Addition is the process of combining numbers to find a total sum. The key principles of addition are that the order and grouping of numbers does not change the sum. Subtraction is the inverse of addition, where the minuend is the starting number and the subtrahend is subtracted to find the difference. Multiplication provides a shortcut to repeated addition by multiplying the multiplicand by the multiplier to find the product. The principles of multiplication state that the order or grouping of factors does not change the product, and multiplying a number by 1 or 0 does not change the number or results in 0, respectively.

2.  It is the summation of two or more
numbers into one single total. The
numbers to be added are called
addends and the number that
expresses the total is the sum.

3. Principles of Addition. There are three
general rules or principles we should keep
in mind when we add numbers.
1. When we add two numbers, the order in w/c we
add them does not affect the sum. Thus, 5+3=3+5.
This is called the commutative principle of addition.
This principle enables us to add columns either
upward or downward. We use it to check addition
by adding in the opposite direction.
2. When we have three or more numbers to add, the
way we group the numbers does not affect the sum.
This is called the associative principle of addition.
The commutative and associative principles
enable us, when adding several numbers, to skip
around to find combinations that make 10 or some
other number easier to add.
3. Adding 0 to a number does not change the number,
example, 7+0=7. Thus, 0 is called the identity number
for addition.

4. Shortcuts in Addition
Methods 1. When adding integers, group and
add at sight integers whose sum is 10.
Example 1. 4+3+6+7+5= 25
Method 2. When adding more than two numbers of
two digits each, add the tens numbers first multiplied
by 10, and add the units numbers in sequence.
Example 1. Add 43 and 32.
Solution: Add 40+30=70
To 70 add 3 and 2=70+3+2=75

5. The methods used for checking an answer in
addition are the following:
•Reverse order adding. Before adding, arrange the
numbers according to their place values. The
checking operation is then performed from bottom
to the top.
Example 1. Add 6, 253; 2,498; 1,031 and 2,488

6. › The process of determining the
difference between two numbers is
called subtraction. Minus (-)
indicates subtraction. The number to
be subtracted is called subtrahend
and the number from which we
subtract is called minuend. The result
is what we call remainder or
difference.

7. 65 minuend
-42 subtrahend
23 difference
(Check: 23 + 42 = 65)
In the expression 65 = 42, 65 represents the sum of
two addends. One of them is 42. The other is the number to
w/c 42 was added to give 65. That is, X+42 = 65. To do this,
we have to reverse the operation by subtracting 42 from
65. The difference, 23, is the other addend. Thus X, (the
other addend) 65-42 = 23. We see that subtraction is the
inverse operation of addition , and addition is the inverse of
subtraction, as shown below.
Subtraction Addition
65 minuend 23 addend
-42 subtrahend +42 addend
23 difference 65 sum

8. › Multiplication is the short-cut way to add. If we are
to add a number several times, simply multiply the
number by the number of times it is to be added.
For example, add 12 four times is the same as 12
multiplied by 4. the symbols used to indicate
multiplication are “x,” brackets, parentheses, and
the decimal point (.) which is placed slightly higher
than our usual fractional decimal point.

9. For example, 12 times 4 can be expressed as
follows:
1. 12x4 = 48
2. (12) (4) = 48
3. [12] [4] = 48
4. 12. 4 = 48

10. The multiplier indicates how many
times the multiplicand would be added
if the product was to be found by
addition. Thus, in 12x4 = 48, 12 is the
multiplicand, 4 is the multiplier and 48 is
the product. The multiplicand and
multiplier are also called factors of the
product.
1.Interchanging multiplicand and
multiplier
2.Dividing the product by one of the
factors

11.  1. The Commutative Law of
Multiplication
 This principles states that changing the
orders of the factors does not change
the value of the product.
 Example 1) 6x4 = 4x6
 24 = 24
› Example 2) 6.3.5 = 5.3.6
90 = 90

12.  This principle states that factors may be
grouped together and treated as one
product without changing the value of
the final product. Thus, the way we
group the numbers does not affect the
product.
 Example 1) (4.2).3 = 2.(4.3)
8. 3 = 2. 12
24 = 24

13. › This principle states that the multiplier
must be made to operate upon each
term of the sum or difference. Thus, this
law implies that certain variable is to be
assigned and distributed to each of the
other variables.
› Example 1)3. (5+4) = 3.5+3.4
3. 9 = 15 + 12
27 = 27

14. › This principles states that a
number is not changed when it
is multiplied by 1.
› Example 1. 7 x 1 = 7
› Example 2. 1,ooo x 1 = 1,000

15. › This principle states that when a
number is multiplied by 0 , the
product is always o.
› Example 1. 8 x 0 = 0
› Example 2. 1,500 x 0 = 0

16. › When