Page 214 - Ganit Kaushal

Ex 12. What is wrong with the following additions?
1 2 1
(a) 8 = 8 4 (b) 6 2
2
1 1 1
+ 4 = 4 + 4
4 4 4
3 2 1
= 12 = 8 = 8
8 6 3

Sol. (a) In the given sum, the denominators are also added, which is wrong. The correct sum would be:
2 1  2 1 21 3 3
+
+ )
8 + 4 = ( 84 +  +  = 12 + = 12 + = 12
4 4  4 4 4 4 4
(b) In the given sum, the numerators and denominators have been added, which is wrong.
Also, the sum of the wholes is wrong. The correct sum would be:
1 1  1 1 21 3
+
6 + 4 = ( 6 + )  +  = 10 + = 10
4 +
2 4  2 4 4 4
3 4
Ex 13. The fish caught by Neetu weighs3 kg, and the fish caught by Narendra weighs 3 kg. Whose fish
4 5
weighs more and by how much? Give your answer in grams.
×
3 15 15 5 75
Sol. Weight of Neetu’s fish = 3 = = = kg
×
4 4 45 20
4 19 19 4 76
×
Weight of Narendra’s fish = 3 = = = kg
×
5 5 54 20
−
76 75 76 75 1
Now, − = = kg
20 20 20 20
∴ Narendra’s fish weighs more than Neetu’s fish by 1 kg = 1 × 1000 g = 50 g.
20 20
Ex 14. Assertion (A): Out of three hours, Dhruv spends 20 minutes studying. We can say that he spends
1 th of the time studying.
6
Reason (R): 1 and 5 are like fractions.
6 6
Choose the correct option out of the choices given below for each question:
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.

(d) A is false but R is true.
Sol. (d) Total time = 3 hours = 60 × 3 = 180 minutes
Time spent studying = 20 minutes
20 1
Therefore, fraction of time spent studying = 180 = 9 .
Thus (A) is false.
We know that like fractions have the same denominators.
Thus, (R) is true.

Thus, (A) is false, but (R) is true.

212 Mathematics-6