Download Lesson 34: Proportions and Ratio Word Problems

Bell Work:
Simplify
(-12) – (-3)
Answer:
-9
LESSON 34:
PROPORTIONS
AND RATIO WORD
PROBLEMS
Proportion*: a statement that
two ratios are equal.
The ratios 2/4 and 6/12 are
equal and form a proportion.
Equal ratios reduce to the same
ratio. Both 2/4 and 6/12 reduce to
½. Notice these multiplication
relationships between the
numbers in the proportion.
2x3=6
2x2=4
2 = 6
2 = 6
4
4
12
4 x 3 = 12
12
6 x 2 = 12
One ratios in a proportion can
be expressed as the other
ratio by multiplying the terms
by a constant factor.
2 x 3 = 6
4
3
12
We can use this method to
test whether ratios form a
proportion. For example, to
park for 2 hours, a lot charges
$3. to park for 3 hours, the lot
charges $4.
Time (hr) 2 3
Charge ($) 3 4
Is the time parked and the fee
charged by the lot a
proportional relationship?
Answer:
No, the relationship is not
proportional because the
ratios are not equal. They do
not reduce to the same ratio.
Example:
Nora is paid $12 an hour. Is
her pay proportional to the
number of hours she works?
Answer:
The ratio of pay
to hours is
constant. The
ratio doesn’t
change. The
pay is
proportional
Nora’s Pay
Hours
Pay
Pay
Hours
12/1
1
$12
2
$24
24/2 =
12/1
3
$36
4
$48
36/3 =
12/1
48/4 =
12/1
Example:
Nelson has a paper route. If he
works by himself the job takes
60 minutes. If he splits the route
with a friend, it takes 30 minutes.
If two friends help, the job takes
20 minutes. Is the amount of
time it takes to complete the
route proportional to the number
of people working?
Answer:
Relationship
is not
proportional
Time for Paper Route
Number
Time
Time
Working (min.) Workers
1
60
60/1
2
30
30/2 =
15/1
3
20
20/3
We can use proportions to
solve problems where one of
the numbers in the proportion
is missing. A variable
represents the missing
number in the proportion.
2 = 6
8
x
One way to find the missing
number in a proportion is to use
the multiple between the terms
of the ratios. This method is like
finding equivalent fractions.
2x3=6
2 = 6
8
x
8 x 3 = 24
By multiplying 2/8 by 3/3, we find
that the missing term is 24. below
we show another relationship we
can use to find a missing number
in a proportion.
2x4=8
2 = 6
8
x
6 x 4 = 24
Again we find that the missing
number is 24
Example:
Solve
24 = 8
m
5
Answer:
24 = 8
m
5
8 x 3 = 24 5 x 3 = 15
m = 15
Ratio word problems can
include several numbers, so
we will practice using a table
with two columns to sort the
numbers. In one column we
write the ratio numbers. In the
other column we write the
actual counts. We can use a
ratio table to help us solve a
wide variety of problems.
Example:
The ratio of boys to girls in the
class is 3 to 4. if there are 12
girls, how many boys are
there?
Answer:
3 = b
4
b=9
12
Ratio
3
4
Actual Count
b
12
Practice:
Which pair of ratios forms a
proportion?
a) 3/6, 6/9
b) 3/6, 6/12
c) 3/6, 6/3
Answer:
B 3/6, 6/12
HW: Lesson 34 #1-30
Due Tomorrow