In-Text Questions Try These (Textbook Page No. 1,3,6) - Chapter 1 Numbers Term 2 6th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

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On April 24, 2024, 11:35 AM

In-Text Questions : Chapter 1 Numbers Term 2 Class 6th std Maths Guide Samacheer Kalvi Solutions
Try These (Textbook Page No. 1)
Question $1 .$
(i) Observe and complete:
$\begin{aligned}
&1+3=? \\
&5+11=? \\
&21+47=? \\
\end{aligned}$
From this observation, we conclude that "the sum of any two odd numbers is always an
(ii) Observe and complete:
$5 \times 3=?$
$7 \times 9=?$
$11 \times 13=?$
$=?$
From this observation, we conclude that "the product of any two odd numbers is always an' Justify the following statements with appropriate examples:
(iii) The sum of an odd number and an even number is always an odd number.
(iv) The product of an odd and an even number is always an even number.
(v) The product of only three odd numbers is always an odd number.

Solution:

(i) $1+3=4$ $5+11=16$ $21+47=68$
$\begin{aligned}
&5+11=16 \\
&21+47=68
\end{aligned}$
An odd number $+$ another odd number $=$ An Even number
From this observation, we conclude that the sum of any two odd numbers is always an even number.
(ii) $5 \times 3=15$
$7 \times 9=63$
$11 \times 13=143$
An odd number $\times$ Another odd number $=$ An odd number
From this observation, we conclude that "the product of any two odd numbers is always an odd number."
(iii) Take the odd number 5 and the even number 10
Their sum $=5+10=15$, which is odd.

$\therefore$ Sum of an odd number and an even number is always an odd number.
(iv) Take the odd number 5 and the even number 10 .
Their product $=5 \times 10=50$, which is even
Thus the product of an odd and an even number is always an even number.
(v) Consider $7 \times 5 \times 3$
We know that the product of any two odd numbers is an odd number
$7 \times 5=35$, odd number.
Also we have $35 \times 3=105$
$\therefore 7 \times 5 \times 3=105$, an odd number.
So the product of three odd numbers is always an odd number.

Try These (Textbook Page No. 3)
Question $1 .$
(i) Say True or False
(a) The smallest odd natural number is $1 .$
(b) 2 is the smallest even whole number.
(c) $12345+5063$ is an odd number.
(d) Every number is a factor of itself.
(e) A number which is a multiple of 6 is also a multiple of 2 and $3 .$
(ii) Is 7, a factor of $27 ?$
(iii) Is 12, a factor or a multiple of $12 ?$
(iv) Is 30, a factor or a multiple of $10 ?$
(v) Which of the following numbers has 3 as a factor?
(a) 8
(b) 10
(c) 12
(d) 14
(vi) The factors of 24 are $1,2,3, \ldots, 6, \ldots 12$ and 24 . Find the missing ones.
(vii) Look at the following numbers carefully and find the missing multiples.

Solution:

(i) (a) True
(b) False
(c) False
(d) True
(e) True
(ii) No, 7 is not a factor of 27 . Because 7 does not divide 27 exactly
(iii) 12 is both a factor and a multiple of 12
(iv) 30 is a multiple of 10
(v) (a) Factors of 8 are $1,2,4,8$
(b) Factors of 10 are $1,2,5,10$

(c) Factors of 2 are $1,2,3,4,6,12$
(d) Factors of 14 are $1,2,7,14$
$\therefore$ The number 12 has 3 as a factor
(vi) Factors of 24 are $1,2,3,4,6,8,12,24$.
Missing Factors 4,8 .
(vii)

Try These (Textbook Page No. 6)
Question $1 .$
Express 68 and 128 as the sum of two consecutive primes.
Solution:
$68=31+37$
$128=61+67$
 

Question 2 .
Express 79 and 104 as the sum of any three odd primes.
Solution:
$79=37+31+11$
$79=41+31+7$
$79=61+11+7$
$79=59+13+7$
$79=53+19+7$ and so on.
104 cannot be expressed as the sum of three odd primes.
Because we know that " the sum of any two odd numbers is an even number".
Also the sum of an odd and even number is always an odd number.
$104=61+41+2$
$104=97+5+2$
$104=89+13+2$ and so on.