NCERT Solutions Class 9 Maths Chapter 11 The World of Algorithms on Padhaiwise

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 11 The World of Algorithms Exercise Set 11.1

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 11 — Exercise Set 11.1#

The book’s algorithm to add two numbers:

Write the numbers one below the other in the Indian base-ten place-value system so that the digits are aligned from right to left.
Add the rightmost digits. If the sum is less than 10, write it below and set carry to 0; otherwise write the units digit below and set carry to 1.
Move to the next column on the left. Add the two digits and the current carry. (Same rule for writing the sum and setting the carry.)
Repeat Step 3 until there are no more digits on the left.
If the carry is 1, write 1 to the left of the bottom row.

1. Add two 4-digit numbers using the steps we have written down. Make sure you follow the steps precisely; do not perform any action that is not explicitly mentioned. Are you able to obtain the correct result? #

Solution

Take $4738 + 5964$.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 11 The World of Algorithms Exercise Set 11.2

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 11 — Exercise Set 11.2#

An algorithm is written as numbered steps, using names for the values we keep track of (such as list-of-divisors) and simple actions we already know how to do (such as checking whether one number divides another).

1. Suppose List 1 and List 2 are two lists of numbers in increasing order. #

(i) Write an algorithm to find elements in List 1 that are not present in List 2.

Algorithm only-in-1

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 11 The World of Algorithms Exercise Set 11.3

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 11 — Exercise Set 11.3#

Recall the two versions of the gcd algorithm in this section:

Original: list the divisors of $m$ and of $n$ in increasing order, list their common divisors, and report the rightmost one.
Last version: start with most-recent-common-divisor = 1, scan $k$ from 2 up to $\min(m, n)$, and update it whenever $k$ divides both numbers.

1. How would our original algorithm change if we computed the divisors of n by examining the numbers from 1 to n in reverse order, from n down to 1? #

Solution

Checking from $n$ down to 1, the divisors are added to the list in decreasing order, for example divisors(18) = [18, 9, 6, 3, 2, 1].

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 11 The World of Algorithms End-of-Chapter Exercises

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 11 — End-of-Chapter Exercises#

Improved Euclid (Āryabhaṭa’s division) algorithm for gcd(m, n):

If $m < n$, reverse the numbers and compute gcd(n, m).

If $n = 0$, report the answer as $m$.

Otherwise, reduce the problem to computing gcd(n, m mod n), where m mod n is the remainder when $m$ is divided by $n$.

1. Compute the following using the improved version of Euclid’s algorithm. #

Each row divides the larger number by the smaller; the next row uses the divisor and the remainder.