3. In geometry, two objects are said to be similar if they have the same shape,
even if they are in different sizes. An object similar to another can be obtained by
uniformly stretching or reducing the same amount on all directions.
.
In geometry, two objects are said
to be similar if they have the same
shape, even if they are in different
sizes. An object similar to another can
be obtained by uniformly stretching
or reducing the same amount on all
directions.
4. In the world of
similarities, it is very
important for you to
study the concept of
ratio and proportion.
5. Ratio is a way to
compare two or more
quantities. It says how
much of one thing there
is compared to another
thing.
6. 𝑎
𝑏 a to b a:b
A ratio can be written in different ways -
as a fraction, using the word “to”, or using a
colon “:”. The ratio of a to b can be written as
follows:
7. 20
35
20 to 35 20:35
Another example, “Out of 35 survivors of the
Pulmonary Disease in a certain barangay in
Tanauan City, 20 of them are males.”. The ratio of
the number of males to the total number of survivors
in that barangay can be written as follows:
8. Ratio of male survivors
to female survivors
Ratio of female survivors
to total survivors
.
Ratio of total survivors to
male survivors
20
15
or
4
3
“Out of 35 survivors of the Pulmonary Disease
in a certain barangay in Pasig City, 20 of them
are males”,
15
35
or
3
7
35
20
or
7
4
9. A proportion is the equality of two
ratios. It is an equation in which there are
ratios on both sides and can be written in
two ways – as two equal fractions or use
of colons.
10. 𝑎
𝑏
=
𝑐
𝑑
a: b = c:d
The proportions above can be read as “a is to b as c
is to d” or “a is to b is equal to c is to d”.
In the proportion a : b = c : d, the outer terms a
and d are called extreme while the inner terms b and c
are called means.
11. In the proportion a : b = c : d, the outer terms a and d are called extreme while the inner terms b and c are called means.
The proportions above can be read as
“a is to b as c is to d” or “a is to b is equal to c is
to d”.
In the proportion a : b = c : d, the outer
terms a and d are called extreme while the
inner terms b and c are called means.
12. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent
rutrum maximus mauris sed sodales. Ut rhoncus lacinia nisi eu
tempus. Proin justo eros, mollis laoreet massa non, tincidunt
pharetra leo. Cras facilisis leo non nibh congue volutpat.
13.
14. Solution 2
“product of extremes = product of
means”
Solution 1
“cross
multiplication”
Solve for x in
𝑥
5
=
12
15
Illustrative examples:
Solution 2
“product of
extremes = product
of means”
15. Solution 2
“product of extremes = product of
means”
Solution 1
“cross
multiplication”
Solve for x in
𝑥−3
7
=
27
21
Illustrative examples:
Solution 2
“product of
extremes = product
of means”
16. Solution 2
“product of extremes = product of
means”
Solution 1
“cross
multiplication”
Solve for x in (x+5): (x+3)= 2:6
Illustrative examples:
Solution 2
“product of
extremes = product
of means”
17. Direction: Study the given situation and write
the required ratio:
Miss Lorna Babol conducted a survey on
the availability of students’ gadgets and internet
connections to her Mathematics Class in
preparation for their Mathematics activity at
home. She found out 18 of them have gadgets
with internet connection, 12 have gadgets but
with no internet connection and 10 of them do
not have gadget nor internet connection.
18. Find the ratio of the following.
1. ratio of students with gadgets with internet connection to the
total number of students
2. ratio of students with no gadgets and with no internet
connection to the total number of students
3. ratio of students with gadgets to the total number of students
4. ratio of students with gadgets to the students with no gadgets
5. ratio of students with internet connection to students with no
internet connection.
