... division
of fractions which can be trickier.
Example
ᎏ
2
3
ᎏ
m +
ᎏ
1
2
ᎏ
=12
–
ᎏ
1
2
ᎏ
=–
ᎏ
1
2
ᎏ
ᎏ
2
3
ᎏ
m =11
ᎏ
1
2
ᎏ
ᎏ
3
2
ᎏ
•
ᎏ
2
3
ᎏ
m =11
ᎏ
1
2
ᎏ
•
ᎏ
3
2
ᎏ
ᎏ
3
2
ᎏ
•
ᎏ
2
3
ᎏ
m =
ᎏ
2
2
3
ᎏ
• ... 2x + 3y = 5.
There are an infinite number of values for x and y that that satisfy the equation. Instead, we are
asked to isolate y on one side of the equation.
2x + 3y...
... density of water. The table of densities
below shows that mercury (Hg) has a density of 13. 6g/cm
3
. This means that a cubic
centimeter of mercury has 13. 6 times the mass of a cubic centimeter of ... relative
to the density of water.
10.
This …………… that a cubic centimeter of mercury has 13. 6 times the mass of a
cubic centimeter of water.
Exercise 3: Decide whe...
... majority of the population
c. and the Malays form the majority of the population
d. the Malays forming the majority of the population
33 . Malaysia is a founding member of the Association of Southeast ... organization
b. the development of all countries allover the world
c. the aims and purposes of the organization
d. the laws of the members of the organization
38 . The th...
... the additive inverse of 3?
– THEA MATH REVIEW–
93
This means, “what number can I add to 3 to give me the additive identity (0)?”
3 + ___ = 0
3 + 3 = 0
The answer is 3.
■
The multiplicative ... integer.
Example
5 ϫ 7 = 35
The number 35 is, therefore, a multiple of the number 5 and of the number 7. Other multiples of 5 are 5,
10, 15, 20, etc. Other multiples of 7 are 7,...
... number of decimal places.
Example
What is the sum of 0.45, 0.8, and 1 .36 ?
11
0.45
0.80
+ 1 .36
2.61
Take away 0 .35 from 1.06.
1
0
.0
1
6
–0 .35
0.71
MULTIPLICATION OF
DECIMALS
Multiplication of decimals ... share.
Example
Some multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32 , 36 . . .
Some multiples of 6 are: 6, 12, 18, 24, 30 , 36 , 42, 48 . . .
Some common multiples...
... square of a number is the product of the number and itself. For example, in the statement 3
2
= 3 ϫ 3 = 9, the
number 9 is the square of the number 3. If the process is reversed, the number 3 is ... be familiar with:
Fraction Decimal Percentage
ᎏ
1
2
ᎏ
.5 50%
ᎏ
1
4
ᎏ
.25 25%
ᎏ
1
3
ᎏ
.33 3 . . . 33 .3
––
%
ᎏ
2
3
ᎏ
.666 . . . 66.6
––
%
ᎏ
1
1
0
ᎏ
.1 10%
ᎏ
1
8
ᎏ
.125 12.5%
ᎏ...
... multiple of 3 on the roll of a die?
The probability of getting an even number on the roll of a die is
ᎏ
3
6
ᎏ
, because there are three even
numbers (2, 4, 6) on a die and a total of 6 possible ... The probability of getting a multiple
of 3 is
ᎏ
2
6
ᎏ
, because there are 2 multiples of three (3, 6) on a die. But because the outcome of rolling a 6
on the die is an ove...
... 2:
To change feet to yards, divide the number of feet given (9), by the number of feet in a yard (3) .
9 feet ÷ 3 feet in a yard = 3 yards
Then multiply 3 yards by 4 yards = 12 square yards.
(Note: ... subtracted.
Examples
7x + 3x = 10x
6y
2
– 4y
2
= 2y
2
3cd
2
+ 5c
2
d cannot be simplified. Since the exponent of 2 is on d in 3cd
2
and on c in 5c
2
d, they are not like
terms.
The p...
... REVIEW–
126
Reciprocal Rules
There are special rules for the sum and difference of reciprocals. The reciprocal of 3 is
ᎏ
1
3
ᎏ
and the reciprocal
of x is
ᎏ
1
x
ᎏ
.
■
If x and y are not 0, then
ᎏ
1
x
ᎏ
+
ᎏ
1
y
ᎏ
= ... same, therefore, make the two expressions equal to each other:
12x =15x – 3. 75
–15x = –15x
ᎏ
–
–
3
3
x
ᎏ
=
ᎏ
3
–
.
3
75
ᎏ
x = 1.25
Be careful, 1.25 is not t...