Math Lesson 3
Fractions, Decimals II


Instruction 3-3

Round off Decimals | Compare and Order Positive and Negative Fractions, Decimals, Mixed Numbers | Interpret and Use Ratios | Use Proportions to Solve Problems | Using LCM to Solve Fraction Problems | Calculate Percentages and Solve Problems

CA GR6 NS 1.2
A ratio is a comparison of two quantities.

There are three types of ratios. Each kind of ratio can be written in three different ways. One way in which you can write a ratio is as a fraction. Both ratios and fractions show the relationship between two quantities.

The three types of ratios are part to part, part to total, and total to part. Below are explanations of the three types of ratios as well as the way in which they can be written.

Part to Part 4 to 7
4 : 7

Read 4 to 7

Part to Total 4 to 11
4 : 11

Read 4 to 11

Total to Part 11 to 4
11 : 4

Read 11 to 4

Equivalent ratios are ratios that are represented by equivalent fractions. But how do you find an equivalent fraction? Follow the directions below:

Express the ratio as a fraction. Ratio
3 : 5
Multiply the numerator and denominator by the same number. You can use any number except zero.

So 6:10 is equivalent to 3:5.    

A ratio is a comparison of two numbers or measurements. Each number being measured is called a term. A rate is a special ratio in which the two numbers being compared are in different units. For example, if a man walks 7 miles in two hours, we can write this as a rate of . The first term of the ratio is in miles, the second in term in hours. If you were to solve this ratio, you would get a rate of 3.5 miles walked per hour.

Rates are used in everyday life. Some examples include 15 miles per gallon or 12 dollars per hour. When rates are expressed as a comparison with one term being one, they are called unit rates. By creating equal fractions with one fraction having a denominator of one, we can solve multiple-unit rate problems.

Example 1. The price for a can of three tennis balls is $3.60. How much is the price per ball?

To solve this problem, we set up equal fractions and solve:

This is a comparison of two fractions or a proportion. We solve by cross-multiplying and then dividing, where P = the price of one ball.

In this case, since we are dealing with prices, this is called a unit price.

Example 2. Jane earns $60.00 for working 10 hours. How much would she earn if she worked 40 hours?

To solve this problem, we set up equal fractions and solve:

We solve by cross-multiplying and then dividing, where E is Janeís earnings.

Example 3. Five pens cost $2.10. How much would 27 pens cost?

To solve this problem, we find the unit price (the cost for one pen) by dividing $2.10 by 5, and then multiply the answer by 27 or we can create equal fractions, cross multiply and then divide to get the answer. Letís look at both ways to solve this problem.

Method I.

Method II.

  • Find the unit price:

  • Multiply the unit price by 27:
  • Set up equal fractions and cross-multiply, where
    P = price of 27 pens:


    Either way, we get the same answer, that 27 pens cost $11.34.

    Worksheet 1 Ratio Using Shapes.

    Worksheet 2 Ratio Using Shapes.  

    Worksheet 3 Find Equivalent Ratios  

    Worksheet 4 Write the Ratios in Fraction Form.

    Links for Students, Parents and Teachers

    Now let's do Practice Exercise 3-3 (top). 


    Next Page:  Use Proportions to Solve Problems (top)