1) This document contains notes and examples on ratios from a 9th standard algebra class. It defines ratios, shows how to write ratios in different forms, and provides examples of simplifying and equivalent ratios. 2) Examples are given for writing compound ratios that involve more than two quantities. Practice problems are included for writing and interpreting ratios in word problems. 3) The document concludes with a challenge question involving using a ratio to solve for the height of a rectangle given its perimeter and the ratio of its base to height.

1. 
NIRAJ SHARMA
Roll No: 58
Year : 2012-2013
Subject: ALGEBRA
Standard: IX

2. DO NOW (not later):
 Compare the number of
boys to girls in the class.

3. The number of boys =
The number of girls =
If we compare boys to girls we get
___ boys to _____ girls.
BOY’S GIRL’S

4. RATIO

5. 

6. • For every 4 basketballs there
are 6 footballs.
• The ratio is 4 to 6.

7. 4 to 6
4 : 6
4
6
What are some other ways we can
write the ratio of basketball to
footballs?
First quantity to Second quantity
First quantity : Second quantity
First quantity divided by the second
quantity (as a fraction).
Every ratio can be written in 3 ways:
Careful!!
Order matters in a ratio.
4 to 6
Is NOT the same as
6 to 4

8. 6:8 , 6 to 8, and 6
8
Write the ratio of sandwiches to coke
bottles 3 different ways.
Since a fraction can be simplified, We can simplify the ratio 6/8
to 3/4. The ratio of sandwiches to coke bottles can also be
expressed as 3 : 4 or 3 to 4.
In other words, ratios can be simplified to form
equivalent ratios.

9.  Simplify the following ratios:
 4 to 8
 10 to 8
 8 to 10
EQUIVALENT RATIOS
Step 1 – Write the ratio as a fraction
Step 2 – Simplify the fraction (Find the greatest common factor (GCF) of
both numbers and divide the numerator and denominator by the GCF).
Step 3 – Write the equivalent ratio in the same form as the question
4 = 4 / 4 = 1 = 1 to 2
8 8 / 4 2
GCF = 4

10. Equivalent Ratios can be formed by
multiplying the ratio by any number.
 For example, the ratio 2 : 3 can also be written as
 4 : 6 (multiply original ratio by by 2)
 6 : 9 (multiply original ratio by by 3)
 8 : 12 (multiply original ratio by by 4)
The ratio 2 : 3 can be expressed
as
2x to 3x (multiply the original
ratio by any number x)

11. A ratio that compares more than 2 quantities is called a
compound ratio.
Example:
A cake recipe says the ratio of cups of milk, sugar, and batter are 1:2:4.
This means that there is one cup of milk for every two
cups of sugar and four cups of batter.
COMPOUND RATIOS

12. A bag contains 18 yellow,blue, and red marbles. The ratio of
yellowto blue to red marbles is 4 : 2 : 3.
1) Write the ratio of yellow to blue marbles in
simplest form.
2) What is the ratio of yellow to red marbles?
3) How many yellow marbles are there?
4 : 2 can be simplified to 2 : 1
4 : 3
Yellow : Blue : Red is 4 : 2 : 3
Since any multiple of this is an equivalent ratio, this can also
be written as 4x : 2x: 3x
Let 4x = yellow, 2x = blue , 3x = red
4x + 2x+ 3x = 18
9x = 18
X= 2
Since the question asks for yellow marbles,
there are 4x or 4 (2) = 8 yellow marbles.

13. PRACTICE PROBLEM #
1
(1) You have 100 different shirts. The ratio of blue to
black shirts is 20 .
30
b) Write the ratio in simplest form.
c) Explain what this ratio tells us.
d) How many black shirts do you have?
a) Write the ratio of blue to black shirts different
ways.

14. Practice Word
Problems
(1) Mindy has 72 candy bars. If the
ratio of Mars to Snickers is 8:4,
Find the number of each type of
candy.
(2) Explain what this ratio tell us.

15. Challenge Question
The perimeter of a rectangle is
500 feet. The ratio of the base
and height is 3:2. What is the
measure of the height?

16. 
Value

17. EVALUATION
 Write a ratio of the first number to second
one it’s 44;99
1. 4/9
2. 11/99
3. 2/47
4. 1/9

18. BACK BACK BACK

19. NEXT NEXT NEXT

20. 1.13/16
2.21/12
3.61/31
4.2/1

21. Write a ratio of the second
one to first it’s 52;117
1. 13/17
2. 26/30
3. 9/4
4. 20/13

22. PREPAIR BY
NIRAJ SHARMA
 FROM DIVINE PROVIDEMCE
HIGH SCHOOL
NALLASOPARA, MUMBAI
 IT IS BASED ON 9TH STD AS PER
AS MUMBAI BOAR