Transcript Thursday, April 14th, 2005

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
 Fractions, Decimals, and
Percents
 Rates
 Percents Greater than
 Proportions
 Scale Drawings
100% and Less than 1%
 Percent of a number
 Expressing Fractions  Percent Proportion
as Decimals
3 Ways to Write a Ratio
A: B
 A to B
A

B
Simplifying Ratios
Steps 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
GCF is 3
• 10 and 22
GCF is 2
• 6 and 27
GCF is 3
Now Let’s Simplify
 Using the GCF you just found, simplify
these ratios!
• 3:9
=
33 1

93 3
10  2 5

• 10:22 =
22  2 11
63 2

• 6:27 =
27  3 9
Your Turn!
Simplify:
6
1.
42
33
2.
22
3. 48
12
=
1
7
=
3
2
=
4
1
Caution!!!:
*Do Not get rid of the denominator if it
equals 1!
4
4
1
* We want to keep the 1 as the
denominator, so the simplified ratio is:
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
8 8 1
1. 8:24 =

24  8 3
77 1

and 7:21 =
21  7 3
1
Both of these ratios simplify to
3
so 8:24 and 7:21 are equivalent ratios!
Example 2
2. 5 in. to 3 ft
= 5 in. to 36 in.
= 5 1  5
36  1 36
and
12 in. to 5 ft
= 12 in. to 60 in.
= 12  12  1
60  12
5
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!
Homework:
Worksheet 8.1 due Tomorrow
Have a great day!