NCERT Solutions Class 8 Maths Ganita Prakash Chapter 5 — Number Play#

Chapter 5 of Ganita Prakash Part I uses algebra to reason about numbers: writing numbers with a given remainder as expressions like $5k + 3$, explaining the divisibility shortcuts for 2, 3, 4, 5, 8, 9, 10 and 11, the digital root of a number, and solving cryptarithms, where letters stand for digits.

Figure it Out — Page 122 Figure it Out — Page 126 Figure it Out — Page 131 Figure it Out — Page 132

Exercises#

Figure it Out — Page 122 — Consecutive numbers, always/sometimes/never true, remainders, the pebble riddle (8 questions)
Figure it Out — Page 126 — Divisibility by 9 (4 questions)
Figure it Out — Page 131 — Digital roots (4 questions)
Figure it Out — Page 132 — Divisibility puzzles, missing digits, consecutive numbers, cryptarithms (16 questions)

What you will learn#

Numbers that leave remainder $r$ when divided by $n$ have the form $nk + r$.
If $a$ divides $m$ and $n$, then $a$ divides $m + n$ and $m - n$.
A number is divisible by 9 (or 3) when the sum of its digits is.
A number is divisible by 11 when the alternating sum of its digits is 0 or a multiple of 11.

Key formulas and results#

Any number $\ldots dcba = \ldots + 1000d + 100c + 10b + a$.
Every power of 10 is 1 more than a multiple of 9, and alternately 1 more or 1 less than a multiple of 11.
The digital root of a number (adding its digits again and again) equals its remainder when divided by 9, except that multiples of 9 have digital root 9.

Read and revise#

NCERT Class 8 Maths Chapter 5 (PDF) — the Ganita Prakash Part I chapter itself.
All Class 8 Maths chapters from Ganita Prakash Part I and Part II.

Frequently asked questions#

How many questions are in Class 8 Maths Chapter 5?

Four Figure it Out sets — page 122 (8 questions), page 126 (4 questions), page 131 (4 questions) and pages 132–134 (16 questions). Every question is solved step by step here.

What is the smallest number that leaves remainders 2, 3 and 4 when divided by 3, 4 and 5?

Each remainder is one less than its divisor, so the number is one less than a common multiple of 3, 4 and 5. Their LCM is 60, so the smallest such number is $60 - 1 = 59$.

5. Number Play