This document defines key terms and concepts in algebra, including: 1. Algebra uses both digits and symbols to represent quantities, extending arithmetic operations. 2. Terms like product, factor, coefficient, power, expressions, and brackets are defined for representing algebraic expressions. 3. The rules of multiplication and division are extended from arithmetic and include attention to signs when combining terms.

1. MATHEMATICAL
OPERATIONS
(ALGE B RA)

2. 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.

3. • 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.

4. DEFINITIONS:

5. 1. PRODUCT
• When two or more numbers or expressions are
multiplied together the result is called the product
of the two expressions.

6. 2. FACTOR
• The quantities which are multiplied together to form
a product are called factors of the product.

7. 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.

8. 4. POWER
• When several factors which are all the same are
multiplied together, their product is called power of
the factor

9. 5. ALGEBRAIC EXPRESSION
• A collection of numbers and symbols connected by
the signs +, -, ×, 푎푛푑 ÷ is called an algebraic
expression.

10. 6. TERM
• Each part of an expression between + or – signs is
called a term ( the signs × 푎푛푑 ÷do not separate
terms)

11. 7. SIMPLE EXPRESSION
• A simple expression consists of one term

12. 8. COMPOUND EXPRESSION
• A Compound expression consists of two or more
terms.

13. 9. LIKE TERMS
• Terms which differ only in their numerical
coefficients are called “like terms”
• All others are “unlike terms”.

14. BRACKETS
• Brackets such as , , , are used to show that
the terms inside them are to be considered and
treated as one quantity.

15. MULTIPLICATION
• The rules for multiplication which are used in
arithmetic apply also in algebra, but there is also
the complication due to signs.

16. 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.

17. 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.

18. 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.

19. NOTE:
• THE INDICES OF DIFFERENT LETTERS CANNOT BE
COMBINED.

20. 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.

21. • 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.

22. 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.