Question 1 :
Write the ratio 12 : 16 in its simplest form.
Question 2 :
Write the ratio 0.5 ; 1.5 in its simplest form.
Question 3 :
Is the order of the terms in a ratio important? Explain.
Question 4 :
Is there ratio between number of students in a class and the salary of a teacher?
Question 5 :
Is there ratio between the weight of one child and the age of another child?
Question 6 :
Is there ratio between 2 hours and 50 minutes ?
Question 7 :
Find the ratio between 150 grams and 2 kilograms.
Question 8 :
Find the ratio between 25 minutes and 45 seconds.
1. Answer :
In the ratio 12 : 16, both the first term 12 and second term 16 are multiples of 4. So, divide both the terms of the ratio by 4 to get its simplest form.
12 : 16 = (12 ÷ 4) : (16 ÷ 4)
= 3 : 4
2. Answer :
In both the terms of the 0.5 : 1.5, we have one digit after the decimal point.
So, multiply both the terms of the ratio by 10 to get rid of the decimal point.
0.5 : 1.5 = (0.5 x 10) : (1.5 x 10)
= 5 : 15
In the ratio 5 : 15, both the first term 5 and second term 15 are multiples of 5. So, divide both the terms of the ratio by 5 to get its simplest form.
= (5 ÷ 5) : (15 ÷ 5)
= 1 : 3
3. Answer :
Yes, the order of the terms in a ratio is important.
Explanation :
Consider a 10 liters of liquid mixture, there are 7 liters of milk and 3 liters of water.
So, ratio between milk and water in this liquid mixture of 10 liters is
M : W = 7 : 3
In the ratio 7 : 3, if we change the order, that is, we write 7 : 3 as 3 : 7, what will happen ?
M : W = 3 : 7
Now, when people look at the above ratio 3 : 7, they will understand that there are 3 liters of milk and 7 liters of water.
When we change the order of the terms in a ratio, the meaning is completely changed.
So, the order of the terms in a ratio is important.
3 : 7 is not same as 7 : 3.
7 : 3 ≠ 3 : 7
4. Answer :
Ratio exists only between quantities of the same kind.
Number of students in a class and the salary of a teacher are not of same kind, they are different kinds and we can not compare them.
So, there is no ratio between number of students in a class and the salary of a teacher.
5. Answer :
Ratio exists only between quantities of the same kind.
The weight of one child and the age of another child are not of same kind, there are different kinds and we can not compare them.
So, there is no ratio between the weight of one child and the age of another child.
6. Answer :
Both 2 hours and 50 minutes are time durations, so they are of same kind.
Even though they are of same kind, the units are different (hours and minutes).
We can convert both 2 hours and 50 minutes to the same unit (hours or minutes) and find ratio between them.
So, there is a ratio between 2 hours and 50 minutes.
7. Answer :
Both 150 grams and 2 kilograms are weights, so they are of same kind. But, the two quantities are in different units grams and kilograms.
Convert both of them to the same unit and do ratio between them.
We can convert kilograms to grams multiplying by 1000, because 1 kilogram = 1000 grams.
2 kilograms = 2 x 1000 grams
= 2000 grams
Ratio between 150 grams and 2 kilograms :
= 150 : 2000
= (150 ÷ 50) : (2000 ÷ 50)
= 3 : 40
8. Answer :
Both 25 minutes and 45 second are time duration, so they are of same kind. But, the two quantities are in different units minutes and seconds.
Convert both of them to the same unit and do ratio between them.
We can convert minutes to seconds multiplying by 60, because 1 minute = 60 seconds.
25 minutes = 25 x 60 seconds
= 1500 seconds
Ratio between 25 minutes and 45 seconds :
= 1500 : 45
= (1500 ÷ 15) : (45 ÷ 15)
= 100 : 3
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