Question

The additive inverse of Tow by eight is 

Answer 1

1. (-2/8)

2. (+5/4)

3. (-4/7) = (-0.571) = (-0.6) approx. -1 ,

(-0.6) means just right of (-0.5)

i.e,half the way between 0&-1,

it is the sixth mini point.

4. check commutative property

A + B = B + A

and

A × B = B × A

here, the number are 1/5 and 4/3

so, A + B = (1/5 + 1/3) = (3+5)/15 = 8/15

&. B + A = (1/3 + 1/5) = (5+3)/15 = 8/15

SO, (A + B) = (B + A)

A × B = 1/5 × 1/3 = 1/15

B × A = 1/3 × 1/5 = 1/15

So, A × B = B × A

we can say that devisions are commutative

5. (9/16 × 4/12) + (9/16 × -3/9)

= 3/16 - 3/16

= 0

6. 5 rational numbers between -3/5 and 1/4

(-3/5)×(4/4) = -12/20

& (1/4)×(5/5) = 5/20

so, the 5 numbers are between (-12/20) & (5/20)

= -10/20, -7/20, -4/20, -1/20, 4/20

(*you can choose any number between this range)

7. Prove Addition is associative or not

We prove associativity by first fixing natural numbers a and b and applying induction on the natural number c.

For the base case c = 0,

(a+b)+0 = a+b = a+(b+0)

Each equation follows by definition [A1]; the first with a + b, the second with b.

Now, for the induction. We assume the induction hypothesis, namely we assume that for some natural number c,

(a+b)+c = a+(b+c)

Then it follows,

(a + b) + S(c)

= S((a + b) + c) [by A2]

= S(a + (b + c)) [by the induction hypothesis]

= a + S(b + c) [by A2]

= a + (b + S(c)) [by A2]

In other words, the induction hypothesis holds for S(c). Therefore, the induction on c is complete.