Ratio

We denote ratio using symbol “ : ’’.Ratio can exist only between two quantities of same kind.Mathematically it can appear as 3/1 or as 3:1. In words, it should be written out as the ratio of three to one.Please remember that ratios compare parts to parts, rather than parts to a whole .Ratio does not have any unit.A ratio is always expressed in its lowest terms.

**Can we find the ratio between 6 km and 8 hours? why?
No, because both are in different quantities.**

The value of ratio unchanged ,if both of its terms are multiplied or divided by the same non zero number.
Ex: 2: 5 = 4: 10.
Example :
Find the Ratio of $150 to $85.
150/85 (divide numerator and denominator by 5)
30/17(which are in lowest terms)
30 : 17

practice:
Cost of pen is $ 2,and cost of pencil box is $6. how many times the cost
of pencil box is the cost of a pen
Find the Ratio of $50 to $75
To find the ratio of 2 m 25 cm to 75 cm, we first change 2 m 25 cm into cm, which equals 225 cm. Now, we have to find 225 cm to 75 cm
Find the ratio of 2 hours 30 minutes to 55 minutes.
Find the ratio of 750g ; 3 kg

Answers:
3 times
2:3
3:1
30:11
1:40
Can we find the ratio between $45 and 78 books? why?

Problems:

For every 50 Americans who buy books online, 15 buy books at bookstores. What’s the ratio of those who buy books online to those who buy books at bookstores?

Out of 30 students in a class ,6 like football,12 like cricket and the remaining tennis. find the ratio of:(Hint : find number of students who like tennis)
1 . Number of students liking football to number of students liking tennis
2. Number of students liking cricket to total number of students.

In a college out of 4320 students,2300 are girls. Find the ratio of,
1. number of girls to the total number of students
2. number of boys to number of girls
3. number of boys to the total number of students( Hint:first find number of boys)

Comparison of ratios :
If two or more ratios are given, express the each ratio in decimal form then compare the decimals.
Example: which is greater 4 : 5 or 19 : 25
4:5 = 4/5 = 0.80
19 : 25 = 19/25 = 0.76 clearly 0.80 > 0.76
so 4 : 5 > 19 :25

Practice: which is greater
4: 9 or 3: 7
5:14 or 4:11
7:10 or 5:7
Arrange the following ratios in ascending order,
(3 : 4) ,( 5:8) ,(7:9) and (13 : 15)
(5 :9) ,( 2:3) ,(4:7) and (11 : 7)
Arrange the following ratios in descending order,
(3 : 10) ,( 1:2) ,(5:11) (4:13)and (7 : 15)
(6 :5) ,( 8:9) ,(5:9) and (13 : 6)