Download MATH TIPS - Project Goodwill Africa

QUICK MATH REVIEW & TIPS
1
Basic Facts & Rules To
Remember
Word of Advise

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

For a good and lasting foundation in Math, know
your multiplication tables by all means.
Knowing multiplication translates to being able to
figure out division problems in the shortest
amount of time.
Working with fractions, algebra, ratios and
percentages also become easy to handle.
Start solving Math problems using the facts, the
rules & information you already know to guide
you.
If you multiply two negative numbers
the result will be positive:
 -4



×-9 = 36
-3 ×-9 = 27
-7 ×-8 = 56
-6 ×-9 = 54
If you multiply a negative and a
positive number the result will be
negative :



-4
x 9 = -36
4 x -9 = -36
5 x -8 = -40
If you subtract a larger number from a
smaller number the result will be
negative:


12 - 25 = -13
18 - 38 = -20
If you add two negative numbers the
answer will be a “bigger” negative number:



-5
+ -7 = -5 + (-7) = -12
-23 + -12 = -23 + (-12) = -35
-51 + -10 = -61
( If you owe money and you borrow more you will owe
more money. More negative )
Any number multiplied by ONE gives
the same number:


5x1=5
100 x 1 = 100
Any number multiplied by ZERO gives
ZERO as the result:
3
x 0 =0
 12 x 0 = 0
 A x 0 = 0
 10,000 x 0 = 0
If you divide two negative numbers the
answer will be positive:



-24
÷ -8 = 3
-42 = 6
-7
-72 = 9
-8
If you divide a negative number by a
positive number the answer will be negative:


-24
÷ 8 = -3
-42
= -6
7

-72
8
= -9
If you divide a positive number by a negative
number the answer will be negative :

24 ÷ -8 = -3

42 = -6
-7

72 = -9
-8
 18
÷ 6 is the same as
18
6

24 ÷ 3 is the same as

18 is the same as 18 ÷ 3
3
24
3
Some tips on Simplification



Minus, Minus is Plus
5 - -8 = 5 + 8 = 13
Minus, Plus is Minus
15 - +8 = 15 - 8 = 7
Plus, Minus is Minus
15 + - 8 = 15 - 8 = 7

The easiest way to simplification problems involving order of operations is to use the BEDMAS or
PEDMAS or PEMDAS approach. Learn and use the one you can easily remember.

PEMDAS is short for Parenthesis Exponents Multiplication Division Additions Subtraction

BEDMAS is short for Brackets Exponents Division Multiplication Additions Subtraction

PEDMAS is short for Parenthesis Exponents Division Multiplication Additions Subtraction

This means when working on long simplification problems, do Brackets or Parenthesis first, then
Exponents, then Division, then Multiplication, followed by Addition and finally Subtraction

13 + 3(14 -5)-5+20

16 - 2 + 39 ÷ 3+(7×2-18)

Always follow the order but skip operations that are not mentioned in the simplification question.
Practice Questions


(4(12 - 4) + 10) ÷ 7=
Calculate 113 – 3(3 + 2)2 + 12 ÷ 2
How Percentages, Fractions and
Decimals relate to each other

2% is the same as 2

25% is the same as 25

10% is the same as 10 which is the same as 0.10

12.5% is the same as 12.5 and also be written as 0.125

which is the same as 0.02
100
100
which is the same as 0.25
100
100
Notice that when you write the percentage as a fraction each
zero in the denominator represent a single move of the decimal
point to the left in the numerator when you convert it to
decimals.
Some Tips & Tricks in Converting
fractions to decimals.






In the absence of a calculator always check to see if the
denominator of the fraction can be converted to a ten, a hundred,
a thousand and so forth by multiplying by a number.
If you can multiply the denominator by a number to get 10, 100,
1000 etc., then multiply both the numerator and denominator by
this number.
Now convert the numerator to the decimal number by moving the
decimal point to the left as many times as there are zeros in the
denominator.
Note that each zero in the denominator represents a “one decimal
place move” to the left.
If the numerator did not originally contain a decimal point, start
by assuming that there is a decimal point right after the last digit.
(14 is the same as 14.0 or 14.)
Examples

Write 3 as a decimal.
5
First we look at the denominator
We can convert this to 10 by multiplying by 2.
We have to also multiply the numerator
by 2 so the value of the fraction remains the
same
3 = 3 x 2 = 6 = 0.6
5 5 x 2 10
 Write
7=7
20
7 as a decimal.
20
x
5 = 35 = 0.35
20 x 5
100
THE OF KEYWORD
A given percentage OF a certain quantity is
equal to the Percentage multiplied by that
quantity.

