There are 48 animals in the field, with 20 cows and the remaining 28 being horses. The ratios are: a) The ratio of cows to horses is 20:28 or 20/28. b) The ratio of horses to total animals is 28:48 or 28/48. c) The ratio of cows to total animals is 20:48 or 20/48.

1. There are 48 animals in the field. Twenty are cows and the rest
are horses.
Write the ratio in three ways:
a. The number of cows to the number of horses
b. The number of horses to the number of animals in the field

2. What is a Ratio?
• A ratio is a comparison of two numbers.
• Ratios can be written in three different ways:
a to b
a:b
Because a ratio is a fraction, b can not be zero
b
a
Ratios are expressed in simplest form

3. How to Use Ratios?
• The ratio of Pen and Notebook in the class is 13 to11.
4cm
1cm
This means, for every 13 Pens
you can find 11 notebook to
match.
• There could be just 13 pen, 11
notebook.
• There could be 26 pen, 22
notebook.
• There could be 130 pen s, 110
notebook …a huge class
What is the ratio if the
rectangle is 6cm long and
2cm wide?
Still 3 to 1, because for every
3cm, you can find 1cm to
match
• The ratio of length and width of this rectangle
is 3 to 1.
.
• The ratio of cats and dogs at my home is 3 to 1
How many dogs and cats do I
have? We don’t know, all we
know is if they’d start a fight,
each dog has to fight 3 cats.

4. How to simplify ratios?
• The ratios we saw on last
slide were all simplified.
How was it done?
b
a
Ratios can be expressed
in fraction form…
This allows us to do math
on them.
The ratio of boys and girls in the
class is
The ratio of the rectangle is
The ratio of cats and dogs in my
house is
13
11
b
a
3
1
3
1

5. How to simplify ratios?
• Now I tell you I have 12 cats and 4 dogs. Can you
simplify the ratio of cats and dogs to 3 to 1?
12
4
=
12/4
4/4
=
3
1
Divide both numerator and
denominator by their
Greatest Common Factor 4.

6. How to simplify ratios?
A person’s arm is 60cm, he is 2m tall.
Find the ratio of the length of his arm to his total height
60𝑐𝑚
2𝑚 
60𝑐𝑚
200𝑐𝑚
60
200
 3
10
To compare them, we need to convert both
numbers into the same unit …either cm or m.
• Let’s try cm first!

height
arm

Once we have the
same units, we can
simplify them.

7. How to simplify ratios?
• Let’s try m now!
height
arm 60𝑐𝑚
2𝑚 
0.6𝑚
2𝑚

Once we have the
same units, they
simplify to 1.
6
20 
3
10

To make both numbers
integers, we multiplied both
numerator and denominator by
10

8. How to simplify ratios?
• If the numerator and denominator do not have the
same units it may be easier to convert to the smaller
unit so we don’t have to work with decimals…
3cm/12m = 3cm/1200cm = 1/400
2kg/15g = 2000g/15g = 400/3
5ft/70in = (5*12)in / 70 in = 60in/70in = 6/7
2g/8g = 1/4 Of course, if they are already in the same units, we
don’t have to worry about converting. Good deal

9. More examples…
24
8
9
27
200
40
=
=
=
5
1
3
1
50
12
=
25
6
18
27
=
2
3
1
3

10. Chocolates at the candy store cost $6.00 per dozen.
How much does one candy cost? Round your answer
to the nearest cent.
Solution:
$ 6.00 x
candy 12 1
6.00 (1) = 12x
0.50 = x
$0.50 per candy
(Use equivalent rates
to set up a proportions)
=

11. Example 2:
There are 3 books per student. There are 570 students.
How many books are there?
Set up the proportion:
Books
Students
3 Where does the 570 go?
1
3 x__
1 570
3 570 1x
x 1,710 books
=
=
=
=

12. Example 3:
The ratio of boys to girls is 4 to 5. There are 135
people on a team. How many are girls?
Set up the proportion:
Girls
People How did we determine this ratio?
5 Where does the 135 go?
9
5 x_
9 135
5 135
675 = 9x
x = 75
75 girls
=
9x
=
=