MA.6.AR.3.1 Given a real-world context, write and interpret ratios to show the relative sizes of two quantities using appropriate notation: 𝑎/𝑏, 𝑎 to 𝑏, or 𝑎: 𝑏 where 𝑏 ≠ 0.
Objective: Students will be able to write and interpret ratios as part-to-part and part-to-whole using a colon, fraction notation, and the word "to".
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Activity
1. Complete the following quizzes to test your understanding of part-to-part ratios and part-to-whole ratios. Remember, you have unlimited attempts.
2. Complete the following worksheet. You may print the worksheet or record your answers in your notebook.
Write and Interpret Ratios
We can use ratios to represent and compare two quantities or relationships!
Ratios can be used to compare to quantities. In this lesson, you will learn how to represent quantities using ratios. You will also learn the difference between part-to-part and part-to-whole ratios.
Part-to-Part Ratios
A part-to-part ratio provides the relationship between two distinct groups. For example, if you have a classroom with 8 boys and 10 girls, your ratio would be written as 8:10.
A part-to-whole ratio provides the relationship between a particular group and the whole population (including the particular group). For example, if you have a classroom with 8 boys and 10 girls, your ratio of boys to the total class would be written as 8:18.
Example One:
What is the ratio of stars to rectangles?
Step One: Is this a part-to-part ratio or a part-to-whole ratio? We are asked to write a ratio that represents stars to rectangles, so we know we will be writing a part-to-part ratio.
Step Two: Count how many stars and rectangles there are. There is one star and two rectangles.
Step Three: Write the number of stars and rectangles as a part-to-part ratio. Remember, order matters and don't forget that there are three different ways you can write your answer! Any of the three are correct forms to write your answer.
Answer: 1:2
1 to 2
Example Two:
What is the ratio of triangles to total shapes?
If we count the number of triangles and stars, we will see that we have a total of 3 triangles and 7 stars.
Step One: Is this a part-to-part ratio or a part-to-whole ratio? We are asked to write a ratio that represents triangles to total shapes, so we know we will be writing a part-to-whole ratio.
Step Two: Which is our "part", triangles or stars? Since the question specifically asked for the ratio of triangles to total shapes, we know that our "part" is the total number of triangles. Our whole will be the sum of all triangles AND stars.
Step Three: Write the number of triangles and total shapes as a part-to-whole ratio. Remember, order matters and don't forget that there are three different ways you can write your answer! Any of the three are correct forms to write your answer.
Answer: 3:10
3 to 10
Watch the videos below to learn more about part-to-part ratios and part-to-whole ratios. Pause the video during the examples and try to work them out yourselves!