10% of a certain quantity can be
expressed as (10% x the quantity )
10% of 200
= 10% × 200
= 10 × 200 = 20
100
1
A given Fraction OF a certain quantity is equal to
the Fraction multiplied by that quantity:

¾ of a certain quantity can be expressed as
(¾ x the quantity )
¾ of 20
=¾
×
20
=3
41
×
205 = 15
1
EXAMPLES
1.) What is 15% of 500 ?
Answer:
15% of 500
15 x 500 = 15 x 5 = 75
100 1
1
1
2.) What is two-fifth of 80 ?
Answer:
2 of 80
5
2
51
x
8016 = 2 x 16 =32
1
1 1
3.) What percentage of 250 is 40 ?
Answer:
Lets represent “what percentage” which we don’t yet know with
the letter p ( you can use any letter).
Then we can write the following:
p% of 250 is 40
p x 250 = 40
100 1
(We can now solve for p)
2.5p = 40
p = 40 = 16
2.5
So 16% of 250 is equal to 40
4.) What fraction of 120 is 36?
Answer:
Let p represent the unknown fraction (i.e “what fraction”)
p of 120 is 36
p x 120 = 36
p = 36 = 3
120
10
(Notice that we did not divide p by 100 because we want a fraction)
5.) 55% of the students in a school are boys. If there are 330 boys, what is the
total number of students in the school?
Answer:
We ask ourselves, “What is the unknown here?”
The unknown is the “total number of students”
Lets represent the total number of students by T.
We can write the following mathematical statement:
55% of T is equal to 330
55
100
x
T = 330
0.55T = 330
T = 330 = 600
.55
What is a Reciprocal?

The reciprocal of a whole number is 1 divided by the whole
number.
So the reciprocal of 5 will be 1
5

As you can see, the reciprocal of a whole number becomes
a fraction.

The reciprocal of a fraction is the fraction you get when the
numerator and denominator switch places.
So the reciprocal of 7 will be 9
9
7
LEAST COMMON MULTIPLE (LCM)


In LCM we are looking at the multiples of two or more numbers
to find out which of the multiples appear in all (COMMON) the
numbers and at the same time the smallest.
For example to find the LCM of 8 and 12 lets write out the
multiples of each to a point:
8=>8,16,24,32,40, . . .
12=>12,24,36,48, . . .

Right away you notice that 24 is the first multiple of both 8 and
12. It is also the smallest or least of the multiples.
So the LCM of 8 and 12 is 24

To summarize 24 is both the Common Multiple and the Least.
Finding LCM using the traditional method

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Start out by making a list of the multiples of each
given number
Look through the multiples for each given
number and find which of the multiples appear in
both lists or are common to both numbers.
For example we want to find the LCM of 16 and
24:
16 : 16, 32, 48, 64, 80 …….
24 : 24, 48, 72, 96 ……..
We notice that 48 is the first multiple that is
common to both 16 and 24 so 48 is our LCM

LEAST COMMON MULTIPLE (LCM) IN FOUR STEPS:
1.)Write out the prime factors of each given number.
2.) Look for each COMMON factor and write it down only once for
each time the common factor appears.
3.)Look for each Non-Common factor and write it down once.
4.)Multiply the factors from steps 2. and 3. above.
For example to find the LCM of 16 and 24, write each number
using its prime factors:
16 = 2.2.2.2
24 = 2.2.2.3
LCM= 2.2.2.2.3 =48
Practice Questions
 What
is the least common multiple of
4, 6 and 10 ?
 What
is the least common multiple of
6,10 and 14?
 Try
using both method to arrive at
your answers and see which one is
faster.
GREATEST COMMON FACTOR (GCF)

In GCF we are looking at the factors of two or more given numbers to
determine which of the multiples appear in all (COMMON) the given numbers.
This common factor should also be the greatest or largest or highest.

GCF is also referred to as HCF (Highest Common Factor). They both mean the
same thing.

For example to find the GCF or HCF of 8 and 12 lets write out the factors of
each number:
8=>1, 2, 4,8
12=>1, 2, 3, 4, 6, 12

We notice from the list of factors that 1, 2 and 4 are common to both lists. Of
these three common factors 4 is the greatest or highest.
So the GCF of 8 and 12 is 4

To summarize two or more given numbers may have more than one factor
which is common to them but we are only interested in the greatest of the
common factors.
GCF or HCF using the traditional method

Start out by making a list of the factors of each given number.

Look through the factors for each number and find which of the
factors appear in both lists.

The largest or highest of the common factors is the GCF or HCF.

For example we want to find the GCF or HCF of 16 and 24:



16 : 1,2,4,8,16
24 : 1,2,3,4,6,8,12,24
We notice that of the common factors 1,2,4,8 the greatest or
highest one is 8 so 8 is our GCF or HCF.

Greatest Common Factor (GCF) or Highest Common
Factor (HCF) in THREE STEPS

1.) Write out the given number as a product of its prime factors


2.) Look for each prime factor that is COMMON to all the given
numbers and write it down only once for each time that the
factor appears common.
3.) Multiply the common prime factors from steps 2 to get the
GCF or HCF.

e.g.
16 = 2·2·2·2
24 = 2·2·2·3
The GCF is 2·2·2 = 8

What is the greatest common factor of 9, 12 and 15?

Find the GCF of 24, 36 and 54
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