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
A part-to-whole ratio compares one part to the whole. For example, if there are
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,
Figs | Pawpaws | Ratio |
---|---|---|
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
A tape diagram with 2 tapes of unequal lengths. The first tape has 3 equal parts, each labeled 4. A curved bracket above the first tape is labeled Figs. The second tape has 1 part of the same size as in the first tape, each labeled 4. A curved bracket below the second tape is labeled Pawpaws.
A tape diagram with 2 tapes of unequal lengths. The first tape has 3 equal parts, each labeled 2. A curved bracket above the first tape is labeled Figs. The second tape has 1 part of the same size as in the first tape, each labeled 2. A curved bracket below the second tape is labeled Pawpaws.
The diagrams show that the ratios are equivalent, because in each case, there are
And here is a double number line that shows that
A double number line with 5 equally spaced tick marks. The line labeled Figs, reads from left to right: 0, 3, 6, 9, 12. The line labeled Pawpaws, reads from left to right: 0, 1, 2, 3, 4.
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
A coordinate grid with the x-axis labeled Figs and the y-axis labeled Pawpaws. The points (3,1), (6, 2), (9, 3) and (12, 4) are plotted. A straight line connects the points and passes through the origin.
We can see that the graph is a straight line that passes through the origin
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
Inches | Centimeters |
---|---|
So
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
to mix cup of lemon juice with cups of water. If we want to make more or less lemonade, we can use equivalent ratios, such as or , 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
by photo, we can use the ratio to find the dimensions of the rectangle. If we want to make the rectangle larger or smaller, we can use equivalent ratios, such as or , to keep the same shape. We can also use ratios to mix colors, such as 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
to mean 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 to mean miles per gallon. We can also use ratios to find the best design for a project, such as to mean the optimal ratio of wingspan to length for a paper airplane.