Exercise 1.3 - Chapter 1 Number Systems Term 1 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question 1 .
Fill in the blanks.
(i) $-80 \times \quad=-80$
(ii) $(-10) \times \quad=20$
(iii) $100 \times \overline{=}-500$
(iv) $\quad \times(-9)=-45$
(v) $\quad \times 75=0$
Solution:
(i) 1
(ii) $-2$
(iii) $-5$
(iv) 5
(v) 0

Question 2 .
Say True or False:
(i) $(-15) \times 5=75$
(ii) $(-100) \times 0 \times 20=0$
(iii) $8 \times(-4)=32$
Solution:
(i) False
(ii) True
(iii) False

Question $3 .$
What will be the sign of the product of the following:
(i) 16 times of negative integers.
(ii) 29 times of negative integers.
Solution:

(i) 16 is an even interger.
If negative integers are multiplied even number of times, the product is a positive integer.
$\therefore 16$ times a negative integer is a positive integer.
(ii) 29 times negative integer.
If negative integers are multiplied odd number of times, the product is a negative integer. 29 is odd. $\therefore 29$ times negative integers is a negative integer.

Question $4 .$
Find the product of
(i) $(-35) \times 22$
(ii) $(-10) \times 12 \times(-9)$
(iii) $(-9) \times(-8) \times(-7) \times(-6)$
(iv) $(-25) \times 0 \times 45 \times 90$
(v) $(-2) \times(+50) \times(-25) \times 4$
Solution:
(i) $35 \times 22=-770$
(ii) $(-10) \times 12 \times(-9)=(-120) \times(-9)=+1080$
(iii) $(-9) \times(-8) \times(-7) \times(-6)=(+72) \times(-7) \times(-6)=(-504) \times(-6)=+3024$
(iv) $(-25) \times 0 \times 45 \times 90=0 \times 45 \times 90=0 \times 90=0$
(v) $(-2) \times(+50) \times(-25) \times 4=(-100) \times-25 \times 4=2500 \times 4=10,000$

Question $5 .$
Check the following for equality and if they are equal, mention the property.
(i) $(8-13) \times 7$ and $8-(13 \times 7)$
Solution:
Consider $(8-13) \times 7=(-5) \times 7=-35$
Now $8-(13 \times 7)=8-91=-83$
$\therefore(8-13) \times 7 \neq 8-(13 \times 7)$
(ii) $[(-6)-(+8)] \times(-4)$ and $(-6)-[8 \times(-4)]$
Solution:
$[(-6)-(+8)] \times(-4)=[(-6)+(-8)] \times(-4)=(-14) \times(-4)=+56$
Now $(-6)-[8 \times(-4)]=(-6)-(-32)$
$=(-6)+(+32)=+26$
$\therefore[(-6)-(+8)] \times(-4) \neq(-6)-[8 \times(-4)]$
(iii) $3 \times[(-4)+(-10)]$ and $[3 \times(-4)+3 \times(-10)]$
Solution:
Consider $3 \times[(-4)+(-10)]=3 \times-14=-42$
Now $[3 \times(-4)+3 \times(-10)]=(-12)+(-30)=-42$

Here $3 \times[(-4)+(-10)]=[3 \times(-4)+3 \times(-10)]$
It is the distributive property of multiplication over addition.

Question $6 .$
During summer, the level of the water in a pond decreases by 2 inches every week due to evaporation. What is the change in the level of the water over a period of 6 weeks?
Solution:
Level of water decreases a week $=2$ inches.
Level of water decreases in 6 weeks $=6 \times 2=12$ inches
 

Question $7 .$
Find all possible pairs of integers that give a product of $-50$.
Solution:
Factor of 50 are 1, 2, 5, 10,25, 50 .
Possible pairs of integers that gives product $-50$ :
$(-1 \times 50),(1 \times(-50)),(-2 \times 25),(2 \times(-25)),(-5 \times 10),(5 \times(-10))$

Objective Type Questions
Question $8 .$
Which of the following expressions is equal to $-30$.
(i) $-20-(-5 \times 2)$
(ii) $(6 \times 10)-(6 \times 5)$
(iii) $(2 \times 5)+(4 \times 5)$
(iv) $(-6) \times(+5)$
Solution:
(iv) $(-6) \times(+5)$
Hint:
(i) $-20+(10)=-10$
(ii) $60-30=30$
(iii) $10+20=30$
(iv) $(-6) \times(+5)=-30$
 

Question $9 .$
Which property is illustrated by the equation: $(5 \times 2)+(5 \times 5)=5 \times(2+5)$
(i) commutative
(ii) closure
(iii) distributive
(iv) associative
Solution:
(iii) distributive

Question 10 .
$11 \times(-1)=$
(i) $-1$
(ii) 0
(iii) $+1$
(iv) $-11$
Solution:
(iv) $-11$

Question $11 .$
$(-12) \times(-9)=$
(i) 108
(ii) $-108$
(iii) $+1$
(iv) $-1$
Solution:
(i) 108