Learn more about color mixtures for paint, dye, and food coloring as a real-life application of ratios, and about how ratios are represented. After trying the questions, click on the buttons to view answers and explanations in text or video.
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Let’s see what color-mixing has to do with ratios.
Illustrative Math Unit 6.2, Lesson 4 (printable worksheets)
4.1 - Number Talk: Adjusting a Factor
Find the value of each product mentally.
6 · 15
12 · 15
6 · 45
13 · 45
6 · 15 = 90
12 · 15 = 180
6 · 45 = 270
13 · 45 = 585
Notice how 12 · 15 = 180 is equal to 2 · 6 · 15 = 180.
4.2 - Turning Green
When you mix yellow and blue, a shade of green is formed. If you add more blue than yellow, you will get blue-green, and so on.
Open the applet.
Write out the ratio of blue to yellow in one batch of green. An example sentence is: The ratio of blue to yellow is 5:15, or 1:3.
2. Options b, c, and d will give you more of the same shade of green, while options a and e will not.
Option a will give a total of 5 + 20 = 25 ml of blue and 15 + 20 = 35 ml of yellow, which is equivalent to 5:7, not equivalent to the original ratio of 1:3.
Option b multiplies both the amount of blue and the amount of yellow by 2. This gives the ratio 10:30, which is equivalent to 1:3.
Option c multiplies both the amount of blue and the amount of yellow by 3. This gives the ratio 15:45, which is equivalent to 1:3.
Option d is to mix multiple batches. As long as each batch follows the original ratio, the original shade of green will be preserved.
Option e will give a total of 5 · 2 = 10 ml of blue and 15 · 3 = 45 ml of yellow, which is equivalent to 2:9, not equivalent to the original ratio of 1:3. This is because the amounts of blue and yellow have been multiplied by different numbers. 3. For option b, you will use 10 ml of blue and 30 ml of yellow. This makes 2 batches of the same shade of green. 4.
5. As the ratio of blue to yellow in this shade of green is 1:3, there must be 3 times as much yellow as blue in the final mixture. They can add 40 ml of yellow to achieve a total of 20 ml blue and 20 + 40 = 60 ml yellow. 6. You can use 10 ml blue and 10 ml yellow to make a bluer shade of green. In this recipe, there is 1 ml of yellow for every 1 ml of blue, compared to the original recipe which had 3 ml of yellow for every 1 ml of blue.
The above image demonstrates how this shade of green is bluer than the original.
Someone has made a shade of green by using 17 ml of blue and 13 ml of yellow. They are sure it cannot be turned into the original shade of green by adding more blue or yellow. Either explain how more can be added to create the original green shade, or explain why this is impossible.
It is possible to add more of each color to create the original green shade.
Work out what amounts of blue and yellow to add so that the final amounts of blue and yellow are in the same ratio (1:3) as the original green shade.
In the original green shade, the ratio of blue to yellow was 1:3. We can multiply this ratio so that it will represent volumes larger than those which we have already mixed. Multiplying by 20 gives us a ratio of 20:60.
We can add 20 - 17 = 3 ml of blue and 60 - 13 = 47 ml of yellow so that our final amounts of blue and yellow will be in the ratio 20:60. As this is equivalent to the ratio of blue and yellow in the original green shade, the shade of green will be the same.
4.3 - Perfect Purple Water
The recipe for Perfect Purple Water says, “Mix 8 ml of blue water with 3 ml of red water.”
Jada mixes 24 ml of blue water with 9 ml of red water. Andre mixes 16 ml of blue water with 9 ml of red water.
Lesson 4 Summary
When mixing colors, doubling or tripling the amount of each color will create the same shade of the mixed color. In fact, you can always multiply the amount of each color by the same number to create a different amount of the same mixed color.
For example, a batch of dark orange paint uses 4 ml of red paint and 2 ml of yellow paint.
To make two batches of dark orange paint, we can mix 8 ml of red paint with 4 ml of yellow paint.
To make three batches of dark orange paint, we can mix 12 ml of red paint with 6 ml of yellow paint.
Here is a diagram that represents 1, 2, and 3 batches of this recipe.
We say that the ratios 4:2, 8:4, and 12:6 are equivalent because they describe the same color mixture in different numbers of batches, and they make the same shade of orange.
Add to the diagram so that it shows 3 batches of the same shade of brown paint.
B will produce the same shade of green paint. A, C and D will not.
The ratio of yellow paint to blue paint in Diego’s mixture is 10:2, which is equivalent to 5:1. B is equivalent (note that the order of the blue and yellow paints has been swapped). The ratios in the other options are not equivalent.
a. We can multiply both numbers in Clare’s original recipe by 2. This means we will use 2 · 2 = 4 cups of blue paint and 1 · 2 = 2 gallons of white paint.
b. To get a darker shade of blue, we can increase the ratio of blue to white. For example, we can use 4 cups of blue paint for every 1 gallon of white paint.
c. To get a lighter shade of blue, we can decrease the ratio of blue to white. For example, we can use 1 cup of blue paint for every 1 gallon of white paint.
b. The ratio of cups of milk to frozen bananas to tablespoons of chocolate syrup is 3 to 2 to 1.
The ratio of cups of milk to frozen bananas to tablespoons of chocolate syrup is 3:2:1.
For every 3 cups of milk, there are 2 frozen bananas and 1 tablespoon of chocolate syrup.
The missing numbers are 3, 9, 12, and 18. This number line shows skip-counting by 3, or multiples of 3.
The formula for the area of a parallelogram is b · h.
The base of this parallelogram is 3 units and the height is 7 units. Hence the area is 3 · 7 = 21 square units.
a. 11 · 1⁄4 = ______
b. 7 · 1⁄4 = ______
c. 13 · 1⁄27 = ______
d. 13 · 1⁄99 = ______
e. x · 1⁄y = ______ (As long as y does not equal 0.)
a. 11 · 1⁄4 = 23⁄4
b. 7 · 1⁄4 = 13⁄4
c. 13 · 1⁄27 = 13⁄27
d. 13 · 1⁄99 = 13⁄99
e. x · 1⁄y = x⁄y (As long as y does not equal 0.)
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