres of corn to hours of time (4 acres : 5 hours). The unknown variable is the time needed. If we write the unknown amount of time with the known amount of land we are left with in the same format it would be written as: (160 acres : x hours). To solve this, we would solve the ratio for the missing variable using the format 4:5 = 160: x. We would cross multiply and end up with 200 hours as our answer.