Lesson 1 introduces ratios and proportions. A ratio compares two or more quantities and can be written in fraction or colon form. Ratios can be simplified by dividing both quantities by their greatest common factor. Two ratios are equivalent if they can be expressed as the same simple ratio. A proportion is a statement of equality between two ratios. It involves setting the product of the means equal to the product of the extremes, where the extremes are the first and last terms and the means are the second and third terms. To solve a proportion, the ratios are set up as fractions, cross-multiplied, and then solved.

1. Lesson 1: Ratio and
Proportion
Prepared by: Mr. Alphie Zarriz

2. What is “ratio”?
- it is the comparison and
relationship of two or more
quantities.
Ratio can be written in fraction form and colon form.
1. The colon ( : ) and the fraction bar ( - ) are the
symbols used to separate the two terms being
compared.
Ex. Ratio of stars to squares.
The ratio of stars to square is 9 is to 6.
The ratio can be written as 9:6 or
9
6

3. 2. Ratio can be simplified by dividing
the quantities by their GCF.
Ex.
The ratio of heart to circle is 8:6.
The GCF of 8 and 6 is 2, so
8
6
÷
2
2
=
4
3
𝑜𝑟 4: 3
3. Two ratios are equivalent if both of
them can be expressed into the same
simple ratio.
32:80 34:85
=
32
80
÷
16
16
=
34
85
÷
17
17
=
2
5
𝑜𝑟 2: 5 =
2
5
𝑜𝑟 2: 5

4. What is proportion?
- It is a statement of equality
between two ratios.
- In a proportion, the product of the
means is equal to the product of the
extremes.
- An extreme is the first or the last
terms of a proportion, while means
is the second and the third terms in
a proportion.
Example: 1:3 = n:9 (“n” means unknown.)
extremes
means
1
3
=
𝑛
9
To solve for the “n”
• Make fraction form
• Cross multiply
3𝑛
3
=
9
3
3𝑛
3
=
9
3
• Cancel and divide
n = 3 Therefore, 1:3 = 3:9