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Ratio and Proportion

RATIOS

are comparisons made between two sets of numbers.

 

 


Example:

 

 

There are eight girls and seven boys in a class.

 

The ratio of girls to boys is 8 to 7.

 

 

 



THERE ARE 3 WAYS TO WRITE RATIOS.



1. Write the ratio using the word "to" between the two numbers being compared.

Example

Ratio

There are 11 girls and 6 boys in my class.
What is the ratio of girls to boys?

11 girls to 6 boys
11 to 6

2. Write a ratio using a colon between the two numbers being compared.

Example

Ratio

There are 5 apples and 4 oranges in the basket.
What is the ratio of apples to oranges?

5 apples to 4 oranges.
5:4

3. Write a ratio as a fraction.

Example

Ratio

Jerick and Brandon were playing basketball. Brandon scored 5 baskets and Jerick scored 6 baskets.
What was the ratio of baskets Jerick scored to the baskets Brandon scored?

6 baskets to 5 baskets
65\frac{6}{5}6/5


Example: 
Direction: Write the ratio in three different ways.

There are 13 boys and 27 girls in sixth grade.
Find the ratio of boys to the girls in sixth grade.


Answer:
3 WAYS TO WRITE RATIOS

1

2

3

13 to 27

13:27

13/27



PROPORTIONS
are two ratios of equal value





DETERMINING TRUE PROPORTIONS:

 


To determine a proportion true, cross multiply.

 

If the cross products are equal, then it is a true proportion.



The cross products were equal, therefore 4/

5 a

nd 20/25 makes a true proportion.



Practice:

Direction: Solve to see if each problem is a true proportion.



1.     47=1221

    

    
12×7 = 4×21
84 = 84
= true



2.     47=1221

    

    
12×7 = 4×21
84 = 84
= true






SOLVING THE PROPORTIONS:

When solving proportions, follow these rules:

 

 


Problem:



1. Cross multiply.

 

2. Divide both sides by the number connected to the variable.

 

3. Check the answer to see if it makes a true proportion.

 




Sample Problem:

524 = n7\dfrac{52}{4}\ =\ \dfrac{n}{7}    Cross multiply

4 × n = 52×74\ \times \ n\ =\ 52\times 7

4n = 3644n\ =\ 364
Since 4 is connected to the variable.

4n4 = 3644\dfrac{4n}{4}\ =\ \dfrac{364}{4}  Divide both sides by 4.

n=91n=91n" on one side.