The Factor Tree
Example 12 Evaluate x + 3 if x = 4.
Replace x with 4. Add.
Example 13 Evaluate 2 ( r – 5 ) if r = 3.
Replace r with 3. Simplify within the
parentheses by subtracting .
Multiply .
Example 14 Evaluate 2 ( x + y ) if x = 4 and y = –1.
Replace x with 4 and y with –1. Simplify within
the parentheses by adding.
Multiply.
Example 15 Evaluate
if
a = 2 and b = 8.
Replace a with 2 and b with 8.
The fraction bar serves as a grouping symbol .
Completely simplify the top and completely
simplify the bottom before dividing. Start by
adding on the top .
Divide.
Example 16 Evaluate
if r = 16 and s = –5.
Replace r with 16 and x with –5. Evaluate the
root and exponent .
Multiply.
Subtract.
Example 17 Evaluate
if
x = 5, y = 2 and z = 4.
Replace x with 5, y with 2, and z with 4.
The fraction bar serves as a grouping symbol.
Completely simplify the top and completely
simplify the bottom before dividing. Start by
evaluating the exponent.
Add or subtract in order from left to right.
Divide.
In application problems you may find it necessary to first write an algebraic
expression before
you can evaluate the expression. Recall from chapter 1 the words that represent
the different
mathematical operations .
Example 18 Write an algebraic expression for each of the following. Use x
to
represent “a number”. Evaluate the expression when x = 2.
a) Twice a number
| Words: | Twice | a number |
| Algebraic 2 Expression : | 2 | • x |
| Evaluate: |
 |
b) Negative ten minus a number
| Words: | Negative ten | minus | a number |
| Algebraic Expression: | 10 | - | x |
| Evaluate: |
 |
c) Seven more than a number (the word than will reverse the order )
d) The product of a number and negative three
| Words: | a number | The product of and |
negative hree |
| Expression: | 3 | • | (-3) |
| Evaluate: |
 |
e) Eight times a number divided by four.
| Words: | eight | times | a number | divided by | four |
| Expression: | 8 | • | x | ÷ | 4 |
| Evaluate: |
 |
In 21-25, find the average.
21. Find the average of 12, 7, 0, 8, & 23. 22. Find the average of –5, –10, 18,
& –27.
23. Tommy’s allowance for the last 6 weeks was $10, $12, $15, $10, $8, and $11.
What was
his average weekly allowance?
24. Cali’s test scores in her English class were 84%, 73%, 98% and 90%. What was
her
average test score.
25. The morning temperatures for the last week were
. What
was the average morning temperature?
In 26-33, evaluate the following expressions for x = 5, y = –2, and z = 3.
In 34-41, write an algebraic expression for the each of
the following. Use x, to represent “a
number”. Evaluate the expression when x = 2.
34. The sum of three and a number.
35. The difference between a number
and twelve.
36. The quotient of six and a number.
37. The product of a number and
negative seven.
38. Fifteen less than a number.
39. Twenty-four decreased by twice a
number.
40. The square of a number increased by
negative seven.
41. The difference of three times a
number and four.
2.4 REVIEW EXERCISES
In 1-4, use a factor tree to write the prime factorization of each number.
In 43-46, write an algebraic expression for the each of
the following. Use x, to represent “a
number”. Evaluate the expression when x = 2.
43. The sum of a number and (–5).
44. 4 less than a number.
45. The quotient of (–8) and a number.
46. Twice a number increased by 3.
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