 # NCERT Maths Solutions Class 10 Real Numbers

## NCERT Maths Solutions Class 10 Real Numbers

In this article, we will discuss the Class 10 Maths Chapter 1 Real Numbers

Maths Class 10 live classes are available.

In  Class 9 Maths, we studied the real numbers, especially about irrational numbers. Real numbers are the numbers that can be easily plotted on a number line.

Euclid’s Division Algorithm

For any two given positive integers a and b there exist unique whole numbers q and r such that

A=bq +r, where 0<r<b

Here a is called dividend is called a divisor, q is called a quotient and r as a remainder.

Dividend = (divisor*quotient) +remainder

Eg: – If we divide 117 by 14 then we will get 8 as quotient and 5 as remainder.

Dividend =117, divisor=14, quotient=8 and remainder=5

117= (14*8) +5

117=112+5

Few Solved examples for Maths Class 10th students

NCERT Maths Solutions Class 10

Eg 1-A number, when divided by 53, gives 34 as quotient and 21 as remainder. Find the number.

Soln-Using Euclid’s division algorithm we have

Dividend= (divisor*quotient) +remainder

= (53*34) +21

= (1802+21)

=1823

NCERT Maths Solutions Class 10

Eg 2 – Show that one and only one out of n, (n+1) and (n+2) is divisible by 3, where n is any positive integer?

Sol – let’s assume that on dividing n by 3, q will be the quotient and r will be the remainder.

N=3q+r where r=0, 1 or 2

N=3q or n =3q+1 or n 3q+2

Case 1 – if n=3q, then n is clearly divisible by 3.

Case 2 – if n= (3q+1), then (n+2)=3q+3=3(q+1),which is clearly divisible by 3,hence (n+2) is divisible by 3

Case 3 – if n= (3q+2), then (n+1)=(3q+3)=3(q+1),which is clearly divisible by 3,hence (n+1) is divisible by 3

Hence only one out of 3 is divisible by 3.

For any two numbers a and b, we always have

(A*B)=product of their HCF and LCM

The above result is not true in case of three or more numbers.

Eg:-The HCF of two numbers is 27 and their LCM is 162. If one of the numbers is 54, find the other.

Soln-For two number a and b,we know that

(a*b)=HCF of a,b* LCM of a,b

A=54,HCF=27 and LCM =162

54*b=27*162

B=27*162/54=81

For complete chapter explanation and questions for practice, register with us, click Online Classes for Maths Class 10 for more details.

Sample papers, practice zone, NCERT Solutions for all subjects of Class 10th are available. Takshila Learning offers offline animated classes as well as online live classes for school courses. Customised packages are available as per students requirement. Kindly visit our website and explore options.
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