Virginia SOL Math / Grade 8 / Computation & Estimation
Proportional Reasoning
What you'll learn
- Solve practical problems using proportional reasoning
- Find and apply a unit rate
- Solve percent problems including tax, tip, and percent change
Words to know
- Ratio —
- a comparison of two quantities
- Proportion —
- an equation stating two ratios are equal
- Unit rate —
- a rate with a denominator of 1
- Percent —
- a ratio out of 100
- Percent change —
- the amount of change as a percent of the original
Why it matters Proportional reasoning drives everyday math like scaling a recipe, converting units, figuring a tip, and finding a sale price.
Worked examples
Model ItI do
A car travels 120 miles on 4 gallons of gas. What is the unit rate in miles per gallon?
Divide miles by gallons: 120 divided by 4 equals 30. The unit rate is 30 miles per gallon.
Try It TogetherWe do
A shirt costs 25 dollars and is marked down 20 percent. Find the sale price.
The discount is 20 percent of 25, which is 0.20 times 25 = 5 dollars. Subtract from the original: 25 - 5 = 20 dollars.
Now YouYou do
A meal costs 40 dollars. Find the total after adding a 15 percent tip.
Find 15 percent of 40, then add it to the bill. Check your answer in the back of this chapter.
Practice
Mastered 0 of 11
Warm-up
Ease in with the basics.
1.Find the unit rate: 60 miles in 2 hours.
2.What is 10 percent of 50?
3.Solve the proportion: 2/4 = x/8.
On Level
The core Quick Check from the book.
1.Find the unit rate: 84 dollars for 6 hours.
2.Solve the proportion: 3/5 = x/20.
3.What is 30 percent of 90?
4.A 50 dollar item is discounted 10 percent. What is the sale price?
5.A price rises from 20 to 25 dollars. What is the percent increase?
Challenge
Stretch your thinking.
1.A 60 dollar jacket is discounted 25 percent, then 6 percent sales tax is added to the sale price. Find the final total.
2.A recipe for 4 servings uses 6 cups of flour. How many cups are needed for 10 servings?
3.A stock price rose from 40 dollars to 52 dollars. What is the percent increase?