Virginia SOL Math / Grade 6 / Patterns, Functions & Algebra

6.PFA.2

Proportional Relationships

What you'll learn

  • Represent proportional relationships with tables and ratios
  • Determine whether a relationship is proportional
  • Use unit rates to solve problems

Words to know

Proportion —
an equation stating two ratios are equal
Unit rate —
a rate with a denominator of 1, like miles per hour
Proportional —
having a constant ratio between quantities
Cross product —
the result of multiplying across a proportion
Scale —
a ratio used to enlarge or reduce

Why it matters Proportions let us scale up recipes, convert units, and find prices, so a small comparison predicts a larger one.

Worked examples

Model ItI do

If 2 pens cost 6 dollars, what is the cost of 1 pen?

Find the unit rate by dividing the cost by the number of pens: 6 divided by 2 = 3. Each pen costs 3 dollars.

Try It TogetherWe do

If 3 apples cost 2 dollars, how much do 9 apples cost?

The quantity of apples tripled from 3 to 9, so the cost triples too: 2 times 3 = 6 dollars for 9 apples.

Now YouYou do

A car travels 120 miles in 2 hours. What is its speed in miles per hour?

Divide the distance by the time to find the unit rate. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.If 3 pens cost 6 dollars, what is the cost of 1 pen?

  2. 2.If 1 apple costs 2 dollars, how much do 4 apples cost?

  3. 3.A car travels 60 miles in 1 hour. How far does it travel in 3 hours?

On Level

The core Quick Check from the book.

  1. 1.If 4 pencils cost 8 dollars, what is the cost of 1 pencil?

  2. 2.If 1 book costs 5 dollars, how much do 3 books cost?

  3. 3.A runner goes 10 miles in 2 hours. What is the unit rate in miles per hour?

  4. 4.If 2 cups of rice serve 6 people, how many people do 4 cups serve?

  5. 5.Solve the proportion: 3/6 = x/12. Find x.

Challenge

Stretch your thinking.

  1. 1.If 4 notebooks cost 10 dollars, how much do 10 notebooks cost?

  2. 2.A runner goes 12 miles in 3 hours. At the same rate, how far in 5 hours?

  3. 3.Solve the proportion: 4/10 = x/25. Find x.