Simplify the following using distributive property:

(i)

(ii)

(iii)

Find the value of

Find all integers n for which the number (n + 3)(n – 1) is also an integer.

Check the commutative property of addition for the following pairs:

(i) (ii)

(iii)

A bus shuttles between two neigbouring towns every two hours. It starts from 8 AM in the morning and the last trip is at 6 PM. On one day the driver observed that the first trip had 30 passengers and each subsequent trip had one passenger less than the previous trip. How many passengers travelled on that day?

Show that for each natural number n, the fraction is in its lowest form.

What is the value of

Simplify:

(i) 100(100 – 3) – (100 × 100 – 3);

(ii) (20–(2011–201) + (2011–(201–20))

Define an operation * on the set of all rational numbers □ as follows:

r*s = r + s –(r × s),

for any two rational numbers r, s. Answer the following with justification:

(i) Is ℚ closed under the operation *?

(ii) Is * an associative operation of ℚ ?

(iii) Is * a commutative operation of ℚ?

(iv) What is a * 1 for any a in ℚ?

(v) Find two integers a ≠ 0 and b ≠ 0 such that a * b = 0.

Suppose m is an integer such m ≠ –1 and m ≠ –2. Which is larger or ? State your reasons.