NIRAJ SHARMARoll No: 58

Year : 2012-2013

Subject: ALGEBRA

Standard: IX

DO NOW (not later): Compare the number of

boys to girls in the class.

The number of boys =

The number of girls =

If we compare boys to girls we get

___ boys to _____ girls.

BOY’S GIRL’S

What do we call a comparison between two or more quantities?

RATIO

AIM:

A ratio shows the relative sizes of two or more values.

How many basketballs to footballs are there?

• For every 4 basketballs there are 6 footballs.

• The ratio is 4 to 6.

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

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.

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 2GCF = 4

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)

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

A bag contains 18 yellow, blue, and red marbles. The

ratio of yellow to 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 : 3Yellow : 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.

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.

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.

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?

Value

Save The Girl Child India to save this world - YouTube.flv

EVALUATION

Write a ratio of the first number to second one it’s 44;99

1. 4/92. 11/993. 2/474. 1/9

BACK

BACK

BACK

NEXT NEXT NEXT

Write a ratio of the first number to second one it’s 63;36

1.13/162.21/123.61/314.2/1

Write a ratio of the second one to first it’s 52;117

1. 13/172. 26/303. 9/44. 20/13

PREPAIR BY NIRAJ SHARMA FROM DIVINE PROVIDEMCE

HIGH SCHOOL NALLASOPARA, MUMBAI

IT IS BASED ON 9TH STD AS PER AS MUMBAI BOAR