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Learn more about ratios and how to describe the relationship between two quantities in words. After trying the questions, click on the buttons to view answers and explanations in text or video.
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Introducing Ratios and Ratio Language
Let’s describe two quantities at the same time.
1.1 - What Kind and How Many?
1. If you sorted this set by color (and pattern), how many groups would you have?
2. If you sorted this set by area, how many groups would you have?
3. Think of a third way you could sort these figures. What categories would you use? How many groups would you have?
1. There would be 4 groups: white (solid), green (cross-hatches), yellow (stripes) and blue (dots).
2. There would be 4 groups: 2-squares, 3-squares, 4-squares, and 5-squares.
3. One possible third way to sort these figures would be by shape. There are 7 distinct shapes (counting different rotations of a certain shape as 1 shape).
1.2 - The Teacher’s Collection
Your teacher will show you a collection of objects. Alternatively, consider the following collection:
1. Think of a way to sort your teacher’s collection into two or three categories. Record your categories in the top row of the table and the amounts in the second row.
category name | |||
---|---|---|---|
category amount |
2. Write at least two sentences that describe ratios in the collection. Remember, there are many ways to write a ratio as a sentence:
3. Make a visual display of your items that clearly shows one of your statements. Be prepared to share your display with the class.
A ratio is an association between two or more quantities. We can use this to compare quantities of objects between categories.
1.
category name | small | medium | large |
---|---|---|---|
category amount | 6 | 6 | 3 |
2. The ratio of small to large clips is 6:3.
There are 6 medium clips for every 3 large clips.
1. Use two colors to shade the rectangle so there are 2 square units of one color for every 1 square unit of the other color.
2. The rectangle you just colored has an area of 24 square units.
Draw a different shape that does not have an area of 24 square units, but that can also be shaded with two colors in a 2:1 ratio. Shade your new shape using two colors.
1.
There are 16 red squares for every 8 blue squares, which is the same as 2 red squares for every 1 blue square.
2.
There are 8 red squares for every 4 blue squares, which is the same as 2 red squares for every 1 blue square.
Lesson 1 Summary
A ratio is an association between two or more quantities. There are many ways to describe a situation in terms of ratios. For example, look at this collection:
Here are some correct ways to describe the collection:
The ratio of squares to circles is 6:3.
The ratio of circles to squares is 3 to 6.
Notice that the shapes can be arranged in equal groups, which allow us to describe the shapes using other numbers.
There are 2 squares for every 1 circle.
There is 1 circle for every 2 squares.
Glossary Terms
ratio
A ratio is an association between two or more quantities.
For example, the ratio 3:2 could describe a recipe that uses 3 cups of flour for every 2 eggs, or a boat that moves 3 meters every 2 seconds. One way to represent the ratio 3:2 is with a diagram that has 3 blue squares for every 2 green squares.
Practice Problems
1. In a fruit basket there are 9 bananas, 4 apples, and 3 plums.
2. Complete the sentences to describe this picture.
3. Write two different sentences that use ratios to describe the number of eyes and legs in this picture.
The ratio of eyes to legs is 4:8.
For every 1 eye, there are 2 legs.
4. Choose an appropriate unit of measurement for each quantity: cm, cm^{2}, or cm^{3}.
5. Find the volume and surface area of each prism.
a. Prism A: 3 cm by 3 cm by 3 cm
b. Prism B: 5 cm by 5 cm by 1 cm
c. Compare the volumes of the prisms and then their surface areas. Does the prism with the greater volume also have the greater surface area?
a. Volume = 3^{3} cm^{3} = 27 cm^{3}
Surface area = 6(3^{2}) = 54 cm^{2}
b. Volume = 5 × 5 × 1 = 25 cm^{3}
Surface area = 2(5 × 5) + 4(5) = 70 cm^{2}
c. No. Prism A has a greater volume, but Prism B has a greater surface area.
6. Which figure is a triangular prism? Select all that apply.
A, C, and D are triangular prisms.
Recall that prisms are polyhedra which consist of two congruent bases connected by rectangular faces, and that prisms are named after the shape of their bases. B is a pentagonal prism. E is a rectangular pyramid.
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