1. Express each of the following as a single integer: (i) $6 - 4$ $$6 - 4 = 2$$ (ii) $-6 + 4$ $$-6 + 4 = -2$$ (iii) $-3 - 7$ $$-3 - 7 = -10$$ (iv) $2 - 4 - 5$ $$2 - 4 - 5 = 2 - 9 = -7$$ (v) $-3 \times 5$ $$-3 \times 5 = -15$$ (vi) $-6 \times (-3)$ $$-6 \times (-3) = 18$$ (vii) $-18 \div 6$ $$-18 \div 6 = -3$$ (viii) $-24 \div (-12)$ $$-24 \div (-12) = 2$$ --- 2. List these numbers in order of size, starting with the smallest: (i) $4, -3, 9, 0, -12, -1, 6$ Ordering from smallest to largest: $$-12 < -3 < -1 < 0 < 4 < 6 < 9$$ (ii) $-3, 2, 14, -9, -4, 7$ Ordering from smallest to largest: $$-9 < -4 < -3 < 2 < 7 < 14$$ --- 4. Insert the symbols $>$ or $<$ between each pair: (i) $3 \; \square \; -2$ Since $3 > -2$, we write: $$3 > -2$$ (ii) $-5 \; \square \; -4$ Since $-5 < -4$, we write: $$-5 < -4$$ (iii) $0 \; \square \; -7$ Since $0 > -7$, we write: $$0 > -7$$ (iv) $-1 \; \square \; -8$ Since $-1 > -8$, we write: $$-1 > -8$$ --- 5. Choose pairs of numbers from the loop to make these calculations correct: (i) $\square + \square = -6$ Possible pair: $-3 + (-3) = -6$ (ii) $\square \times \square = -15$ Possible pair: $-3 \times 5 = -15$ (iii) $\square \times \square = 40$ Possible pair: $-5 \times -8 = 40$ (iv) $\square + \square = -13$ Possible pair: $-9 + (-4) = -13$ --- 7. Simplify each of these: (i) $6 - 8 + 5 - 10$ Calculate stepwise: $$6 - 8 = -2$$ $$-2 + 5 = 3$$ $$3 - 10 = -7$$ (ii) $6 - (-4) + 3$ Recall that subtracting a negative is adding: $$6 + 4 + 3 = 13$$ (iii) $4 \times (-3) \times (-5)$ Calculate stepwise: $$4 \times (-3) = -12$$ $$-12 \times (-5) = 60$$