What is a Ratio Worksheets
When we want to compare quantities between two or more things, we often use ratios. For instance, if we had a bag full of lacrosse and tennis balls, we may want to understand how many there were in relation to on another. If there were 3 tennis balls for every 1 lacrosse ball, we would write the ratio as 3:1. The things that we are comparing are often found in the same system, but do not necessarily have to be in the same units. You may find that ratios are used to describe mathematical relationships that are composed of more than just two variables. These relations are expressed in one of three ways part-to-part which is the most common, part-to-whole, or whole-to-part. When we described the lacrosse and tennis balls, we were comparing part-to-part. If we were to compare the part to whole, we would need to know the exact number of each type of balls in the bag.
Aligned Standard: Grade 6 Proportional Relationships - 6.RP.A.1
- Picnic Step-by-step Lesson- Compare the number of students that are staying home versus going on a picnic.
- Guided Lesson - We create ratios for everything. Yellow to pink dogs, people at the beach, and chocolate cake or truffles.
- Guided Lesson Explanation - I don't do everything for them in this one. They must do a little bit of thinking.
- Practice Worksheet - A whole bunch of word problems that you are to pull proportions from.
- Missing Proportions Five Pack- Fill in the missing part of each proportion / ratio.
- Ratio Tables Five Pack - Complete each table. It's all the same ration (top and bottom).
- Matching Worksheet - A visual proportion match set for you.
- Answer Keys - These are for all the unlocked materials above.
Homework Sheets
I really ran with different types of problems here. They are all in word problem form.
- Homework 1 - 4 children are watching T.V. 2 children are not watching T.V. What is the ratio of the number of children who are watching T.V. to the number of children who are not watching T.V.?
- Homework 2 - 7 people are going to a wedding and 4 people are staying at home. What is the ratio of the number of people who are staying at home to the number of people who are going to the wedding?
- Homework 3 - At a party, 9 couples are dancing. 5 couples are not dancing. What is the ratio of the number of couples that are dancing to the number of couples that are not dancing?
Practice Worksheets
We start with some visual ratios and then it's back to word problems.
- Practice 1 - What is the ratio of flowers to chocolate cones?
- Practice 2 - 10 students want to use laptops and 6 students want to use tablets. What is the ratio of the number of students that want to use laptops to the number of students that want to use tablets?
- Practice 3 - 9 boys and 5 girls took part in the music competition. What is the ratio of the number of girls to the number of boys who participate in the competition?
Math Skill Quizzes
We moved the word problems from this section; they can be found in the test for this grade level.
- Quiz 1 - Find the value of x. Work on your cross-multiplication.
- Quiz 2 - Find the value of c.
- Quiz 3 - What is the ratio of ice cream to watermelon? Use the images that are provided to establish this.
How to Use Ratios to Solve Problems
Ratios are mathematical expressions that help students in comparing values directly with each other. Ratio allows comparison of absolute amounts and quantities of a larger whole. The gives us a concept of how the two values relate to one another. This concept is easy to understand when we think about ecological communities. If I said that the number of squirrels to deer was in an 8 to 1 ratio, you would instantly understand that the community was dominated by squirrels.
Ratios are calculated and written in multiple ways, but their rules are universal. They are commonly written in three ways with the use of a separator. The function of the separator is to provide a reflection of comparison between the values. The most frequently used separator is the colon (:). You will also find that ratios are written in fraction form (a/b) where the (/) serves as the separator. The word “to” often serves as a separator. The end goal is to substantiate the concept of a scale. You should become comfortable with all these various forms of notation as you will see all of them in various texts and applications as you progress.
A very unique feature of ratios is that the variables do not necessarily need to be in the same units. The purpose is to create a degree of scale between the variables. You must respect the order in which the ratio was served to you. We can easily determine the ratio in a group for unknown variables using basic mathematical rules. The most common principle for finding unknown ratios is using cross-multiplication method which is fairly simple. The method involves writing ration in the form of a fraction then set two rations equal to one another and then cross-multiplying them.
Let's take an example. There is a small group of students on the playground in consistent 5 girls : 2 boys ratio. If this ratio is to be maintained. How many boys are there in a class where number of girls is 20?
Solution: to solve this problem, we need to make two ratios including our unknown variables:
2 boys : 5 girls = x boys : 20 girls
Converting these ratios into fractions: 2/5 and x/20
Now, cross-multiplication will give us: 5x = 40 or x = 8 Hence, in this case, there will be 8 boys in a class of 20 girls.