# 27 - Introducing to Algebraic Expressions Contributed by: This pdf includes the following topics:-
Expressions
What is a variable?
Algebraic Expressions
What are coefficients?
What is a term?
What are constants?
Writing Algebraic Expressions
1. Algebraic Expressions and
Terms
Unit 1
2. Expressions
You are familiar with the following type of
numerical expressions:
12 + 6
3 (12)
6 (3 + 2)
15 - 4 (6)
3. What is a variable?
In the expression 12 + B, the letter “B” is a
variable.
A variable is a letter or symbol that
represents an unknown value.
4. Algebraic Expressions
When variables are used with other
numbers, parentheses, or operations, they
create an algebraic expression.
a + 2
(a) (b)
3m + 6n - 6
5. What are coefficients?
A coefficient is the number multiplied by the
variable in an algebraic expression.
Algebraic Expression Coefficient
6m + 5 6
8r + 7m + 4 8, 7
14b - 8 14
6. What is a term?
A term is the name given to a number, a
variable, or a number and a variable
combined by multiplication or division.
Algebraic Expressions Terms
a + 2 a, 2
3m + 6n - 6 3m, 6n, - 6
7. What are constants?
A constant is a number that cannot
change its value.
In the expression: 5x + 7y - 2
the constant is - 2.
8. Figure it out!
Identify the terms, coefficients, and constants.
1. 12a - 6b + 4
2. 4x - 2y
3. c - 32
4. 3x + 2
9. Writing Algebraic Expressions
 You can translate word phrases into variable
expressions.
 Examples:
1. Three more than a number =
2. The quotient of a number and 8 =
3. Six times a number =
4. 15 less than a number =
5. The quotient of 30 and a number plus 10 =
10. Key words to look for:
Plus Difference
Sum Subtract
Total Less than
Increased by Decreased by
More than less
11. Cont…
 Multiplication  Division
Product Quotient
Times divide
multiply
12. Write algebraic expressions for
these word phrases
1. Four more than s
2. The product of 7 and c
3. Nine less than x
4. A number divided by the sum of 4 and 7.
5. Twice the sum of a number plus 4.
6. The sum of ¾ of a number and 7.
7. Ten times a number increased by 150.
13. Write an algebraic phrase for these
situations
1. A car was traveling 35 miles per hour
for a number of hours.
2. Bob ran 7 times a week for a number of
weeks.
3. The plumber added an extra \$35 to her
bill.
4. Thirty-five fewer people came than the
number expected.
14. How do you describe a
variable expression?
Variable Meaning Operation
5x, 5·x, (5)(x) 5 times x Multiplication
(same as x·5)
5÷ x 5 divided by Division
5/x x
5 + x (same as x + 5 plus x Addition
5–x 5 minus x subtraction
15. Evaluate a Variable Expression
 Example 1: Evaluate each expression
when n = 4. Simplify
Simplify(means
(meansto tosolve
solvethe
theproblem
problemor
orperform
perform
as many of the indicated operations as possible.)
as many of the indicated operations as possible.)
a. n + 3
Solution: n + 3 = 4 + 3Substitute 4 for n. Simplify
=7
b. n – 3
Solution: n – 3 = 4 – 3 Substitute 4 for n. Simplify
=1
16. Evaluate an Algebraic
Expression
 Example 2: Evaluate each expression if x = 8.
a. 5x
Substitute 8 for x. Simplify
5x = 5(8)
Solution: Using
Usingparenthesis
parenthesisisisthe
thepreferred
preferredmethod
methodtotoshow
show
Solution: = 40 multiplication.
waystotoshow
showmultiplication
multiplicationare
are
55· ·88and 5 x 8.
and 5 x 8.
b. x÷4
Substitute 8 for x.
x÷4=8÷4
Simplify
Solution:
=2 x 8
Recall 
Recallthat
thatdivision
divisionproblems
problemsare
arealso
also 4 4
fractions – this problem could be
fractions – this problem could be 2;
written
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as: because
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x 4 
4
17. Evaluating More Expressions
 Example 3: Evaluate each expression if x
= 4, y = 6, and z = 24.
a. 5xy Substitute 4 for x; 6 for y. simplify
Solution: 5xy = 5(4)(6)
= 120
b. z Substitute 24 for z; 6 for y. Simplify.
y
Solution:
z 24

y 6
=4
18. Now You Try…
Evaluate each expression given that a = 6, b =
12, and c = 3.
1. 4ac A
2. a÷c A
3. a+b+c A
4. ba A
5. b–c A
6. c÷b
A
19. You Try #1
Evaluate each expression given that a = 6, b
= 12, and c = 3.
1. 4ac Substitute
Substitutethe
thevalue
valuefor
foraa==66and
andcc==33
into
intothe
theproblem
problemand
andmultiply
multiply
4ac = 4(6)(3)
= (24)(3)
= 72
Click
Clickto
toreturn
returntoto
“You try it” slide
“You try it” slide
20. You Try #2
Evaluate each expression given that a = 6, b
= 12, and c = 3.
2.a ÷ c Substitute
Substitutethe
thevalue
valuefor
foraa==66and
andcc==33
into
intothe
theproblem
problemand
anddivide
divide
a÷c=6÷3
=2
Click
Clickto
toreturn
returntoto
“You try it” slide
“You try it” slide
21. You Try #3
Evaluate each expression given that a = 6, b
= 12, and c = 3.
3. a + b + c Substitute
Substitutethe
thevalue
valuefor
foraa==6,6,b=12,
b=12,
and
and c = 3 into the problem, thenadd.
c = 3 into the problem, then add.
a + b + c = 6 + 12 + 3
= 18 + 3
= 21
Click
Clickto
toreturn
returntoto
“You try it” slide
“You try it” slide
22. You Try #4
Evaluate each expression given that a = 6, b
= 12, and c = 3.
4.ba Substitute
Substitutethe
thevalue
valuefor
forb=12
b=12and
andaa==66
into
intothe
theproblem,
problem, then
thenmultiply.
multiply.
ba = (12)(6)
= 72
Click
Clickto
toreturn
returntoto
“You try it” slide
“You try it” slide
23. You Try #5
Evaluate each expression given that a = 6, b
= 12, and c = 3.
5.b - c Substitute
Substitutethe
thevalue
valuefor
forb=12
b=12and
andaa==33
into
intothe
theproblem,
problem, then
thensubtract.
subtract.
b – c = 12 – 3
=9
Click
Clickto
toreturn
returntoto
“You try it” slide
“You try it” slide
24. You Try #6
Evaluate each expression given that a = 6, b
= 12, and c = 3.
6.c ÷ b Substitute
Substitutethe
thevalue
valuefor
forc=3
c=3and
andbb==12
12into
into
the
theproblem,
problem, then thenDivide
Divide
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