Pls answer these I need help
Answers
Answer- Here are the solutions of questions along with explanation:
Sol. 8- Additive inverse of -7/19 is 7/19.
Explanation: Additive inverse means the inverse of sign of a given number i.e. - becomes + and + becomes - .
Sol. 9- - (-x)= x
i) x=3/5
LHS= -(-x) = -(-3/5)= + 3/5= 3/5
RHS= 3/5
∵LHS= RHS, ∴ -(-x)= x
ii) x= -7/9
LHS= -(-x)= -{-(-7/9)} = -(+7/9)= -7/9
RHS= -7/9
∵LHS= RHS, ∴ -(-x)= x
iii) x=13/-15
LHS= -(-x)= -(-13/-15)= -(13/15)= -13/15
RHS= -13/15
∵LHS= RHS, ∴ -(-x)= x
Sol. 10- Verification of x+y= y+x i.e. Commutative property over addition
i) x= 1/2, y=1/2
LHS= x+y= 1/2+ 1/2= (1+1)/2= 2/2= 1
RHS= y+x= 1/2+ 1/2= (1+1)/2= 2/2= 1
∵LHS= RHS, ∴x+y= y+x
ii) x= -2/3, y= -5/6
LHS= x+y= -2/3 + (-5/6)= (-4-5)/6= -9/6= -3/2
RHS= y+x= -5/6 + (-2/3)= (-5-4)/6= -9/6= -3/2
∵LHS= RHS, ∴x+y= y+x
Sol. 11- Simplification i.e. reducing in the lowest form:
i) [1/2 × 1/4] + [1/2 × 6]
= 1/8 + 3
= (1+24)/8
=25/8
ii) [1/5 × 2/15] - [1/5 × 2/5]
= 2/75 - 2/25
= (2-6)/75
= -4/75
Sol. 12- Verification of x × (y× z) = (x × y) × z i.e. Associative law over multiplication
a) x= 1, y= -1/2 and z= 1/4
LHS= x × (y× z) = 1 × (-1/2 × 1/4)= 1 × -1/8= -1/8
RHS= (x × y) × z= (1 × -1/2) × 1/4= -1/2 × 1/4= -1/8
∵LHS= RHS, ∴x × (y× z) = (x × y) × z
b) x= 2/3, y= -3/7 and z=1/2
LHS= x × (y× z)= 2/3 × (-3/7 × 1/2)= 2/3 × -3/14= -1/7
RHS= (x × y) × z = (2/3 × -3/7) × 1/2= -2/7 × 1/2= -1/7
∵LHS= RHS, ∴x × (y× z) = (x × y) × z
Sol. 13- Verification of x × (y+z)= x × y+ y × z i.e Distributive law
a) x= -1/2, y= 3/4 and z=1/4
LHS= x × (y+z)= -1/2 × (3/4 + 1/4)= -1/2 × 1= -1/2
RHS= x × y+ y × z= -1/2 × 3/4 + -1/2 × 1/4= -3/8 + (-1/8)= -4/8= -1/2
∵LHS= RHS, ∴x × (y+z)= x × y+ y × z
b) x= -1/5, y= 2/15 and z= -3/10
LHS= x × (y+z)= -1/5 × {2/15 + (-3/10)}= -1/5 × (4-9)/30= -1/5× -5/30= -1/5× -1/6= 1/30
RHS= x × y+ y × z= -1/5×2/15 + (-1/5× -3/10)= -2/75 + 3/50= (-4+9)/150= 5/150= 1/30
∵LHS= RHS, ∴x × (y+z)= x × y+ y × z
Answer:
Step-by-step explanation:
