Whole Numbers
Number is an idea of a given
quantity.
Numeral is a symbol to represent a number.
A digit is any numeral from 0 to 9 and can represent different numbers depending on its position. This is called the place value.
The Factors of a given number are numbers which when multiplied together from the given number.
Example: The complete set of factors of 15 are 1, 3, 5 and 15.
Prime factors are those numbers which have no other factors except one and itself.
Example: The prime factor of 36 are 2,2,3,3
The Greatest Common Factor is the largest common factor of two or more numbers. It is the product of all the prime factors which they have in common.
Example: Find the GCF of 25
and 125 25= 5 x 5
125 = 5 x 5 x 5, therefore the
GCF is 5 x 5 = 25
ADDITION
The numbers that are to be added are called addends. The
number resulting in the addition of these numbers is called the sum of the
numbers.
Example:
45
395
+ 4396
890
___________
5726 SUM
SUBSTRACTION
Minuend is the number from which another is to be subtracted. Subtrahend is the number to be subtracted. Difference is the answer or the result in the process of subtraction.
Example:
5283 minuend
- 4997 subtrahend
_____________
286 DIFFERENCE
MULTIPLICATION
Multiplicand refers
to the number to be multiplied. Multiplier refers to the number of times
another number is to be multiplied. Product is the answer in the process of
multiplication.
Example:
1937 Multiplicand
X 86 Multiplier
_________________
11622
15496
166582 Product
DIVISION
Dividend refers to the number to be divided into equal groups.
Divisor refers to the size of each group. Quotient refers to the number of
groups resulting from division.
Example:
54,528 ÷ 64 = 852
↓ ↓ ↓
Dividend divisor quotient
Multiples
The multiples of a number are those numbers that are devisable by the given number.
Characteristics:
1.
A number has an infinite number of multiples.
2. A number is always a multiple of itself.
Example: The multiples of 3 are 3,6,9,12,15,18,21,24 . . .
Divisibility are ways of quickly determining factors without having to perform a complete division.
Divisibility Test for 2
A number divisible by 2 is an even number.
Example: 300, 12, 254, 1008
Divisibility Test for 3
A number is devisable by 3 if the sum of the digits of the number is devisable by 3.
Example: 186585 is devisable
by 3 because 1+8+6+5+8+5=33, and 33 is divisible by 3.
Divisibility Test for 4
A number is divisible by 4 if the number formed by its last 2 digits is divisible by 4.
Example: 128 & 524 are
divisible, by 4 since 28 and 24 are divisible by 4.
Divisibility Test for 5
If the ones digit is 0 or 5, then the number is divisible by 5.
Example: 300, 505, 2090 are
divisible by 5.
Divisibility Test for 6
A number is divisible by 6 if it is an even number and divisible by 3.
Example: 634128 is an even number. It is divisible by 3 since 6+3+4+1+2+8=24
And 24 is divisible by 3
Divisibility Test for 7
Steps:
1.
Double the last digit.
2.
Subtract the product in step 1 from the number
without the last digit.
3.
If the difference is a multiple for 7, then the
number is divisible by 7.
Note: If the difference is big, repeat steps 1 to 3.
Example: Is 6853 divisible by
7?
Solution:
1. 3(2) =6 3.(Repeat 1 & 2) 9(2)=18
2. 685-6=679 4.
67-18=49 is divisible by 7,
Divisibility Test for 8
If the last 3 digits of a number is divisible by 8, then the number is divisible by 8.
Example: Is 4912 a multiple of 8?
The last 3 digit is 912 & 912
= (114)(8). Therefore, 912 is divisible by 8 and 4912 is
divisible by 8.
Divisibility for 9
A number is divisible by 9 if
the sum of its digits is a multiple of 9.
Example: 845721 is divisible
by 9 because 8+4+5+7+3+1 = 27 and 27 is a multiple of 7
Divisibility for 10
If any number except 0 end in 0, the number is divisible by 10.
Example: 3,000, 10,000, 000, 200, 500 are divisible by 10
Divisibility for 11
A number is divisible by 11 if after subtracting and adding the digits successively, the answer is divisible by 11.
Example: Is 4972 divisible by 11?
4-9 +7 -2 = 0, 0 is divisible
by 11. Therefore, 4972 is divisible by 11.