Using Ratios to Compare Totals
Using ratios to compare totals means setting up a ratio between two quantities and using it to find how each part relates to the whole or to each other. If the ratio of red to blue marbles is 3:5, the total number of parts is 3 + 5 = 8. Red is 3/8 of the total and blue is 5/8. Given 24 total marbles: red = 3/8 x 24 = 9 and blue = 5/8 x 24 = 15. This 6th grade skill from enVision Mathematics Grade 6 is foundational for proportional reasoning, percent problems, and real-world data interpretation.
Key Concepts
Property To compare the total quantities represented by two ratios, first scale one or both ratios to find equivalent ratios with a common term. Then, sum the parts of each new equivalent ratio. The ratio with the larger sum corresponds to the greater total quantity.
Examples Two paint mixtures have a red to blue pigment ratio of $2:5$ and $3:7$ respectively. To compare which mixture has more paint for the same amount of red, we find a common term for red. The LCM of $2$ and $3$ is $6$. The first ratio becomes $6:15$ (total $21$) and the second becomes $6:14$ (total $20$). The first mixture has a greater total quantity ($21 20$). A class has a boy to girl ratio of $3:4$, and another class has a ratio of $1:2$. To compare totals based on the number of boys, we scale the second ratio. The first ratio is $3:4$ (total $7$). The second ratio becomes $3:6$ (total $9$). The second class is larger when there are $3$ boys in each.
Explanation This skill extends ratio comparison to determine which situation represents a larger overall amount. By finding equivalent ratios with a common reference point, you can calculate the total for each scenario. You sum the two parts of the scaled ratio to find its total. Comparing these totals allows you to make decisions, such as determining which recipe yields more, or which group is larger.
Common Questions
How do you use a ratio to compare totals?
Add the ratio parts to find the total number of parts. Then divide the actual total by this number to find the value per part, and multiply to find each share. For ratio 3:5 and total 24: each part = 24/8 = 3; red = 9, blue = 15.
What is a ratio and how is it different from a fraction?
A ratio compares two quantities (3:5). A fraction compares a part to a whole (3/8). A ratio can be converted to fractions once you know the total number of parts.
How do you find a missing value using a ratio?
If you know one value and the ratio, find the value per part and scale up. If one group is 9 and the ratio is 3:5, each part = 9/3 = 3, so the other group = 5 x 3 = 15.
What grade uses ratios to compare totals?
Using ratios to compare totals is a 6th grade skill in enVision Mathematics Grade 6, Chapter 1, bridging ratio concepts to fraction and proportion work.
How is comparing totals with ratios used in real life?
It appears in recipe scaling (3 parts flour to 2 parts sugar means 3/5 is flour), mixing paints, sharing costs, and interpreting survey data.
What is the difference between a part-to-part and part-to-whole ratio?
A part-to-part ratio compares two groups (3:5). A part-to-whole ratio compares one group to the total (3:8 or 3/8). Both are used in the same problem when the total is known.