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Lesson 4: Ratio application

# Ratios FAQ

## What is the difference between a part-to-part ratio and a part-to-whole ratio?

A part-to-part ratio compares two parts of a whole. For example, if there are 12 dogs and 8 cats in a shelter, the part-to-part ratio of dogs to cats is 12, colon, 8, or 3, colon, 2. This means that for every 3 dogs, there are 2 cats.
A part-to-whole ratio compares one part to the whole. For example, if there are 12 dogs and 8 cats, but no other animals, in a shelter, the part-to-whole ratio of dogs to animals is 12, colon, left parenthesis, 12, plus, 8, right parenthesis, or 12, colon, 20, or 3, colon, 5. This means that 3 out of every 5 animals in the shelter are dogs.

## How can we visualize equivalent ratios?

Equivalent ratios are ratios that have the same value or meaning, even if they use different numbers. For example, 12, colon, 4 and 6, colon, 2 are equivalent ratios, because they both mean 3 figs for every pawpaw fruit. We can visualize equivalent ratios by using tables, tape diagrams, or double number lines. For example, here is a table that shows some equivalent ratios of figs to pawpaws:
FigsPawpawsRatio
12412, colon, 4
626, colon, 2
313, colon, 1
939, colon, 3
We can also draw tape diagrams or double number lines that show how the quantities are divided into equal parts. For example, here are tape diagrams that show 12, colon, 4 and 6, colon, 2:
The diagrams show that the ratios are equivalent, because in each case, there are 3 figs for every 1 pawpaw.
And here is a double number line that shows that 12, colon, 4 and 9, colon, 3 are equivalent:

## How can we use ratios on the coordinate plane?

We can use ratios on the coordinate plane to create graphs that show the relationship between two variables. For example, if we want to graph the ratio of figs to pawpaws, we can use the x-axis to represent the number of figs and the y-axis to represent the number of pawpaws. Then, we can plot points that correspond to different ratios, such as left parenthesis, 12, comma, 4, right parenthesis, left parenthesis, 6, comma, 2, right parenthesis, left parenthesis, 3, comma, 1, right parenthesis, and left parenthesis, 9, comma, 3, right parenthesis. We can connect the points with a line to show the pattern. Here is what the graph would look like:
We can see that the graph is a straight line that passes through the origin left parenthesis, 0, comma, 0, right parenthesis. The graph shows that as the number of figs increases, the number of pawpaws also increases proportionally.

## How can ratios help us with units of measurement?

We can use ratios and units of measurement to convert between different units, such as inches and centimeters, or ounces and grams. For example, if we know that 1 inch is equal to about 2, point, 54 centimeters, we can use the ratio 1, colon, 2, point, 54 to convert any length in inches to centimeters, or vice versa. For example, if we have a length of 8 inches, we can multiply it by the ratio 2, point, 54, colon, 1 to get the equivalent length in centimeters:
InchesCentimeters
start color #a75a05, 1, end color #a75a05start color #7854ab, 2, point, 54, end color #7854ab
\downarrow, times, 8\downarrow, times, 8
start color #a75a05, 8, end color #a75a05start color #7854ab, 20, point, 32, end color #7854ab
So 8 inches is about 20, point, 32 centimeters. We can use the same method to convert between other units, as long as we know the ratio that relates them.

## Where are ratios used in the real world?

Ratios are used in many situations in the real world, such as:
• Cooking and baking: We can use ratios to measure ingredients, adjust recipes, and make mixtures. For example, if we want to make lemonade, we can use the ratio 1, colon, 6 to mix 1 cup of lemon juice with 6 cups of water. If we want to make more or less lemonade, we can use equivalent ratios, such as 2, colon, 12 or 0, point, 5, colon, 3, to keep the same flavor.
• Art and design: We can use ratios to create shapes, patterns, and colors. For example, if we want to make a rectangle that has the same proportions as a 4 by 6 photo, we can use the ratio 4, colon, 6 to find the dimensions of the rectangle. If we want to make the rectangle larger or smaller, we can use equivalent ratios, such as 8, colon, 12 or 2, colon, 3, to keep the same shape. We can also use ratios to mix colors, such as 3, colon, 1 to make orange from red and yellow.
• Science and engineering: We can use ratios to compare data, calculate rates, and solve problems. For example, if we want to compare the speed of two cars, we can use the ratio of distance to time, such as 60, colon, 1 to mean 60 miles per hour. If we want to calculate the fuel efficiency of a car, we can use the ratio of miles to gallons, such as 30, colon, 1 to mean 30 miles per gallon. We can also use ratios to find the best design for a project, such as 2, colon, 1 to mean the optimal ratio of wingspan to length for a paper airplane.