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Section 11—Writing Expressions and Equations
Background:
1.
An algebraic expression can contain numbers, variables, powers, and operations
(addition, subtraction, multiplication, and division), but NO equal sign.
For example:
•
3x + 4
•
5x
•
6xy
•
x  y
2.
A numerical expression contains numbers, powers, and operations.
For example:
•
7 + 5
•
2 – 3 • 4
•
3
7
3.
An algebraic equation is an algebraic expression that also contains an equal sign
4.
Word and Symbols Equivalencies
Addition Symbol
plus
“the sum of”, “and”
increased by
more than
added to
+
the total of
Subtraction Symbol
minus
decreased by
“the difference of”, “and”
fewer than

subtracted from
Multiplication Symbol
times
“the product of”, “and”
multiplied by
at
•
(
)
x
of
Division Symbol
divided by
“the quotient of”, “and”
the ratio of
fraction bar
÷
per
Switch
than
from
Equal Sign
is equal to
is the same as
is as much as
=
is identical to
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View Full Document Procedure and Examples:
A.
Writing an algebraic expression for each verbal expression
1.
Replace each word with a symbol or number
•
If the word sum, difference, product, or quotient is used then replace the
word “and” with the correct symbol
•
If the word “than” or “from” is used then switch the order of the numbers
or variables directly before and after the operation (for example the
number or variable before the operation goes after the operation, and the
number or variable after the operation goes before the operation
•
Parentheses can only be written using the words “sum, difference, product,
and quotient”
2.
Reduce the fraction
3.
Rewrite the ratio as a to b or a:
•
The numerator is the first number
•
The denominator is the second number
A.
Examples:
On a separate sheet of paper, write an algebraic expression for each
verbal expression–
1.
Four more than t
2.
eleven decreased by the quotient of x and 2
3.
the product of 7 and x increased by 5 is nine
4.
the quotient of p and 8
5.
seven less than three times g is 3
6.
twelve subtracted from the sum of g and 8
B.
Writing a verbal expression for each algebraic expression
1.
Replace each symbol or number with a word
2.
If the word sum, difference, product, or quotient is used then replace the
word “and” with the correct symbol
•
If parentheses are needed then the words “sum, difference, product, and
quotient” must be used
B.
Examples:
On a separate sheet of paper, rite an algebraic expression for each
verbal expression —
1.
7
q
2.
3x – 8
3.
10 = 4r – 6
4.
5(b – 3)
5.
=
20
8
t
6.
7 = (8 + q)
2
Section 12—Order of Operations
Background:
1.
The order of operations is the order in which a problem with many steps in it is
solved.
2.
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