The document explains the concepts of ratio and proportion, defining a ratio as the comparison of two quantities and proportion as the equality of two ratios. It includes formulas for expressing ratios and proportions, as well as examples demonstrating how to determine if two ratios are in proportion. Additionally, it provides practical illustrations involving students' preferences and recipe measurements related to ratios.

1. RATIO
and
PROPORTION
-
Josephine D. Llanas BSED Math 4

2. Ratio is the comparison of two quantities which is
obtained by dividing the first quantity by the other.
The ratio formula for two numbers, a and b is
expressed as a:b or a/b.
The formula for ratio is expressed as a:b ⇒ a/b,
where,
a = the first term or antecedent.
b = the second term or consequent.

3. Example:
3:9 also represented as 3/9, where;
3 is the antecedent and
9 is the consequent
If we divide each term of the ratio by
the same number (non-zero), it doesn’t
affect the ratio.

4. Proportion refers to the equality of two
ratios. Two equivalent ratios are always in
proportion. Proportions are denoted by the
symbol (: :).
Proportion formula:
a/b = c/d or a:b :: c:d where,
b and c = mean or mean terms
a and d = extremes or extreme terms

5. Example:
3:5 :: 4:8 or 3/5 = 4/8
3 and 8 = extremes
5 and 4 = means
Note: The ratio value does not affect
when the same non-zero number is
multiplied or divided on each term.

6. Example 1:
Find out if the ratios 6:8 and 24:32 are in
proportion.
Solution:
The given ratios are 6:8 and 24:32.
*6:8= 3/4 = 0.75
*24:32 = 3/4= 0.75.
Here, both the ratios are equal. Therefore, 6:8 and
24:32 are in proportion.

7. Find out if the ratios 3:6 and 8:16 are
in proportion.
Solution:
*3:6 = ½ = 0.5
*8:16 = ½ = 0.5

8. There are 30 students in a class. The
number of students who like Math and
the ones who like Science is expressed
in the ratio 2:3. Find the number of
students who like Math and the ones
who like Science.

9. Solution:
*Total number of students = 30
*Number of students who like Math = 2x
*Number of students who like Science = 3x
We can say that 2x + 3x = 30 ⇒ 5x = 30
5x = 30
5 5
x = 6
*Substituting the value of x = 6
We can get the number of students who like;
Math = 2x = 2 x 6 = 12
Science = 3x = 3 x 6 = 18
*Therefore, 12 students like Math, and 18 Students like Science.

10. A recipe calls for 3 eggs for every 8 cups of
flour. A head chef will use 32 cups of flour,
so how many eggs must he have?
3: 8
x : 32
8x= 96
x=12

11. TRUE OR FALSE:
1. Two ratios are said to be in
proportion only if they are equivalent.
TRUE
- Two ratios are said to be in
proportion only if they are equivalent.

12. TRUE OR FALSE:
2. In the ratio 1:2, 1 is the consequent,
and 2 is the antecedent.
FALSE
- In the ratio 1:2, 1 is the antecedent,
and 2 is the consequent.