Thursday, April 14th, 2005

Unit 8—Using Proportional Reasoning

Day 1—Writing Ratios and Simplifying Ratios

Homework—Worksheet 8.1

Overview of Unit 8

Equal Ratios

Rates

Proportions

Scale Drawings

Expressing Fractions as Decimals

Fractions, Decimals, and Percents

Percents Greater than 100% and Less than 1%

Percent of a number

Percent Proportion

3 Ways to Write a Ratio

A : B

A to B

A

B

Simplifying RatiosSteps to Simplify:

1. Find the Greatest Common Factor (GCF)

between the two numbers.

2. Divide the GCF into both numbers.

3. Check to make sure that the ratio is simplified.

Let’s Find the GCF!

Find the GCF of:

• 3 and 9

• 10 and 22

• 6 and 27

GCF is 3

GCF is 2

GCF is 3

Now Let’s Simplify

Using the GCF you just found, simplify these ratios!

• 3:9 =

• 10:22 =

• 6:27 =

3 3 1

9 3 3

10 2 5

22 2 11

6 3 2

27 3 9

Your Turn!

Simplify:

1. =

2. =

3. =

6

42

33

22

48

12

1

73

2

4

1

Caution!!!:

*Do Not get rid of the denominator if it equals 1!

* We want to keep the 1 as the denominator, so the simplified ratio is:

44

1

4

1

Equivalent Ratios

How can we determine if two ratios are equivalent?

Simplify both ratios and see if they are equal!

1. Are 8:24 and 7:21 equivalent ratios?

2. Is the ratio 5 inches to 3 feet equivalent to the ratio 12 inches to 5 feet? (hint: there are 12 inches in 1 foot)

Let’s See if we have Equivalent Ratios!

Example 1

1. 8:24 = and 7:21 =

Both of these ratios simplify to

so 8:24 and 7:21 are equivalent ratios!

8 8 1

24 8 3

7 7 1

21 7 3

1

3

Example 2

2. 5 in. to 3 ft and 12 in. to 5 ft

= 5 in. to 36 in. = 12 in. to 60 in.

= =

These ratios do not simplify to the same ratio, so 5 in. to 3 ft. and 12 in. to 5 ft. are NOT equivalent ratios!

5 1 5

36 1 36

12 12 1

60 12 5

Homework:Worksheet 8.1 due Tomorrow

Have a great day!