Page 147 - Start Up Mathematics_6

5 – a 3
⇒ = For a laugh 
10 10
⇒ 5 – a = 3 ⇒ a = 2 Three men travelling in a hot-air balloon,
get lost. They notice a man underneath,
2 one of them leans over and asks, “where
Hence, is the required answer. are we?” 10 minutes later, they hear an
10 echoing voice: “You’re in a balloon!!”
(b) To add like fractions, the One of the men remarks, “That must
denominator should be same. have been a mathematician.” Confused,
the other man ask, “Why do you think
b so?” He replies, “For three reasons: The
So, let the missing fraction be .
13 answer came after a long time, it was
b 7 11 correct and the answer was absolutely
Now, + = useless.”
13 13 13

b + 7 11
⇒ = ⇒ b + 7 = 11 ⇒ b = 4
13 13
4
Hence is the required answer.
13
3
Example 33: Shahrukh was able to solve of the questions given for maths homework. What
7
fraction of the homework was left incomplete?
3
Solution: Shahrukh solved of the questions.
7 3 7 3 4
Fraction of homework left incomplete = 1 – = – =
7 7 7 7
Case 2: Addition and subtraction of unlike fractions
A stepwise method to add or subtract unlike fractions is given below:

Step 1: Find the LCM of the denominators of the given fractions.
Step 2: Convert the given fractions into equivalent fractions so that they have the same
denominators.

Step 3: Now add or subtract the like fractions so obtained, as we did in Case 1.
Example 34: Solve:
2 5 4 2 5 1 2 3 1
(a) + (b) + (c) – (d) + –
3 7 5 3 6 3 3 4 2
2 5
Solution: (a) +
3 7
LCM of 3 and 7 = 21
2 5 2 7 5 3 14 15 29
∴ + = × + × = + =
3 7 3 7 7 3 21 21 21
4 2
(b) +
5 3
LCM of 5 and 3 = 15
4 2 4 3 2 5 12 10 12 + 10 22
∴ + = × + × = + = =
5 3 5 3 3 5 15 15 15 15

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