The document is a presentation on the concept of ratios. It begins with defining ratios and their various forms of expression. It then covers key objectives like expressing one value as a fraction of another given their ratio. Several examples of ratios are provided, including explaining the importance of order and ensuring quantities have the same units. Applications to rates and problem solving with ratios are demonstrated. The presentation concludes with an evaluation section posing additional ratio problems.

1. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
THE CONCEPT OF
RATIO
Hi, I`m Teacher Tin 

2. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
 Express one value as a fraction of another given their ratio and vice versa.
 Find how many times one value is as large as another given their ratio and
vice versa.
 Define and illustrate the meaning of ratio using concrete or pictorial models.
OBJECTIVES

3. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
01
WHAT IS RATIO?
RATIO 02 EXAMPLES
03 APPLICATIONS
AND PROBLEM
SOLVING
04
You can describe
the topic of the
section here
EVALUATE
TABLE OF CONTENTS

4. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
RATIO
Ratio is a spoken language of
arithmetic. It is a way of
comparing two or more quantities
having the same units-the
quantities may be separate entities
or they may be different parts of a
whole.
 Word form → a is to b
 colon form → a:b
 Fraction form →
𝑎
𝑏

5. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
In Mrs. Dela Rosa`s Grade
6 Math class, there are 22
girls and 19 boys. Compare
the number of girls to the
numbers of boys and vice
versa.
To compare, let us use the
concept of ratio.
If there are 22 girls and 19
boys
We can say that 22 is to 19.
Other ways to express such
comparison is by writing them
using colon 22:19 or writing
them in fraction
𝟐𝟐
𝟏𝟗
.
Therefore, comparing the number
of boys to the numbers of girls
can be expressed as:
19 is to 22 , 19:22 and
𝟏𝟗
𝟐𝟐
BACK

6. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Ratio must be expressed in simplest
form, which means that the term are
relatively prime to each other.
If there are 15 boys and 12 girls
in a class, then the ratio of the
boys to the girls is 15 is to 12
and the ratio of the girls to the
boys is 12 is to 15. In ratio 15 is
to 12, the first term is 15 and the
second term is 12. It may also be
written as 15:12 or
15
12
. Even the
ratio is in fractional form, we say
fifteen is to twelve. Since the
ratio is not yet in its simplest
form, we can express it as:
15
12
=
3 𝑥 5
3 𝑥 4
/
/
=
𝟓
𝟒

7. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
The order in which the ratio is expressed is
important. Therefore, the order of the terms in a ratio
must correspond to the order of objects being compared.
In a ratio, a part can be compared to its whole.
In the preceding example, the ratio of the boys to
the total number of the students is 15 is to 27 and the
ratio of the number of girls to the total number of the
students is 12 is to 27.
If we compare the part to the total, the ratio of
the part to the total has the same meaning as a fraction.
BACK

8. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Ratio of the vowels to consonants:
Word form – 3 is to 5
Colon form 3:5 Fraction form
3
5
EXAMPLES
Vowels – A,E,I = 3
Consonants = M,T,H,C and S = 5
Ratio of the consonants to vowels:
Word form – 5 is to 3
Colon form 5:3 Fraction form
5
3
Compare the number of vowels to consonants and vice versa
in word MATHEMATICS, in word, colon and fraction forms.

9. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
EXAMPLES
Express the ratio of two 25 centavo coins to ₱2.50 coins in colon form.
Simplify.
We need to make sure that the two quantities have the same units. ₱2.50
may consist of ten 25 centavo coins. Thus, we can express the ratio of the two
quantities as 2:10. In simplest form, the ratio of two 25 centavo coins to
₱2.50 coins is 1:5.
Remember: The ratio of two quantities has NO units of measure.

10. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
EXAMPLES
Write ratios equivalent to
3
5
.
3 𝑥 2
5 𝑥 2
=
𝟔
𝟏𝟎
3 𝑥 4
5 𝑥 4
=
𝟏𝟐
𝟐𝟎
3 𝑥 6
5 𝑥 6
=
𝟏𝟖
𝟑𝟎
3 𝑥 9
5 𝑥 9
=
𝟐𝟕
𝟒𝟓

11. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
As we have seen the previous examples, the
quantities being compared in any given ratio have the same
unit or clarification. For example, when we compare the
lengths of two objects measuring 45cm and 1m respectively,
we say that the ratio of the lengths is 45 is to 100 or
9:20. This is because there are 100 cm in 1m. Both terms, 45
and 100, are expressed in the same unit- that is cm.
Another example is when we compare the number of
boys to the number of girls. The terms of ratio are the same
classification- they are both persons. We say, the ratio of
15 boys to 20 girls is 3:4.
There are instances when the terms of the ratio do
not have the same units or classifications.
For example, 60 kilometers to an hour or 60 kilometer per
hour. This special ratio is called rate.

12. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joshua scored 81 points in 9
basketball games. Express in
lowest terms, the average
rate of the number of points
that Joshua scored in every
game.
RATE =
81 𝑝𝑜𝑖𝑛𝑡𝑠
9 𝑔𝑎𝑚𝑒𝑠
=
9 𝑝𝑜𝑖𝑛𝑡𝑠
1 𝑔𝑎𝑚𝑒
= 9 points/game
EXAMPLES

13. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Joana can type 100
words in 5 minutes.
How many words can
she type per minute?
Rate =
100 𝑤𝑜𝑟𝑑𝑠
5 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
=
20 𝑤𝑜𝑟𝑑𝑠
1 𝑚𝑖𝑛𝑢𝑡𝑒
= 20 words/minute
BACK EXAMPLES

14. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
APPLICATIONS
AND PROBLEM
SOLVING

15. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Sheena and Nikka joined the ladies
basketball tryout. Sheena scored
34 points in her two games while
Nikka scored 51 in her three
games. Whose average point per
game is higher?
Understand.
a. What is ask?
Who between Sheena and Nikka has the
highest average point per game.
b. What is given?
• Sheena scored 34 points in two games
• Nikka scored 51 points in 3 games
Plan.
What strategy can we use to
solve the problem? We can
solve for each lady`s
average points per game and
compare them to know who
has the higher average.
SOLVE.
Sheena`s Average Points:
34 𝑝𝑜𝑖𝑛𝑡𝑠
2 𝑔𝑎𝑚𝑒𝑠
=
17 𝑝𝑜𝑖𝑛𝑡𝑠
1 𝑔𝑎𝑚𝑒
= 17𝑝𝑜𝑖𝑛𝑡𝑠/𝑔𝑎𝑚𝑒
Nikka`s Average Points:
51 𝑝𝑜𝑖𝑛𝑡𝑠
3 𝑔𝑎𝑚𝑒𝑠
=
17 𝑝𝑜𝑖𝑛𝑡𝑠
1 𝑔𝑎𝑚𝑒
= 17𝑝𝑜𝑖𝑛𝑡𝑠/𝑔𝑎𝑚𝑒
Therefore, between the two of
them, no one scored higher.
Both Sheena and Nikka`s average
points per game is 17
BACK

16. EVALUATE

17. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Write the ratio for each of the following in three ways.
1.
is to
2. 4 wins to 2 losses in a basketball
3. 2 weeks to 8 days
4. 24 girls to 18 boys
5. 8 melons to 36 mango
answer

18. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Express each rate in lowest terms.
1. The ratio of 36 apples to 18 children
2. The ratio of 48 patients to 6 nurses
3. The ratio of 468 students to 9 classrooms
4. The ratio of 112 persons to 16 tables
5. The ratio of 368 students to 8 buses
answer

19. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Write three ratios equivalent to the given ratio.
1.
𝟑
𝟒
= ___ = ___ = ___
2.
𝟓
𝟖
= ___ = ___ = ___
3.
𝟒
𝟕
= ___ = ___ = ___
4.
𝟐
𝟗
= ___ = ___ = ___
5.
𝟔
𝟕
= ___ = ___ = ___
answer

20. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
CREDITS: This presentation template was created by Slidesgo,
including icons by Flaticon and infographics & images by Freepik
THANKS!
DO YOU HAVE ANY QUESTIONS?
GOOD BYE!

21. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
BACK
1. 8 is to 6 , 8:6 and
8
6
2. 4 is to 2 , 4:2 and
4
2
3. 14 is to 8 , 14:8 and
14
8
4. 24 is to 18 , 24:18 and
24
18
5. 8 is to 36 , 8:36 and
8
36

22. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
BACK
1.
36 apples
18 children
=
18x2
18x1
= 2 apples/child
2.
48 patients
6 nurses
=
6x8
6x1
= 8 patients/nurse
3.
468 students
9 classrooms
=
9x52
9x1
= 52 students/classroom
4.
112 persons
16 tables
=
16x7
16x1
= 7 persons/table
5.
368 students
8 buses
=
8x46
8x1
= 46 students/bus

23. A B C D E F G H I J K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
BACK
1.
𝟑
𝟒
=
𝟔
𝟖
=
𝟗
𝟏𝟐
=
𝟏𝟐
𝟏𝟔
2.
𝟓
𝟖
=
𝟏𝟎
𝟏𝟔
=
𝟏𝟓
𝟐𝟒
=
𝟐𝟎
𝟑𝟐
3.
𝟒
𝟕
=
𝟖
𝟏𝟒
=
𝟏𝟐
𝟐𝟏
=
𝟏𝟔
𝟐𝟖
4.
𝟐
𝟗
=
𝟒
𝟏𝟖
=
𝟔
𝟐𝟕
=
𝟖
𝟑𝟔
5.
𝟔
𝟕
=
𝟏𝟐
𝟏𝟒
=
𝟏𝟖
𝟐𝟏
=
𝟐𝟒
𝟐𝟖