Exercise 1.2

1. Find each of the following products:

(a) (–316) × (–1) = .

(b) (–15) × 0 × (–18) = .

(c) 9 × (–3) × (– 6) = .

(d) (–1) × (–2) × (–3) × 4 = .

(e)3 × (–1) =

(f)(–1) × 225 =

(g)(–21) × (–30) =

(h)(–12) × (–11) × (10) =

(i)(–18) × (–5) × (– 4) =

(j)(–3) × (–6) × (–2) × (–1) =

2. Verify the following:

(a) 18 × [7 + (–3)] = , [18 × 7] + [18 × (–3)] =

Therefore LHS and RHS are

(b) (–21) × [(– 4) + (– 6)] = , [(–21) × (– 4)] + [(–21) × (– 6)] =

Therefore LHS and RHS are

3. For any integer a,

(i)what is (–1) × a equal to =

(ii) Determine the integer whose product with (–1) is.

(a) –22 = .

(b) 37 = .

4. Starting from (–1) × 5, write various products showing some pattern to show (–1) × (–1) = 1.

Instruction

-1 × 5 = .

-1 × 4 = = -5 + 1.

-1 × 3 = = -4 + 1.

-1 × 2 = = -3 + .

-1 × 1 = = -2 + .

-1 × 0 = = + 1.

Therefore, - 1 × (- 1) = 0 + 1 = 1.

The pattern demonstrates that multiplying (−1) by itself results in 1.

Integers