Section 1.3A
Write each phrase as an algebraic expression:
a.
The product of b and c.
e.
b divided into c
b.
The ratio of b to c.
f.
The difference of b and c
c.
b subtracted from c
g.
b divided by c
d.
The sum of b and c
h.
The quotient of b and c.
1.3 A Class Exercise
1. On the whiteboard, write an algebraic expression involving a math operation (+, –, ,  or  )
and at least one variable.
2. Exchange papers with another student. (Multiple exchanges are OK!)
3. On your paper, write an English phrase that corresponds to the expression shown.
1.3B Evaluating Algebraic Expressions
Let a = 2, b = 5, c = 12. Evaluate the following:
13 – b
8ab
12
c
c–a
c – ab
0.4c
Page 31 # 6: The registrar at City College predicts a 4% enrollment increase for all
departments next year. This means a department that has p students this year can expect 1.04p
students next year.
a.
If the English department has 5200 students this year, predict next year’s enrollment.
b.
Explain how a department with p students this year can predict next year’s enrollment.
c.
Evaluate the expression
p
600
for the given values of p.
1300
1700
2200
2600
3500
1.4A. Translating English to Algebra
(for everyday situations)
Examples: Match each situation with one of the following algebraic expressions:
m + 15
15
m
m – 15
15m
15 – m
m
15
1. Nolan and Shawn together ate 15 hamburgers last week. If Nolan ate m hamburgers, how
many did Shawn eat?
2. Brook drove 15 miles more than Nicole. If Nicole drove m miles, how many miles did
Heather drive?
3. The sale price of a pair of jeans is $15 less than the regular price. If the regular price is $m,
what is the sale price?
4. Virginia bought 15 candy bars for a group of children. If there are m children in the group,
how many candy bars does each get?
5. Jeff has 15 chapters of a history book to read. If he has m days to complete the assignment,
how many chapters should he read each day?
6. Emily exercises for 15 minutes each day. If she exercises for m days, how many minutes has
she spent?
For each of the following situations (word phrases) do the following:
a.
Identify the unknown quantity.
b.
Choose a variable to represent the unknown quantity.
c.
Write an algebraic expression for the phrase.
1.
Two and one-half inches taller than Lacy.
2.
The quotient of the circumference of a circle and 3.14159.
1.4B Some Common Algebraic Expressions
The distance traveled by by an object moving at constant speed r for a time t.
The time it takes for an object moving at a constant speed r to travel a distance d.
Numeric example:
To find the average of a set of values, divide the sum, S of the values by the number of values n.
Numeric example:
The interest on an amount of money $P (the principal) invested at an annual rate r for t years.
Numeric example:
To find the percentage of a whole amount, multiply the percentage rate r by the whole amount
W.
Numeric example:
Example:
Each member of the Oregon Mathematical Association of Two-Year Colleges (ORMATYC)
pays $8 annual dues. Choose a variable for the number of members and write an expression for
the amount that the association earns in dues.
If the association has 120 members, how much does it earn in dues?