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)
Label the following numbers on a number line.
(b)
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)
(b)
(c)
(+5)  (0) + (−20)  (−4)
(−7) + (+6)  (−2) – (+12)
 1  2
 +  +  +   (−4)  (+2)
 3  3
##
(a) (+5)  (0) + (−20)  (−4)
= 0+5
=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