Reference no: EM133930141
Principles of Mathematics
Lecture Handout
Topic: Apply Ratios and Proportions to Solve Applied Problems
Understanding Ratios
A ratio is a fraction in lowest terms.
Ratios can have decimals in the numerator or denominator (e.g., unit rates, gear ratios).
Example 1
The following are all ratios:
7:3
a:b
2.5:2
12.2:1
4:9
Example 2
Notice that the above have no units. Ratios can be written in multiple forms.
Example 3
Write the ratio of 11 to 6.
Express as: 11:6
Unit Rates
A unit rate is a special kind of ratio.
Example 4
A car travels 342 miles on 8.4 gallons of gas.
Set up ratio: miles ÷ gallons
Problem: Find miles per gallon (MPG) = 342 ÷ 8.4 = ?
Example 5
15 tiles cost $27.50.
Problem: Find cost per tile = 27.50 ÷ 15 = ?
Example 6
700 feet of fence requires 88 posts.
Problem: Find feet per post = 700 ÷ 88 = ?
Example 7: Compare Pudding Cans
Size Cost Cost per Ounce
8 oz $2.55 2.55 ÷ 8 = ?
64 oz $14.50 14.50 ÷ 64 = ?
Problem: Which can is the better deal?
Understanding Proportions
A proportion is an equality between two ratios.
ab=cd
ba=dc
Proportions have many applications (e.g., scaling, recipes, blueprints).
Example 8: Recipe Ratio Problem
Ratio: 3 eggs : 5 cups of flour
Given: 36 eggs → find cups of flour required
Proportion: 35=36c53=c36
Problem: Solve for cc
Example 9: Cats and Dogs Ratio
Ratio: 11 cats : 5 dogs
Given: 77 cats → find dogs
Proportion: 115=77d511=d77
Problem: Solve for dd
Example 10: Employed vs Unemployed Students
Ratio: 24 employed : 7 unemployed
Total students: 1240
Total parts: 24 + 7 = 31
Proportion setup: 31U=12407U31=71240
Problem: Solve for number of unemployed students UU
Example 11: Rounding Issues
Solve the proportions below and round appropriately.
a)
Depending on the situation, round to the nearest logical value (e.g., 2 decimal places for money).
b)
Ratio of Chevy to Ford is 17:23.
Given: 40 vehicles are Fords.
Problem: Find number of Chevys.
c)
Every 3 people need 7 pounds of food every 2 days. Get expert online assignment help in the Australia.
Given: 110 pounds of food.
Problem: Find how many people can be fed for 2 days.
Note: Round down if resources are insufficient.
Equality of Proportions
To check if two ratios are proportional:
Cross multiply the terms.
If cross products are equal, the ratios are proportional.
Example 12
Are 3883 and 924249 proportional?
Cross multiply: 3×24=8×93×24=8×9
Compare results.
Example 13
Are 3553 and 12212112 proportional?
Cross multiply: 3×21=5×123×21=5×12
Compare results.