Transcript RATIOANDPROPORTIONPPTx

A ratio compares two things.
It can compare part to part, a
part to the whole, or the whole
to a part.
The word “to” compares the
two terms in a ratio.
You can write a ratio three different
ways.
In words: 4 to 3
Using a colon: 4:3
Like a fraction 4/3
In this ratio we are comparing the number of pink
squares to the number of blue squares.
RATIO
If a recipe says, “For every cup of rice, add 2
cups of water” that’s a ratio.
In school, if there is 1 teacher to every 5 students,
that’s a ratio, too.
A ratio is a handy way to express the relationship between
numbers.
If you've spent any time in the kitchen, then
you already know quite a bit about ratios.
A rice recipe calls for 2 cups of water to 1 cup
rice.
The ratio of water to rice is 2 to 1.
What is the ratio of oil to vinegar in a
salad dressing recipe that calls for 2
tablespoons oil to 1 tablespoon vinegar?
Separate your numbers by the word "to."
The ratio of oil to vinegar
in the salad dressing
is 2 to 1.
We can also write this
with a colon as 2:1.
A biscuit recipe calls for 7 cups flour
and 1 cup shortening.
What is the ratio of flour to shortening? Write
the ratio with a colon.
Don't add any spaces between the numbers
and the colon.
ANSWER
7:1
Ratios can also be written as fractions.
A tortilla recipe calls for 4 cups
flour and 1 cup water. The ratio of
flour to water would be 4 to 1, or
4:1.
As a fraction we write this as
4/1.
A stew recipe calls for 5 cups of carrots
and 2 cups of onions.
ANSWER
5/2
is the same as
5:2
and
5 to 2.
A recipe for orange juice
calls for 3 cups water and 1
cup orange juice
concentrate.
Write the ratio of water
to concentrate as a
fraction.
Good job.
3 to 1 is
the same
as 3/1.
What if we want to double the amount of orange
juice we make?
 The original recipe calls for 3 cups water and 1 cup
orange juice concentrate.
 The ratio of water to concentrate is 3:1.
To double the recipe, we multiply both terms (in
ratios we call the numbers "terms") in the 3:1 ratio by
2 (because we’re making twice as much).
This is called an equivalent ratio. Two ratios that
equal the same thing.
The new ratio is 6:2.
If we triple the recipe, what is the
ratio of water to concentrate?
Write the ratio as a fraction.
ANSWER
9/3
What if we want to make 5 times the
original amount of orange juice?
The original recipe calls for 3 cups water
and 1 cup orange juice concentrate. The
ratio of water to concentrate is 3:1.
To make 5 times the recipe, we multiply
both terms in the 3:1 ratio by 5. The new
ratio is 15:5.
No matter how much orange juice
we make, we still need 3 cups of
water for every 1 quart of concentrate
So the ratio of 12 cups of water to 4
cups concentrate in the quadrupled
recipe is the same as the ratio of
concentrate to water in the original
recipe.
In other words, the relationship
between the two terms in the ratio
3:1 is the same as that in 12:4.
Just do the math! 3 is three times as
much as 1, and 12 is three times as
much as 4.
Since 3:1 and 12:4 have the same
relationship, these two ratios are
equal.
When two ratios are equal, we
say they are in proportion.
In other words, a proportion is
a mathematical statement that
two ratios are equal.
Equivalent ratio = proportion
We write proportions like this:
3 to 1 equals 12 to 4
3:1 = 12:4
3/1 = 12/4
A recipe for chili calls for 5 oz beans
and 2 oz beef. The ratio of beans to
beef is 5:2. You want to quadruple
the recipe to fill a big pot for a party.
Write the original beans to beef ratio
and the quadrupled recipe ratio as a
proportion. Don’t forget to write your
answer with colons and the equal
sign.
ANSWER
5:2 = 20:8
To figure out the new ratio you
multiply both terms in the original
recipe ratio 5:2 by 4.
Another way to write the same
proportion is 20:8 = 5:2.
Which of the following is not a
proportion?
A) 1:6 = 24:4
B) 3:4 = 15:20
C) 7:6 = 14:12
ANSWER
A
In true proportions, both terms in one ratio must be
multiplied (or divided) by the same number to get the
terms of the second ratio.
If you do the math, you’ll see that 1:6 = 24:4 is not a
proportion.
1 x 24 = 24
but 6 x 24 = 144
--not 4!
In Mrs. Jones’ class there are 20
students. There are 12 boys and
8 girls. 7 students have brown
hair, 10 have blonde hair and 3
have red hair. What is the ratio
of students with blond hair to
those that have red hair?
ANSWER
10:3
Martha has 10 dresses. 3 are red and
the rest are blue. How many red
dresses to blue dresses does she have?
3:7
Tom has 13 video games. 5 are
action games, 2 are adventure
and the rest are sports. How
many sports games to action
games does Tom have?
6:5
In problems involving proportions, there will always be
a ratio statement.
An automobile travels 176 miles on
8 gallons of gasoline. How far can it
go on a tankful of gasoline if the
tank holds 14 gallons?
176 miles
8 gallons
14 gallons
miles
X or any letter because it’s the variable
176 miles = x miles
8 gallons 14 gallons
Math Note: Notice in the previous
example that the numerators of the
proportions have the same units, miles,
and the denominators have the same
units, gallons.
176 = x
8
14
176 = m
8
14
8m = 176 x 14
8m = 2464
8m = 2464
8
8
m= 308 miles
On 14 gallons, the automobile
can travel a distance of 308
miles.
Read the problem .
Identify the ratio statement.
There will ALWAYS be one.
Set up the proportion
Be sure to keep the identical units in the numerators and
denominators of the fractions in the proportion.
Solve for x or the
variable.
Let’s try another
If it takes 16 yards of material
to make 3 costumes of a
certain size, how much
material will be needed to
make 8 costumes of that
same size?
What’ s the next step
 Find the ratio statement.
The ratio statement is:
Be sure to keep the identical units in the
numerators and denominators of the fractions in
the proportion.
yards
costumes
yards
costumes
Setting the proportion
 Identical units
16 yards = x yards
3 costumes 8 costumes
Next step cross multiply
16 yards = y yards
3 costumes 8 costumes
3y = 16 x 8
3y = 128
3
3
Y = 42.666
Remember: Pounds across from
pounds square feet across from
feet.
3075 square feet
$5600
$5070
21 gallons
13 or 13.5 tablespoons