Download Ratio

Lesson 1.1
Core Focus on
Ratios, Rates and Statistics
Ratios
Warm-Up
Simplify each fraction. Write your answer as a proper or
improper fraction, not as a mixed number.
1.
10
15
2
3
2.
16
40
2
5
3.
14
7
2
or 2
1
4.
48
36
4
3
Lesson 1.1
Ratios
Simplify and write ratios three ways.
Explore!
Comparing Students
Step 1 Write a fraction comparing the number of boys to the number of girls for each
teacher
. Write the fraction in simplest form. This fraction means
for every ____ boys there are ____ girls.
Step 2 Find the total number of students in each teacher’s class. Write a fraction
comparing the number of boys to the total number of students for each teacher
. Write the fraction in simplest form. This fraction means for
every ____ boys there are ____ students.
Step 3 Write a fraction comparing the number of girls to the total number of students
for each teacher
. Write the fraction
in simplest form. This fraction means for every ____
girls there are ____ students.
Explore!
Comparing Students
Step 4 Count the number of boys and girls in your class.
a. Find the fraction of boys to girls. This is the ratio of boys to girls.
b. Find the ratio of boys to total number of students.
c. Find the ratio of girls to total number of students.
Step 5 Mr. Jansen’s math class has 3 boys for every 2 girls.
a.
Write a ratio of boys to girls in Mr. Jansen’s class.
b.
There are 30 students in Mr. Jansen’s class. How many are boys?
Explain how you know your answer is correct.
Vocabulary
Ratio
A comparison of two numbers using division.
Good to Know!
 A ratio shows a part to another part or a part to a whole.
 A ratio written as a fraction should be written in
simplest form.
 Ratios can be larger than 1.
 Ratios larger than 1 should be written as simplified
improper fractions.
Writing Ratios
A ratio comparing two numbers, 3 and 5, can be written
in three ways:
3
 As a fraction →
5
 Using a colon → 3 : 5
 Using the word “to” → 3 to 5
Example 1
Paul took a handful of jelly beans. He chose 4 blue, 2 green, 3
red and 3 yellow. Write a ratio using each of the three ways.
a. Compare blue jelly beans to red jelly beans.
a.
Fraction
Using a
Colon
Using
“to”
blue jelly beans 4

red jelly beans
3
4:3
4 to 3
Example 1 Continued…
Paul took a handful of jelly beans. He chose 4 blue, 2 green, 3
red and 3 yellow. Write a ratio using each of the three ways.
b. Compare green jelly beans to the total number
of jelly beans.
Fraction
b. Total number of jelly beans:
4 + 2 + 3 + 3 = 12
green jelly beans
2 1
 
total jelly beans
12 6
Using a
Colon
Using
“to”
1:6
1 to 6
Example 1 Continued…
Paul took a handful of jelly beans. He chose 4 blue, 2 green, 3
red and 3 yellow. Write a ratio using each of the three ways.
c. Compare red jelly beans to the total number
of jelly beans.
Fraction
b. Total number of jelly beans:
4 + 2 + 3 + 3 = 12
red jelly beans
3 1
 
total jelly beans 12 4
Using a
Colon
Using
“to”
1:4
1 to 4
Example 2
The ratio of boys to girls on a soccer team is 8 : 7. What is
the ratio of boys to all players on the soccer team?
The ratio 8 : 7 means there are 8 boys for every 7 girls.
For every 8 boys there are 15 (8 + 7) players.
This makes the ratio of boys to all players 8 : 15.
Example 3
Compare the number of stars to the number of circles. If the ratio
remains the same, how many stars will you have if you have 14
circles?
The amount of stars and
circles changed, but the
ratio of stars to circles
did not change.
Write the ratio of stars to circles as a fraction.
10 5

4 2
Simplify the ratio.
Find an equivalent ratio that has 14 circles.
You will have 35 stars. The ratio 35 : 14 is equivalent to 10 : 4.
Example 4
Petra is filling jars with marbles. The jar sizes change, but the ratio of blue
marbles to green marbles always stays the same. The table below shows
some of the jars and their quantity of blue marbles to green marbles.
a.
blue
6
12
18
27
33
green
10
20
30
45
?
Find the ratio of blue marbles to green marbles in each jar.
Choose any pair of blue and green values
and write the ratio as a fraction.
6 3

10 5
The different quantities
used to make a ratio can
also be written in a table
and the points graphed.
Simplify the ratio.
The ratio of blue marbles to green marbles is 3 : 5 or
3
.
5
Example 4 Continued…
Petra is filling jars with marbles. The jar sizes change, but the ratio of blue
marbles to green marbles always stays the same. The table below shows
some of the jars and their quantity of blue marbles to green marbles.
b.
blue
6
12
18
27
33
green
10
20
30
45
?
Find the number of green marbles when the jar has 33 blue marbles.
Find an equivalent ratio to
3
that has 33 blue marbles.
5
There would be 55 green marbles when the jar has 33 blue marbles.
Example 4 Continued…
Petra is filling jars with marbles. The jar sizes change, but the ratio of blue
marbles to green marbles always stays the same. The table below shows
some of the jars and their quantity of blue marbles to green marbles.
c.
blue
6
12
18
27
33
green
10
20
30
45
?
Let the number of blue marbles be x and the number of green marbles
be y. Plot the ordered pairs (x, y) for each set of values in the table.
What do you notice about the points?
Number of Marbles in Jars
Graph each of the ordered pairs
(6, 10), (12, 20), (18, 30), (27, 45)
and (33, 55).
The points are all in a line with the
origin (0, 0). Each point has a ratio
of its y-value to its x-value of 5 .
3
Communication Prompt
The ratio of boys to girls in math class is 1 : 2.
What does this ratio mean?
Exit Problems
1. Simplify the ratio 100 : 20 and write the ratio as a fraction,
with a colon and using the word “to”.
5
; 5 : 1; 5 to 1
1
2. Lucas had 6 red jelly beans and 9 purple jelly beans. Write
each ratio as a fraction in simplest form.
a. Write the ratio of the number of red jelly beans to the
number of purple jelly beans.
2
or 2 : 3
3
b. Write the ratio of the number of red jelly beans to the total
number of jelly beans Lucas has.
2
or 2 : 5
5