Ratio and proportion

Divide a given quantity in a given ratio:
Use this formula for finding the share ,
Individual share = (Individual ratio/Total ratio) * Total Quantity
Example: Divide 20 pens between sheela and Anil in the ratio 3 :2
Given ratio = 3:2
Step 1 : find sum of the ratio
Sum of the ratio = 3+2 = 5
Total pens = 20
Individual share = (Individual ratio/Total ratio) * Total Quantity
Step 2 : Use the above formula
Sheela ` s share = (3/5) * 20 = 12
Anil`s share = (2/5) * 20 = 8


Problems:
Mother wants to divide $180 among her sons Ajay and Anoop in the ratio of their ages. If the age of Ajay is 12 years and Anoop is 15 years. Find how many dollars each of them will get?( find the ratio of their ages)

Ray and Rosi started a business and invested capital in the ratio 2 : 3. after one year total profit is divided in the ratio of their invested capital, find the share of each?

Present age of father is 42 years and his son is 14 years. Find the ratio of:
a. Present age of father to the Present age of son
b. age of father to the age of son , when son was 12 years old
c. age of father to the age of son , when father was 30 years old

Divide 60 books in the ratio of 2:3 between John and Kennedy.


Proportion:
When two ration are equal,we can say that thay are in proportional.The symbol is :: ,
a : b :: c : d this means a,b,c and d are in proportional. the condition for proportionality is

Product of means = Product of extremes

Example: check whether 6 , 16,39 and 104 are in proportional or not.
6 : 16 :: 39 : 104 check for this condition Product of means = Product of extremes
16 * 39 =6 * 104
624 = 624 so they are in proportional.
Practice:
check whether 8 , 12 18 and 24 are in proportional or not.
check whether 27, 36,36 and 48 are in proportional or not.

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)