Monday, 1 October 2018

R1 Ratio (I)

RATIO
(1) is how much of one thing there is compared to another thing
            
            There are 3 blue triangles to 2 red triangles

(2) comparison between two different things
         
            To compare the quantity of 2 or more things
            There are 3 ovals to 1 star

(3) comparison of two or more quantities
       
There are 2 squares to 1 triangle and 2 squares to 3 circles
There are 1 triangle to 3 circles

Symbol for ratio
It is represented by TWO or more numbers with a colon:
                                    Number1: Number2
How to use ratio to compare?
     
                1          :          2
There is 1 square for every 2 circles.
The ratio of square to circle is 1 to 2
                                      
                                                                   1     :     2
There are 2 circles for every square.
The ratio of circles to square is 2 to 1.

The position of the numbers of the ratio must relate to the items being compared.
The ratio’s position of the numbers is important -> 1:2 is not 2:1
Ratio is comparison of numbers, there is no unit of measure.

Comparing more than 2 Ratios
There are 1 square, 2 circles and 4 triangles in the box.
        
                               1    :   2  :   4
The ratio of number of square to number of circles to number of triangles is 1:2:4.

Equivalent Ratios
Example:
        
Example
What is the missing number in these equivalent ratios?
2 : 5 =  12 :  ____
Method
Step1:  Divide the bigger number with the smaller number
            12 ÷ 2 = 6
Step2: Multiply the equivalent ratio’s number with answer from step1.
      
Step3: Answer the question
The missing number is 30.

Ratio in its simplest form
What is the ratio 5: 15 in its simplest form?
5 is the common factor of 5 and 15.

Method1
Step1: Divide the number in the ratio
            5/15 = 1/3
Answer: 1 : 3
The ratio 5 : 15 in its simplest form is 1: 3.

Example
What is the ratio of 55 min to 30 min in its simplest form?
Ratio  55 : 30
55/30 = 11/6
      →11 : 6
Method2:
Lowest Common Multiple(LCM) Method
Example:
What is the ratio of 1hour 15mins to 45 min in its simplest form?
Change 1 hour 20 min to mins for comparison
1 hour = 60 min, 1 hour 20 min = 80 mins

Method
Step1: Draw the LCM grid and fil in the value.
The ratio 75 : 45 in its simplest form is   5 :  3

Practice
What is the ratio 10 : 6 : 16 in its simplest form?
Answer : 5:3:8

Ratio and Fractions
A fraction is a part of a whole.
             Whole - 1                      Part - ½

In ratio, the larger number is the whole and the small number is the ‘Part’
                              RATIO                                                    FRACTION      
          A ratio is a comparison                              a fraction is the part of a whole

Ratio, Fractions, As a whole(Total)
There are 1 square and 2 circles in the box
            

Total numbers of shapes in the box is 3 (1 square and 2 circles)
            Ratio of number of square to circle is 1 : 2
            Ratio of number of circle to square is 2: 1
            Ratio of number of square to the total numbers of shapes 1 : 3
            Ratio of number of circle to the total number of shapes 2 : 3

            There are twice as many circles as square
            There are ½ as many squares as circles
            1/3 of the shapes in the box are square
            2/3 of the shapes in the box are circle
 The ratio of the number of square to circles to shapes in box is 1:2:3
          ~~~~ END ~~~~ :)