Virginia SOL Math / Grade 7 / Computation & Estimation

7.CE.2

Proportional Relationships in Problems

What you'll learn

  • Set up and solve proportions in context
  • Find and use a unit rate
  • Solve problems involving percent, including tax, tip, and discount

Words to know

Proportion —
an equation stating that two ratios are equal
Unit rate —
a rate with a denominator of 1, such as miles per hour
Percent —
a ratio that compares a number to 100
Constant of proportionality —
the steady multiplier between two related quantities
Cross product —
the product found by multiplying across a proportion

Why it matters Proportional reasoning powers everyday math like scaling a recipe, converting units, figuring a tip, or finding a sale price.

Worked examples

Model ItI do

If 3 pens cost 4.50 dollars, what is the cost of 5 pens?

Find the unit rate: 4.50 divided by 3 = 1.50 dollars per pen. Then 5 pens cost 5 times 1.50 = 7.50 dollars.

Try It TogetherWe do

A 40 dollar shirt is on sale for 25 percent off. What is the sale price?

Find the discount: 25 percent of 40 is 0.25 times 40 = 10 dollars. Subtract from the original: 40 minus 10 = 30 dollars.

Now YouYou do

A car travels 150 miles on 5 gallons of gas. How far can it travel on 8 gallons?

Find the miles per gallon, then multiply by 8. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Find the unit rate: 90 miles in 3 hours.

  2. 2.Find 10 percent of 50.

  3. 3.Solve the proportion: 1 over 2 equals x over 8.

On Level

The core Quick Check from the book.

  1. 1.Find the unit rate: 120 miles in 2 hours.

  2. 2.Solve the proportion: 2 over 5 equals x over 20.

  3. 3.Find 15 percent of 60.

  4. 4.A 20 dollar meal has a 10 percent tip. What is the total cost?

  5. 5.If 4 apples cost 2 dollars, how much do 10 apples cost?

Challenge

Stretch your thinking.

  1. 1.A 60 dollar jacket is on sale for 20 percent off, then a 5 percent tax is added to the sale price. What is the total cost?

  2. 2.A car travels 210 miles on 6 gallons of gas. How far can it travel on 10 gallons at the same rate?

  3. 3.A recipe for 4 servings uses 6 cups of flour. How many cups are needed for 10 servings?