Translate the following into
mathematical expressions.
Choose the letter only.
A number plus five
A. 5 − 𝑛
B. 𝑛 + 5
C. 5𝑛
D. 5 + 𝑛
A number
decreased by nine
A.
9
𝑛
B. 𝑛 − 9
C. 9𝑛
D. 𝑛 + 9
The difference of six and a number
A. 6 + 𝑥
B. 6 − 𝑥
C. 6𝑥
D.
6
𝑥
Eight more than a number
A. 8 + 𝑦
B. 8 − 𝑥
C. 8𝑥
D. 𝑦 + 8
The sum of six and a number is twelve
A. 𝑥 + 6
B. 𝑥 + 6 = 12
C. 6𝑛 = 12
D. 6 + 𝑥=12
The quotient of six and a number is the
product of twice a number
𝑥
6
A. = 3𝑥
6
B. = 2𝑥
6
𝑥
C. = 3 + 𝑥
𝑥
D.
6
= 2𝑥
ALGEBRAIC
EXPRESSIONS VS.
ALGEBRAIC EQUATIONS
OBJECTIVES:
a. define algebraic expressions and algebraic
equation;
b. describe the difference between an algebraic
expressions and algebraic equation, and
c. translate verbal expressions to an algebraic
expressions or equation.
4𝑦 + 3
4𝑦 + 5 = 17
6𝑥 + 3 = 39 8𝑧 = 24𝑧 + 60
8𝑎
4𝑦 + 3
Algebraic
Expressions
8𝑎
3𝑥 − 5
3𝑥 − 5
3𝑥
−
5
=
10
3𝑥 − 5 = 10
5 = 5𝑥
+
10
5 = 5𝑥 + 10
6𝑥 + 3 = 39
Algebraic
8𝑧 = 24𝑧 + 60
Equations
4𝑦 + 5 = 17
1.How would you describe algebraic EXPRESSION?
Algebraic EQUATION?
2.How do they differ?
Determine which of the following are sentences
(complete idea) and which are phrases (not
complete thought).
𝒔𝒆𝒏𝒕𝒆𝒏𝒄𝒆
1.
2.
3.
4.
Ten is five less than a number. (𝟏𝟎 = 𝒙 − 𝟓)
Four increased by a number is nine. (𝟒 + 𝒏 = 𝟗)
𝒔𝒆𝒏𝒕𝒆𝒏𝒄𝒆
Five less than a number. (𝒙 − 𝟓) 𝒑𝒉𝒓𝒂𝒔𝒆
Four increased by a number. (𝟒 + 𝒏) 𝒑𝒉𝒓𝒂𝒔𝒆
Note: The mathematical expression is
equivalent to an English phrase. The
most common mathematical
statements or sentences are called
equations.
An expression is a mathematical
phrase that combines numbers and/or
variables using mathematical
operations. There is no equal sign.
Example:
𝒙−𝟓
𝟒+𝒏
An equation is a mathematical
sentence that combines numbers
and/or variables that shows the
equality of two expressions.
There must be an equal sign.
Example: 𝟏𝟎 = 𝒙 − 𝟓
𝟒+𝒏=𝟗
EXPRESSSION
EQUATIONS
Do not show
Show relationships
relationships
Do not have any
Have solutions
solutions
Typical English phrase Complete sentences
Incomplete sentences
Have equal sign
Can only be simplified
Can be solved
Rubrics for scoring:
Points
3
2
1
Teamwork All the group members
Several group
There is only one
worked together
members are working
working
Accuracy
Identified terms are
Identified terms are
Identified terms
correct and the
correct and the
are incorrect and
translation of verbal
translation of verbal the translation of
phrase to
phrase to
verbal phrase to
mathematical phrase mathematical phrase
mathematical
are accurate
have minimal error
phrase are
inaccurate
Timebound
The output is
The output is
The output is
summitted before the summitted on time summitted beyond
allotted time
the timebound
Group Activity:
TRANSLATE the given verbal phrases or sentences as
mathematical expressions/equations inside the box. Then, identify if
each of the following is algebraic EXPRESSION or EQUATION.
a. A number increased by nine is fifteen.
b. The sum of the numbers x and y.
c. Twice a number is eighteen.
d. Twelve is sixteen more than four times a number.
e. Five subtracted from a number.
THINK-PAIR-SHARE
Translate each item into an algebraic
expressions and equations and find your
answer in the corresponding answer
column. Write the letter of that exercise in
the box that contains the number of the
answer.
Answer: ROBERT RECORDE
Robert Recorde (c.1512-1558) was a
Welsh physician and mathematician. He
invented the equals sign (=) and also
introduced the pre existing plus sign (+)
to English speakers in 1557.
Algebraic expression is a combination of
variables, numbers, and/or operations that
represents a mathematical relationship, but
no statement of equality or inequality.
(DOES NOT HAVE AN equal sign)
Algebraic equation is a mathematical statement that
two or more expressions are equal.
(MUST HAVE AN equal sign)
Write EX if the given item is expression and EQ if its
equation.
________ 1. 5𝑥 + 𝑦 = 7𝑔
______ 6. 4𝑠𝑡 = 6
________ 2. 6𝑡
______ 7. 13 = 5 + 𝑘
________ 3. 4𝑐 − 4ℎ − 2𝑡
______ 8. −4𝑦 = 16 − 2𝑦
________ 4. 12 − 𝑔
_______ 9. 𝑡 − 5
________ 5. 6 + 𝑓 − 7𝑡 = 35
_______ 10. 6 = 𝑦 + 14
ASSIGNMENT:
Give at least three (3) examples
of algebraic expressions and (3)
examples of algebraic equations.