MATH IMAN NAUFAL 101

"Mathematics, Magic, and

Mystery"



Multiples of Whole Numbers

Multiply any whole number • Example
by another whole number
• 5 x 7 = 35, which means
= that 35 is a multiple of 5
and it is also a multiple
Multiple of either of those
numbers. • multiples of 5 are

5 10 15 20 25 30 35 ...

• multiples of 7 are

7 14 21 28 35 42 ...

Factors of Whole Numbers

Any whole The factors of 20 are 1 is always a factor
number that 1 2 4 5 10 20 the and so is the

divides into it factors of 12 are 1 2 3 number itself.
exactly.
4 6 12

When you have found one factor, there is always another factor
that goes with it - unless the factor is multiplied by itself to give the

number.

For example, look at the number 20:
1 × 20 = 20 so 1 and 20 are both factors of 20
2 x 10 = 20 so 2 and 10 are both factors of 20
4 x 5 = 20 so 4 and 5 are both factors of 20

These are called factor pairs.

(LCM)

lowest common multiple of two

numbers is the smallest number that

appears in the multiplication tables of

both numbers. (HCF)
Example,
LCM of 3 and 5 is 15, Highest common factor The highest
LCM of 2 and 7 is 14
LCM of 6 and 9 is 18 common factor of two numbers is the

biggest number that divides exactly into

both of them.

Example,

HCF of 24 and 18 is 6,

HCF of 45 and 36 is 9

HCF of 15 and 22 is

Prime Numbers

1Prime number is a whole number that has only two factors: itself and

1 is not a prime number, since it has only one factor - itself

The prime numbers up to 50 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47

Square Numbers and Root

Multiply any number by itself Short way to write the square of any number.
example: example:
the square of 5 (or 5 squared) is 5 x 5 = 25 5 squared (5 x 5) can be written as

the square of 6 (or 6 squared) is 6 x 6 = 36 13 squared (13 x 13) can be written as

The square root of n is the number whose square is n.
This can he written as
example:
the square root of 16 (4) can be written as

Square numbers have exact square roots, for example:
the square root of 9 is 3: = 3
the square root of 25 is 5: = 5
the square root of 100 is 10: = 10

Real Numbers

There are two sorts of real numbers:
Rational numbers are integers or fractions such as -17, 3 , -8.75 or
Irrational numbers cannot be written as fractions.
Examples of irrational numbers are , , or .

If n is a natural number that is not a square number, Then is irrational.









Introduction To Directed Numbers

Positive and negative numbers together are called directed numbers

Everyday Use of Directed Numbers

On bank statements and bills a
negative number means you owe
money. A positive number means
they owe you money.

The Number Line

Notice that the negative numbers are to the left of 0
and the positive numbers are to the right of 0

Adding and Subtracting Directed Numbers

Adding integers include adding both positive and negative integers. It can be adding only
positive integers, or both positive and negative integers, or only negative integers.

Multiplying and Dividing Directed

Numbers

Rules

 When the signs of the two numbers are the same, the answer is
positive

 When the signs of the two numbers are different, the answer is
negative









Equivalent Fractions

Two or more fractions that represent the same part of a whole

A fraction with the numerator (top number) smaller than the denominator
(buttom number) called a proper fraction.
Example of a proper fraction is

An improper fraction has a bigger numerator (top number) than the denominator
(buttom number).
Example of an improper fraction is . It is sometimes called a top-heavy fraction

A mixed number is made up of a whole number and a proper fraction.
Example : 1

Fractions and Decimals

Percentages, Fractions and Decimals

Calculating a Percentages

Increasing or Decreasing Quantities by a Percentages
Expressing One Quantity as a Percentages

Percentages Change
Using a Multiplier (or decimal)

Simple Interest and Compound Interest
Reverse Percentage







ORDER OF OPERATIONS

There is an order of
operations which you must
follow when working out
calculations

CHOOSING THE CORRECT OPERATION

The process of
"choosing the operation"
involves deciding which
mathematical operation
(addition, subtraction,

multiplication, or
division) or combination
of operations will be useful

in solving a word
problem.

FINDING A FRACTION OF A QUANTITY

Simply multiply the fraction by the quantity.

ADDING AND SUBTRACTING FRACTIONS

Fractions with different denominators can only be
added or subtracted- converted them to equivalent
fractions with the same denominator.

MULTIPLYING AND DIVIDING FRACTIONS

Multiply the
numerators
together and
multiply the
denominators
together.









ROUNDING WHOLE NUMBERS

ROUNDING DECIMALS

ROUNDING TO SIGNIFICANT FIGURES

UPPER AND LOWER BOUNDS

UPPER AND LOWER BOUNDS









SQUARES AND SQUARE ROOTS

The square root of a number is another number which produces the first number
when it is multiplied by itself. For example, the square root of 16 is 4.

CUBES AND CUBE ROOTS

To cube a number, we use the number in a multiplication 3 times. A cube
root goes the other direction. 3 cubed is 27, so the cube root of 27 is 3. The cube

root of a number is the value that when cubed gives the original number.