Use directed numbers to represent the changes in values as described by the underlined phrases. (a) In a Mathematics competition, 100 marks are awarded for each correct answer and 50 marks are deducted for each wrong answer. (b) Mr Wong gained 2 kg weight last month and loses 3 kg weight this month. ## (a) ‘100 marks are awarded’ can be represented by +100 marks, while ’50 marks are deducted’ can be represented by –50 marks. (b) ‘Gained 2 kg’ can be represented by +2 kg, while ‘loses 3 kg’ can be represented by –3 kg. ======================================================= (a) (b) Label the number 3 and its opposite number on a number line. Label the following numbers on a number line. 1 1 +1, , 1.5, +2.5, 3 2 2 ## (a) The opposite number of –3 is +3. (b) ======================================================= With the help of a number line, compare the following numbers. (a) +2 and +4 (b) 2 and 5 1 1 and 3 (c) 2 2 ## (a) On the number line, +2 is to the left of +4. Therefore, +2 < +4. (b) On the number line, –2 is to the left of 5. Therefore, –2 < 5. (c) On the number line, 1 1 1 1 is to the right of 3 . Therefore, 3 . 2 2 2 2 ======================================================= With the help of a number line, find the values of the following expressions. (a) (+2) + (+4) (b) (3) + (+5) ## (a) Move in the positive direction by 4 units from +2 and we get +6. ∴ (2) (4) 6 (b) Move in the positive direction by 5 units from –3 and we get +2. ∴ (3) (5) 2 ======================================================= With the help of a number line, find the values of the following expressions. (a) (+6) + (2) (b) (3) + (7) ## (a) Move in the negative direction by 2 units from +6 and we get +4. ∴ (6) (2) 4 (b) Move in the negative direction by 7 units from –3 and we get –10. ∴ (3) (7) 10 ======================================================= With the help of a number line, find the values of the following expressions. (a) (+4) (+3) (b) (6) (+1) ## (a) Move in the negative direction by 3 units from +4 and we get +1. ∴ (4) (3) 1 (b) Move in the negative direction by 1 unit from –6 and we get –7. ∴ (6) (1) 7 ======================================================= With the help of a number line, find the values of the following expressions. (a) (+5) (3) (b) (4) (6) ## (a) Move in the positive direction by 3 units from +5 and we get +8. ∴ (5) (3) 8 (b) J Move in the positive direction by 6 units from –4 and we get +2. ∴ (4) (6) 2 ======================================================= Applying the rules of signs, find the values of the following expressions. (a) (+4) (+12) (b) (+7.5) + (4) ## (a) (4) (12) 4 12 8 (b) (7.5) (4) 7.5 4 3.5 ======================================================= Applying the rules of signs, find the values of the following expressions. (a) (7) + (+10) (b) (+9) (12) ## (a) (7) (10) 7 10 10 7 3 (b) (9) (12) 9 12 21 ======================================================= Applying the rules of signs, find the values of the following expressions. (a) (7) (5) + (1) (b) (+12) + (20) (+34) ## (a) (7) (5) (1) (2) (1) 2 1 3 (b) (12) (20) (34) (8) (34) 8 34 42 ======================================================= Tom is 260 m to the east of a tree and Mary is 150 m to the west of Tom. Use a directed number to represent the position of Mary from the tree. (Take east as the positive direction.) ## 260 (150) 110 ∴ +110 m represents the position of Mary from the tree. ======================================================= Find the values of the following expressions. (a) (+6) (4) (b) (5) (7) ## (a) (6) (4) (6 4) 24 (b) (5) (7) (5 7) 35 ======================================================= Find the value of the expression (3) (6) (4). ## ( 3) ( 6) ( 4) (3 6) ( 4) ( 18) ( 4) (18 4) 72 ======================================================= Find the values of the following expressions. (a) (56) (7) ( 72) (b) ( 8) ## (a) (56) (7) (56 7) 8 (b) (72) (8) 72 8 9 ======================================================= 2 2 Find the value of the expression 2 1 . 9 3 ## 2 2 2 1 9 3 20 5 9 3 20 5 9 3 20 3 9 5 4 3 ======================================================= Find the value of the expression (84) (+4) (3). ## (84) (4) (3) (84 4) (3) (21) (3) (21 3) 7 ======================================================= Find the values of the following expressions. (a) (15) (+3) + (2) (5) (b) (10) [(4) – (+27) (9)] (c) (+6) – (9) (+8) (6) ## (a) (15) (3) (2) (5) 5 10 5 (b) (10) [( 4) (27) (9)] (10) [( 4) (3)] (10) (1) 10 (c) (6) (9) (8) (6) (6) (72) (6) (6) (12) 6 ======================================================= (a) If +$30 means that the price of a watch has increased by $30, what does $45 mean? (b) If 2 km means 2 km below the ground, what does +1.5 km mean? ## (a) $45 means that the price of a watch has decreased by $45. (b) +1.5 km means 1.5 km above the ground. ======================================================= (a) (b) Label the following numbers on a number line. 1 1 , +2, +3.5, 4, +5 2 Hence, arrange the numbers in (a) in ascending order. ## (a) 1 (b) 4, 1 , +2, +3.5, +5 2 ======================================================= Find the values of the following expressions. (a) (+2) (3) (7) (b) (90) (+5) (6) (c) (+6) (8) (4) ## (a) ( 2) ( 3) ( 7) ( 2 3) ( 7) ( 6 ) ( 7 ) (6 7 ) 42 (b) (90) (5) (6) (90 5) (6) (18) (6) (18 6) 3 (c) (6) (8) (4) (6 8) (4) (48) (4) (48 4) 12 ======================================================= Find the values of the following expressions. (a) (+5) (0) + (20) (4) (b) (7) + (+6) (2) – (+12) 1 2 (c) (4) (2) 3 3 ## (a) (5) (0) (20) (4) 05 5 (b) (7) (6) (2) (12) (7) (3) (12) (10) (12) 22 (c) 1 2 (4) (2) 3 3 2 ( 2) 1 3 ( 4) 3 2 2 3 1 ( 4) 3 4 1 3 3 4 1 1 3 3 0
