2.5 Expressing and Interpreting Ratios
Marilyn Nielson and Morgan Chase
Applications
Ratios are used to help us understand the relationship among a variety of factors we may be measuring in the field. For example, the ratio of native to invasive plant cover can track progress restoring a site. Similarly, prescriptions for plantings will define ratios of species to one another, such as a 2:1 ratio of Ponderosa pine to western larch. Once we are comfortable with ratios, we’ll be able to set up proportions and use that relationship to solve many useful problems!
A ratio is the quotient of two numbers or the quotient of two quantities with the same units. (Pop quiz… Which operation gives you a quotient: addition, subtraction, multiplication, or division?)
When writing a ratio as a fraction, the first quantity is the numerator and the second quantity is the denominator. If the fraction can be simplified, reduce it to lowest terms.
Examples
A) The ratio of Idaho fescue to bluebunch wheatgrass is this planting mix is 3:1. Which number represents the proportion of bluebunch wheatgrass in the mix?
B) During thinning on a forest plantation, I generated 550 cubic yards of hybrid poplar wood chips and 1,100 cubic yards of loblolly pine chips. What is the ratio of poplar chips to pine chips?
C) In my study plot, I find eight western larch, three Douglas fir, and five Ponderosa pine. What is the ratio of larch to fir to pine? What is the ratio of fir to pine to larch? What is the ratio of pine to all trees in the plot?
We can use ratios in a dimensional analysis set up if we keep track of the entities that each part of the ratio represents.
Examples
A) The ratio of Idaho fescue to bluebunch wheatgrass in this planting mix is 3:1. If I’m planting 20 acres at 15 lbs of seed per acre, how many pounds of bluebunch wheatgrass seed will be in the mix?
B) In M15 grade concrete, the ratio of cement to sand to aggregate is 1:2:4 which is a fixed ratio. If I have 2 cubic yards of aggregate, how many cubic yards of cement will I need? How many total cubic yards of material will be in the final mix?
View the answers.
Watch the solutions video.
Problem Set 2.5
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You record 48 invasive species from your sampling plots, and 62 native species. What is the ratio of native to invasive species?
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Sandy Creek is running at 80 cfs. It is a tributary to the Lochsa River, which is running at 460 cfs. What is the ratio of the flow in the Lochsa to that in Sandy Creek?
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My sample plot includes 5 Ponderosa pines, 10 small Douglas fir, and two western larch. What is the ratio of larch to all trees in the plot?
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The ratio of Great Basin wildrye to bluebunch wheatgrass in this planting mix is 2:5. If I’m planting 20 acres at 13 lbs of seed per acre, how many pounds of bluebunch wheatgrass seed will be in the mix?
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Jon weighs 210 pounds and can deadlift 520 lbs. His field partner Bill weighs 140 lbs and can deadlift 370 lbs. Who has the a higher strength to weight ratio?
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We’re baking a cake using a recipe that calls for a butter-to-sugar ratio of 2:3. If we use 6 cups of butter, how many cups of sugar should we add?
