Transcript Ratios, Rates, Unit Rates

Starter #4: Thurs. 1/17/12
Copy the problem. Use the Giant 1 to Simplify: Leave
improper fractions improper. Do not change to mixed
number.
1)
15
25
2)
3) Use the Pythagorean Theorem to
find the missing side:
24
10
c
7 ft.
24 ft.
4) Is a triangle with side lengths of 4ft, 5ft and 6 ft a right triangle?
Show all work.
Learning Targets
• #1: I can write a ratio in 3 different ways.
B: 1 2 3
I have these questions:
A: 1 2 3
7MG1.1
Learning Targets
•#2)
I can write a ratio in simplest form.
B: 1 2 3
I have these questions:
A: 1 2 3
7MG1.1
Learning Targets
•#3)
I can find equivalent ratios.
B: 1 2 3
I have these questions:
A: 1 2 3
7MG1.1
Ratio
A ratio is the comparison of
two whole numbers.
Ratio
Example:
Your school’s basketball team has won 7 games and
lost 3 games. What is the ratio of wins to losses?
Because we are comparing wins to losses the first
number in our ratio should be the number of wins
and the second number is the number of losses.
7
__
games
won
_______
7
games
The ratio is ___________=
=
3 games 3
games lost
Ratio
A comparison of two whole numbers in the same units.
4 carnations to 9 roses
Possible Ways to Write a Ratio
4
9
4:9
4 to 9
4 carnations to 9 roses
Ratio
The Giant One is used to reduce ratios.
4

10
2
2

2
5
A ratio is in simplest form, or is reduced if
the numerator and denominator have no
common factors other than one.
3 1
3
 
4 1
4
Ratio
Ratios can be simplified (reduced), this
is call simplest form. To find the
simplest form divide the numerator and
denominator by the greatest common
factor.
12 6
2
 
18 6
3
Ratio
Put each ratio in simplest form.
3) 36 out of 42
36
6

42
7
4) 24 to 6
24
4

6
1
Ratio
Write the ratio 3 yards to 12 feet in simplest form.
First convert yards to feet.
3 yards = 3 ● 3 feet
= 9 feet
There are 3 feet in a yard.
Multiply.
Now write the ratio.
3 yards = 9 feet
12 feet
12 feet
=
9÷3=3
12 ÷ 3 4
The ratio is 3 , 3:4, or 3 to 4.
4
Simplify.
Ratio
Put each ratio in simplest form.
3 weeks 21 days

1)
5 days
5 days
21

5
You must
always use
the same
unit of
measure!
2) 32 inches  32 inches
1 foot
12 inches
32
8

12
3
Ratio
Write the ratio 24 shirts to 9 jeans in simplest
form.
Write the ratio as a
24
shirts =
fraction.
9
jeans
24
÷
3
=
9÷3
=
8
3
Simplify.
The ratio of shirts to jeans is 8:3, 8 to 3, or 8
3
Equivalent Ratios
Simplify to tell whether the
ratios are
equivalent.
3 and 2
27
18
3
3 ÷ 3 =1
=
27 27 ÷ 3 9
2
2 ÷ 2 =1
=
18 18 ÷ 2 9
1 1
Since = ,
9 9
the ratios
3 and 2
27
18
are equivalent.
Equivalent Ratios
Simplify to tell whether the
ratios are
equivalent.
12 and 27 12 = 12 ÷ 3 4
15
36 15 15 ÷ 3 = 5
27 = 27 ÷ 9 3
36 36 ÷ 9 = 4
Since 4  3 ,
5 4
the ratios are not
equivalent.
Ratio
A ratio that compares two
quantities with different units of
measure is called a rate.
Examples: $23 per foot
55 miles in 5 hours
$20 for 5 tickets
Take Out Your Learning
Targets!!!
LT #1
RATIOS: Comparison of two numbers
GIANT ONE
LT #2
Ratios in Simplest Form
To find the simplest form divide the numerator
and denominator by Giant One.
Example: Write the ratio 15 bikes to
9 skateboards in simplest form.
bikes
15 Write the ratio as a fraction.
=
skateboards 9
5
15
÷
3
=
=
Simplify.
9÷3 3
The ratio of bikes to skateboards is 5:3, 5 to 3, or 5
Or 5 bikes to 3 skateboards.
3
LT #3
Equivalent ratios = equal ratios
Example #1: using Giant one to REDUCE before
comparing. Are the ratios equivalent?
A. 3 and 9
15
45
3
= 3÷3= 1
15
15 ÷ 3 5
9
= 9÷9= 1
45
45 ÷ 9 5
B. 12 and 27
15
36
12 = 12 ÷ 3 4
=
15 15 ÷ 3 5
27 = 27 ÷ 9
3
=
36
36 ÷ 9
4
1= 1
5 5
equivalent
4 3
5 4
not equivalent
LT #3
Equivalent ratios = equal ratios
Example #2: finding COMMON DENOMINATOR
before comparing
Are the ratios equivalent?
?
Since 7 is a factor of
14 it is easy to find a
common denominator
and then compare
the numerators.
?
So,
are equivalent.
LT #3
Equivalent ratios = equal ratios
Example #3: finding COMMON DENOMINATOR
before comparing
Are the ratios equivalent?
?
?
Since 6 is a factor of
48 it is easy to find a
common denominator
and then compare
the numerators.
So,
are NOT
equivalent.
Name___________
January 17, 2013
Period___
Pizazz Worksheet: Bizarre Middle
School and Writer in the Basement
For full credit, Show your work! This includes the giant one!
HAPPY JANUARY!