Sec. 1.2 A: Using letters for Variables
I. Examples of Mathematical Sentences:
Ex. 1: My daughter, Sarah, is two years older than her sister, Katey.
a) Fill in the table, showing each calculation:
Sarah's Age
11
15
18
20
Calculation
Katey's Age
b) Explain in words how to find Katey's age if you know Sarah's age.
c) Write a Mathematical Sentence (using names, operation, and =) giving Katey's age in terms of Sarah's age.
d) Choose a variable to represent Sarah's age.
Let _________ : Sarah's Age in years
e) Write a Mathematical Sentence for Katey's age in term's of Sarah's age using the variable you chose in d).
Ex. 2: A store is offering a 20% OFF SALE.
a) Fill in the table, showing the calculations:
Regular Price
$10
$15
$25
Calculation
Sale Price
b) Explain in words how to find the sale price. (There is more than one way.)
c) Write a Mathematical Sentence for the Sale Price in terms of the Regular Price. (use words, operation, =)
d) Let ________ : Regular Price
e) Write a Mathematical Sentence using the variable from d)
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Sec. 1.2 B Algebraic Expressions:
I. Terminology:
Algebraic Expression:
Simplify:
Evaluate:
Sum:
Terms:
Product:
Factors:
Difference:
Quotient:
Ratio:
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II. Examples: Write Algebraic Expressions for each of the following: (Note: in algebrqa avoid using the "x" for times. Instead, we write variables next to each other, use a dot or parentheses.)
1. 10 reduced by y
2. n split 4 ways
3. p subtracted from 18
4. The quotient of 10 and y
5. The total of c and d
6. The quotient of 9 and t
7. Half of w
8. 5 minus d
9. The product of w and three
10. t divided into d
11. The sum of five and t
12. The difference of x and 6
13. The ratio of R to 3
14. 8 more than u
15. Three times x
16. m decreased by 7
17. The difference of 7 and z
18. m less than 12
19. w less 7
20. 6 plus half of w
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III. Review:
When you add two numbers, the result is called a ____________ and the things added together are called ____________________.
When you multiply two numbers, the result is called a ____________ and the things multiplied together are called ____________________.
When you subtract numbers, the result is called a ____________________ .
When you divide numbers, the result is called a __________________ or a __________________. 4