This document provides an overview of the key concepts in the language of algebra. It discusses that algebra involves expressions with variables, and algebraic expressions combine numbers with variables using letters and operation symbols. The language of algebra contains numerals, variables to represent unknown numbers, constants, and operational symbols to represent addition, subtraction, multiplication, and division. It provides examples of translating word phrases to algebraic expressions and defines terms like algebraic terms, expressions, coefficients and evaluating expressions by substitution.

1. The Language of
Algebra
Prepared by: Jenny Tuazon

3. Algebra
-It is the branch of mathematics
that involves expressions with
variables

4. Algebraic Expressions or
EXPRESSIONS
-It is the result of combining
numbers with variables
Example: 4n is an algebraic
expression where n is called
a variable

5. Algebraic Expressions or
EXPRESSIONS
Letters, symbols and
operation symbols are used
to create words and phrases

6. The Language of Algebra is composed
of the following:
A. Numerals
0,1,2,3,4,5,…
B.Letters or variables to represent unknown
numbers.
Variables – symbol which represents any
number from a given replacement set.
Replacement Set – set of values of the
variable.

7. The Language of Algebra is composed
of the following:
Constant – a symbol which has exactly one
number in its replacement set. Any numeral is a
constant such as 7, 4, 11, …
*The letters, numbers, and mathematical
symbols can be used to translate long word
statements into short mathematical sentences or
expressions

8. The Language of Algebra is composed
of the following:
C. Operational Symbols
There are many ways in expressing
addition, subtraction, multiplication, or
division of algebraic expressions.

9. The Language of Algebra is composed
of the following:
Example ofOperational Symbols
Verbal Phrase Algebraic Translation
The sum of m and 8 m+8
10 added to c c+10
7 plus a 7 +a
10 subtracted from c c – 10
the difference of 8 and m 8 – m
9 take away d 9 – d

10. Example ofOperational Symbols
0
Verbal Phrase Algebraic Translation
the product of 8 and m 8m
10 times c 10c
twice x 2x
the quotient of 8 and m 8
𝑚
x divided into 10 𝑥
10
ratio of 7 to a 7
𝑎

11. Terminologies
Algebraic Term – either a single number, letter,
or a product of several numbers or letters
Algebraic Expression – a statement containing
one or more terms connected by plus or minus
sign
Numerical Coefficient – the number in an
algebraic term
Literal Coefficient – aletter used to represent a
number

12. Terminologies
Similar terms – algebraic terms that have the
same literal factors and in which each letter has
the same exponent in all of the terms.
Constant – anumber, letter, orsymbol whose
value is fixed.

13. Identify the numerical coefficients,variables,
and constants in each expression
1.5n+4
2.-7x +12
3. 𝜋
𝑟
2

14. Evaluating AlgebraicExpressions
Replacing the variable by the
given number value.
(Substitution)

15. Evaluate the following expression
1. 5n+4 ; if n =5
2.-7x +12 ; if x=2
3. 𝜋
𝑟2 ; if 𝜋=3.14

16. PAIRACTIVITY
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VOCABULARY
PRACTICE ANDAPPLICATION