( A L G E B R A )

MATHEMATICAL OPERATIONS

TERMS, DEFINITIONS, BRACKETS, ADDITION, SUBTRACTION

• In arithmetic all numbers are expressed in terms of

the digits, all of which have definite values. In

algebra, as well as these digits, symbols which

usually have no single values are used.

• Algebra includes all the definitions and methods of

arithmetic, so that the signs +, -, ×,÷,=, for example,

have the same meanings as in arithmetic, but these

definitions and methods are extended and applied

in wider and more general uses, and not only to

ordinary numbers but to quantities which are not

found in arithmetic.

DEFINITIONS:

1. PRODUCT

• When two or more numbers or expressions are

multiplied together the result is called the product

of the two expressions.

2. FACTOR

• The quantities which are multiplied together to form

a product are called factors of the product.

3. COEFFICIENT

• If one of the factors in a product is a number and

the other a symbol the number is usually called the

coefficient of the symbol.

4. POWER

• When several factors which are all the same are

multiplied together, their product is called power of

the factor

5. ALGEBRAIC EXPRESSION

• A collection of numbers and symbols connected by

the signs +, -, ×, 𝑎𝑛𝑑 ÷ is called an algebraic

expression.

6. TERM

• Each part of an expression between + or – signs is

called a term ( the signs × 𝑎𝑛𝑑 ÷do not separate

terms)

7. SIMPLE EXPRESSION

• A simple expression consists of one term

8. COMPOUND EXPRESSION

• A Compound expression consists of two or more

terms.

9. LIKE TERMS

• Terms which differ only in their numerical

coefficients are called “like terms”

• All others are “unlike terms”.

BRACKETS

• Brackets such as , , , are used to show that

the terms inside them are to be considered and

treated as one quantity.

MULTIPLICATION

• The rules for multiplication which are used in

arithmetic apply also in algebra, but there is also

the complication due to signs.

MULTIPLICATION CONT.…

• It can be seen from the above cases that the

product is POSITIVE when two factors have the

SAME sign but the product is NEGATIVE when two

factors have OPPOSITE signs.

MULTIPLICATION CONT.…

• When a quantity which is raised to a power is

multiplied by the same quantity also raised to a

power, the product is found by adding together the

powers of the original quantities to find the index of

that quantity in the final product.

DIVISION

• When a quantity which is raised to a power is

divided by the same quantity also raised to a

power, the quotient is found by subtracting the

power of the divisor from that of the dividend to find

the index of the quantity in the final quotient.

NOTE:

• THE INDICES OF DIFFERENT LETTERS CANNOT BE

COMBINED.

MULTIPLICATION OF SIMPLE AND COMPOUND EXPRESSION

• The product of a compound expression by a single

factor is the sum of the products of each term of

the compound expression and the single factor,

due regard being given to sign.

• NOTE: PARTICULAR CARE MUST BE TAKEN WITH SIGNS.

• When multiplying two compound expressions

together multiply each term of the first expression

by each term of the second, with due regards to

sign, and then collect like terms.

DIVISION OF SIMPLE AND COMPOUND EXPRESSION

• To divide a compound expression by a single

factor, divide each term in turn by that factor and

take the sum of the quotients so obtained.