Page 283 - Ganit Kaushal

Subjective/Competency Based Questions

Ex 12. Cancel the zero pairs in the following two sets of tokens. What is the corresponding addition statement
in each case? (NCERT)
(a) (b)

Sol. (a) (b)

The corresponding addition statement is The corresponding addition statement is
(+3) + (–5) = –2. (+6) + (−3) = +3.

Ex 13. Find the value of the following:
(a) (–20) + (–13) (b) 23 – (–12)
Sol. (a) (–20) + (– 13) = – 20 – 13 = – 33 (Using Brahmagupta’s rule, A2)
(b) 23 – (–12) = 23 + 12 = 35 (Using Brahmagupta’s rule, S3)

Ex 14. The sum of two positive integers is always positive but a (positive integer) – (positive integer) can be
positive or negative. What about: (NCERT)
(a) (positive) – (negative) (b) (positive) + (negative)
(c) (negative) + (negative) (d) (negative) – (negative)

(e) (negative) – (positive) (f) (negative) + (positive)
Sol. (a) (positive) – (negative) is always positive. (b) (positive) + (negative) can be positive or negative.
(c) (negative) + (negative) is always negative. (d) (negative) – (negative) can be positive or negative.
(e) (negative) – (positive) is always negative. (f) (negative) + (positive) can be positive or negative.

Ex 15. This string has a total of 100 tokens arranged in a particular pattern. What is the value of the string?
(NCERT)
.....

Sol. +20 ( After cancelling zero pairs, every group of 5 tokens has the values (+3) + (–2) = +1 i.e., 1 plus
token and we have, 100 ÷ 5 = 20 groups).
Ex 16. Complete the following sequences: (NCERT)

(a) (– 40), (– 34), (– 28), (– 22), _____, _____, _____
(b) 3, 4, 2, 5, 1, 6, 0, 7, _____, _____, _____
(c) _____, _____, 12, 6, 1, (– 3), (– 6), _____, _____, _____

Sol. (a) –16, –10, – 4. (Add 6 to each term to get the next term.)
(b) –1, 8, – 2. (Add 1, −2, 3, −4, 5, −6, 7, −8, 9, –10 and so on to get the next terms.)
(c) 27, 19, 12, 6, 1, (–3), (– 6), − 8, − 9, − 9 (Subtract 8, 7, 6, 5, 4, 3, 2, 1, 0 in order to get the next term.)
Ex 17. There are two dice whose faces have these numbers: –1, 2, –3, 4, –5, 6. The smallest possible sum upon
rolling these dice is – 10 = (–5) + (–5) and the largest possible sum is 12 = (6) + (6). Some numbers
between (–10) and (+12) are not possible to get by adding numbers on these two dice.

Find those numbers. (NCERT)

The Other Side of Zero 281