Transcript Ratios

Warm Up #1
1.) Convert 3/8 into a decimal and percent.
0.375, 37.5%
2.) Convert 1.25 into percent and fraction.
125%, 1 1/4
3.) Correna wants to wrap a present. She
has a piece of ribbon that is 2 ¼ feet long
and another that is 3.7 feet long. What is
their combined length?
2 ¼ = 2.25 feet, so 2.25 ft. + 3.7 ft. = 5.95 ft.
Ratio and Proportion
What am I Learning Today?
Ratio and Proportion
How will I show that I learned it?
Understand the concept of ratio by using it as
a fraction.
Use proportions to describe relationships and
solve problems.
Vocabulary
Ratio: A comparison of two
quantities by division and
measured in the same unit
Proportion: An equation that
states that two ratios are
equivalent
Questions
How do I write
a ratio?
What do
ratios
compare?
What are
equivalent
ratios?
How do I find
equivalent
ratios?
Answers
3 ways:
-As a fraction: 1/2
-With the word “to”: 1 to 2
-With the words “out of”: 1 out of 2
- With a colon (:): 1:2
Ratios can compare:
- part to part (boys to girls)
- part to whole (boys to total students)
- whole to part (total students to boys)
Ratios that name the same comparison
Multiplying or dividing both terms in the ratio
by the same number
For a time, the Boston Symphony Orchestra was
made up of 95 musicians.
Violins
Cellos
29
10
Violas
Basses
12
9
Flutes
Double reeds
Clarinets
Horns
5
8
4
6
Trumpets
Percussion
Harp
Trombones
3
5
1
3
For example, you can use a ratio to compare the number of
violins (29) with the number of violas (12). This ratio can
be written in three ways: 29 to 12, 29:12, or 29
12
29 is
Notice that the ratio of violins to violas,___
12
12 .
different from the ratio of violas to violins, ___
The order of the terms is important.
29
Writing Ratios
Use the table to write the ratio.
Animals at the Vet
Cats
Dogs
Rabbits
5
7
2
cats to rabbits
dogs to total number of pets
5 or 5 to 2 or 5:2
__
2
Part to part
7
__
or 7 to 14 or 7:14
14
Part to whole
total number of pets to cats
14
__
or 14 to 5 or 14:5
5
Whole to part
Writing Equivalent Ratios
Write three equivalent ratios to compare the
number of diamonds to the number of spades in
the pattern.
number of diamonds
number of spades
3
__
6
1
__
2
9
__
18
There are 3 diamonds
and 6 spades.
÷3
3 = 3
__
____
There is 1 diamond for
=
6÷3
6
every 2 spades.
If you triple the pattern,
3 = 3•3 =
__
there will be 9 diamonds
6
6•3
for 18 spades.
3 , __
1 , and __
9 are equivalent ratios.
So __
6
2
18
=
TRY THIS: Use the table to write each
ratio.
Brown bears
Giraffes
Monkeys
Polar Bears
1.
2.
3.
4.
3
2
17
4
giraffes to monkeys
2:17
polar bears to all bears 4:7
monkeys to all animals 17:26
all animals to all bears 26:7
Give two equivalent ratios for 4:7 8:14
12:21
Consider this…
When might you want to simplify a ratio?
When making a comparison out of a
large/uncountable group like from a survey, so
you want to know that 1 out of every 4 dentists
recommend a particular product rather than
25,000 out of 100,000
When might you not want to simplify a
ratio?
When you have a finite number of things and it
is important to know the total, so 3 out of the 19
CDs in her collection are bluegrass.
Questions Answers
How do I know
if ratios are
proportionate?
Two ratios are proportionate if their
cross products are equal
1) If possible, treat like equivalent fractions.
4 = __
2.
A proportion shown by the model is __
8
4
4 divided by 2 is 2
8 divided by 2 is 4
2) If not, use cross products to solve for the
missing information.
Cross products in proportions are equal
3 __
n
__
=
5 15
5 • n = 3 • 15
5n = 45
n=9
Find the cross products.
The cross products are equal.
Divide both sides by 5 to
undo the multiplication.
Using Cross Products to
Complete Proportions
Find the missing value in the proportion.
5
n
__
__
=
6
18
6 • n = 5 • 18
6n = 90
90
6n
___
= ___
6
6
n = 15
Find the cross products.
The cross products are equal.
n is multiplied by 6.
Divide both sides by 6 to undo
the multiplication.
Try These: Solving Proportions
Find the missing value in each
proportion.
n=2
n/5 = 4/10
n=6
3/9 = 2/n
n = 14
6/n = 3/7
Using Proportion to solve word problems
Understand: What is asked? Underline the question. What
information is given? Highlight the information.
Grandma can ride the 24 miles to Blackfoot in two hours on her bike. If she
rides at the same rate, how long will it take her to ride her bike the 36 miles
to Rexburg?
Plan: Is a ratio given? If so, set up the problem. Put the
given ratio on one side of the equal sign. Put the other
piece of information on the same level as its label. Put
an “x” in the empty space.
hours
2
x
miles
24

36
Solve: Solve the proportion.
hours
miles
2
x

 2  36  24 x  x  3hours
24 36
Ask: Is the answer realistic? Replace the variable with the answer and solve again.
Caution!
In a proportion, the units must be
in the same order in both ratios.
tbsp ___
tbsp
___
=
gal
gal
gal
gal
___
___
or
=
tbsp tbsp
Measurement Application
According to the label, 1 tablespoon of plant
fertilizer should be used per 6 gallons of water.
How many tablespoons of fertilizer would you
use for 4 gallons of water?
1 tbsp ____
f
_____
=
6 gal
4 gal
1 tbsp ____
f
_____
=
6 gal
4 gal
6•f =1•4
Let f be the amount of fertilizer
for 4 gallons of water.
Write a proportion.
The cross products are equal.
Measurement Application
Continued
6f = 4
4
6f
___
= __
6
6
2
f = __ tbsp
3
f is multiplied by 6.
Divide both sides by 6 to undo
the multiplication.
Write your answer in simplest
form.
2 tbsp of fertilizer for 4 gallons
You would use __
3
of water.
Solving Proportions: Try These!
 Shane’s neighbor pledged $1.25 for every 0.5
miles that Shane swims in the charity swim-athon. If Shane swims 3 miles, how much money
will his neighbor donate? $7.50
 A cocoa recipe calls for 4 tbsp of cocoa mix to
make an 8 oz. serving. How many tbsp of cocoa
mix are needed to make a 15 oz. serving? 7.5 Tbsp
 The label on a bottle of salad dressing states
that there are 3 grams of fat per tablespoon. If
you use 3 tablespoons, how many grams of fat
would you be getting? 9 g