Aim: How do we solve proportion problems?
PROPORTIONS
Aim: How do we solve proportion problems?
RATIO REVIEW
Ratio - comparison between 2 numbers by division.
*Note: To find the ratio of 2 quantities, both quantities must be
expressed in the same unit of measure before finding their
quotient. For example, to compare the value of a nickel to a
penny, we first convert the nickel to 5 pennies and then find the
ratio, which is 5:1 (i.e. a nickel is worth 5 times as much as a
penny).
Aim: How do we solve proportion problems?
Proportion - an equation that states that two ratios are equal
(AKA: equivalent ratios)
st
th
and d are called extremes (1 and 4 terms, 'outers');
nd
rd
b and c are called means (2 and 3 , 'inners')
a
Note: In a proportion, the product of the means is equal
to the product of the extremes
Aim: How do we solve proportion problems?
Using your knowledge of ratios, what is another way you can
write this proportion?
a:b=c:d
Aim: How do we solve proportion problems?
A 6-foot man casts a 10-foot shadow. How many
feet tall is a nearby tree that casts a 50-foot shadow
at the same time?
6
10
=
300
10
x
50
= 10 x
10
x= 30 ft
Aim: How do we solve proportion problems?
Is 5 =
20
4
a
"TRUE"
proportion?
16
To check, you can:
a) Multiply the means and the extremes to see if they are equivalent
b) Reduce each ratio to simplest form to see if they become the same
c) Use a calculator to find the decimal form of each ratio
NO, not a proportion because
-4(20) = 5(16)
-80 = 80
Aim: How do we solve proportion problems?
GUIDED PRACTICE
1.
2. 25:x = 5:2
3.
4.
Aim: How do we solve proportion problems?
GUIDED PRACTICE
3.
1.
4(42) = 6(x)
168 = 6x
28 = x
2.
25 = 5
x
2
50 = 5x
5 5
250 = 25x
10 = x
2x(n) = 4r(m)
2xn = 4rm
2n
2n
x= 2rm
n
4.
3(x-3) = x+7
3x-9 = x+7
2x = 16
x=8
Aim: How do we solve proportion problems?
INDEPENDENT PRACTICE
CHALLENGE:
3x+3
3
=
7x-1
5
Aim: How do we solve proportion problems?
INDEPENDENT PRACTICE
yes
yes
no
We will go over these in class
CHALLENGE:
3x+3
3
=
7x-1
5
HW textbook pg. 146: 18, 22, 44, 48