NCERT Solutions for Ganita Prakash (Part 1) Chapter 5 Number Play
Updated on 2026-09-05
About this chapter
Placing '+' and '–' signs between four numbers gives 8 expressions, and all 8 have the same parity. Switching one sign changes the value by 2 × (that number), an even change — so the parity can never change. The same idea, one level up: even numbers split into 4p and 4p + 2. Two of the same type add to a multiple of 4; one of each type never does. 'Multiple of 4' behaves exactly like 'even' does inside the whole numbers. Four divisibility facts are established and used throughout: if a | M and a | N then a | M + N and a | M – N; if a | A then a divides no more than the multiples of A that k allows — precisely, all multiples of A are divisible by a; if A is divisible by k then A is divisible by every factor of k; and if A is divisible by both k and m then A is divisible by LCM(k, m). Every
- .1 Is This a Multiple Of?
- Breaking Even
- Breaking Even / Pairs to Make Fours
- Pairs to Make Fours
- Always, Sometimes, or Never
- Always, Sometimes, or Never / What Remains?
- What Remains?
- .2 Checking Divisibility Quickly
- A Shortcut for Divisibility by 9
- A Shortcut for Divisibility by 3
Exercises
- .1 Is This a Multiple Of? — In-text Questions Page 1125
- .1 Is This a Multiple Of? — In-text Questions Page 1135
- .1 Is This a Multiple Of? — In-text Questions Page 1145
- Breaking Even — In-text Questions Page 115
- Breaking Even / Pairs to Make Fours — In-text Questions Page 116
- Pairs to Make Fours — In-text Questions Page 117
- Always, Sometimes, or Never — In-text Questions Page 118
- Always, Sometimes, or Never — In-text Questions Page 119
- Always, Sometimes, or Never — In-text Questions Page 120
- Always, Sometimes, or Never / What Remains? — In-text Questions Page 121
- What Remains? — In-text Questions Page 122
- .1 Is This a Multiple Of? — Figure it Out Page 1225
- .2 Checking Divisibility Quickly — In-text Questions Page 1235
- A Shortcut for Divisibility by 9 — In-text Questions Page 124
- A Shortcut for Divisibility by 9 — In-text Questions Page 125
- A Shortcut for Divisibility by 9 — Figure it Out Page 126
- A Shortcut for Divisibility by 3 — In-text Questions Page 126
- A Shortcut for Divisibility by 11 — In-text Questions Page 127
- A Shortcut for Divisibility by 11 — In-text Questions Page 128
- A Shortcut for Divisibility by 11 / More on Divisibility Shortcuts — In-text Questions Page 129
- Divisibility Shortcuts for Other Numbers / Digital Roots — In-text Questions Page 130
- Digital Roots — Figure it Out Page 131
- .3 Digits in Disguise — In-text Questions Page 1315
- .3 Digits in Disguise — In-text Questions Page 1325
- .3 Digits in Disguise — Figure it Out Page 1325