Unit
1 sec 3.1 Negative numbers
25 September 2015
23:28
Negative numbers, fractions and percentages (which can be
thought of as a type of fraction).
Negative numbers are also used to represent debt. You can
think of all the numbers as lying on, called the number line. The positive
numbers are to the right of 0, and the negative numbers are to the left. The
numbers on the number line get bigger as you go from left to right.
Activity 12 comparing temperatures
Answer: Monday and Friday.
You will often need to use negative numbers in MU123.
No matter what number you start with - whether it is
positive, negative or zero - if you want to add a positive number to it then
you move along the number line to the right.
Activity 13 adding and subtracting positive numbers.
a) -6
+2= 4
b) -1
+3= 2
c) 2
-7= -5
d) -3
- 4= -7
e) 5
– 7 -2= -4
Adding and
Subtracting negative numbers
Adding a negative number is this
same as subtracting the corresponding positive number.
Subtracting a negative number is
the same as adding the corresponding positive number.
Notice that some of the negative numbers in this example are
enclosed in brackets. This is because no two of the mathematical symbol +,-,×,÷
should be written next to each other, as that would look confusing. So if you
want to show that you are adding -2 to 4, for example, then you should put
brackets around -2 and write 4 + (-2), not 4 +-2.
Example 7 adding and subtracting negative numbers.
Work the following calculations without using calculator.
a) -3
+ (-6)=
b) 4+
(-2) =
c) 0
- (-6) =
d) 1
- (-2) =
e) -2
- (-3) =
Solution
To add a negative number, subtract the corresponding
positive number.
(A)
-3 + (-6) = -3 -6 = -9
(B)
4+ (-2) = 4-2 = 2
To subtract a negative number, and the corresponding positive number.
(C) 0
- (-6) = 0+6 = 6
(D)
1 - (-2) = 1+2 = 3
(E)
-2 - (-3) = -2+3 = 1
activity 14 adding and subtracting negative numbers.
(A) 2
+ (-7) = -5
(B)
-8+ (-5) = -13
(C)
1 - (-3)
= 4
(D)
-6 - (-9) = 3
(E)
-4 - (-4) = 0
(F)
3 - (-2) + (-4) = 1
(G)
7+ (-6) -3 = -2
Multiplying and
dividing negative numbers.
Now let’s look at how to multiply and divide negative
numbers. The first consider of multiplication is 3 × (-2). This means 3 lots of
-2. The order which you multiplying numbers don’t matter so the calculation
above also tell you that (-2) × 3 = -6.
Multiplying and dividing
negative numbers
v
this signs are
different, then the answer is negative.
v
This signs are the
same then the answer is positive.
Example 8
Work out the following.
(A)
(-5)×6
(B)
9÷(-3)
(C)
(-3) ×(-7)
(D)
(-70) ÷(-10)
(E)
(-2) ×3×(-4)
Solution
(a)
A negative times a positive (different sign)
gives a negative.
(-5)×6=
-30
(b) A positive divided by a negative (different sign) gives
a negative
9÷(-3)=-3
C. A negative times a negative (same sign) gives a positive
(-3) ×(-7)= 21
(d) A negative divided by a negative (same sign) gives a
positive
(-70) ÷(-10)= 7
(e) Do the multiplication one at a time. In the first
multiplication, a negative times a positive gives a negative. Then this
negative, times a negative , gives a positive
(-2) ×3×(-4)= (-6)×(-4)= 24
ACTIVITY 15
(A)
5×(-3)= -15
(B)
(-2)×(-4)= 8
(C)
6×(-10)= -60
(D)
25÷(-5)= -5
(E)
(-49)÷(-7)= 7
(F)
(-36)÷12= -3
(G)
(-2)×(-5)×(-4)= -40
In this calculation -3², the power is dealt with first.
Activity 16
(A)
-213.6+58.8=154.8
(B)
315.12+(-142.26)= 173.34
(C)
37.4-(-25.2)+(-4.7)= 57.9
(D)
13.5×(-22.9)= 309.15
(E)
-56² = -3,136
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