1. Work out: a) $(-4) + (-13)$ - When adding two negative numbers, add their absolute values and keep the negative sign. $$-4 + (-13) = -(4 + 13) = -17$$ b) $(+8) + (-3) + (-2)$ - Add positive and negative numbers by combining positive and negative parts separately. $$8 + (-3) + (-2) = 8 - 3 - 2 = 3$$ 2. Solve the following using a number line: a) $2 - (+6)$ - Subtracting a positive number means moving left on the number line. $$2 - 6 = -4$$ b) $(-4) - (-6)$ - Subtracting a negative number is the same as adding its positive. $$-4 - (-6) = -4 + 6 = 2$$ 3. Find the difference between Janet's and Elsie's arrival times. - Janet was 8 minutes late (+8), Elsie was 5 minutes early (-5). - Difference = $8 - (-5) = 8 + 5 = 13$ minutes. 4. Evaluate: a) $(-8) \times (-3) \times 4$ - Multiply stepwise, remembering that negative times negative is positive. $$(-8) \times (-3) = 24$$ $$24 \times 4 = 96$$ b) $6 \times (-9)$ $$6 \times (-9) = -54$$ c) $(-5) \times (-2) \times (-5)$ $$(-5) \times (-2) = 10$$ $$10 \times (-5) = -50$$ 5. Work out: a) $48 \div (-4)$ $$48 \div (-4) = -12$$ b) Rate of descent = total depth $\div$ time $$\frac{-56}{8} = -7$$ - The diver descends at 7 metres per minute (negative indicates downward). Final answers: 1a) $-17$ 1b) $3$ 2a) $-4$ 2b) $2$ 3) $13$ minutes 4a) $96$ 4b) $-54$ 4c) $-50$ 5a) $-12$ 5b) $-7$ metres per minute