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# Algebraic Expressions Worksheets 2

Lesson Plans > Mathematics > Algebra > Expressions

## Algebraic Expressions Worksheets 2 These worksheets are slightly more advanced than the ones in the previous problem set. In these problems, students are required to convert compound phrases into algebraic expressions. For example, instead of "twice a number," students will have phrases like "three less than twice a number."

Students doing this for the first time will sometimes have difficulty recognizing the order in which phrases should be processed. For instance, the phrase "five less than two times a number" can be interpreted in two different ways:

Five less than (two times a number) = 2n - 5
(Five less than two) times a number = (2 - 5)n = -3n

Another example would be: "Five times two more than a number"

Five times (two more than a number) = 5(n + 2)
(Five times two) more than a number = (5 x 2) + n = 10 + n

In both of these cases, the first interpretation is the proper one. Explaining why this is so can be a challenge. A lot of it has to do with how we naturally group phrases in written and spoken language. The second interpretation of the second expression is verbally awkward.

What if we wanted to interpret "five less than two times a number" as "(five less than two) times a number"? We would probably put a comma after the word two: "Five less than two, times a number."

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Lesson by Mr. Twitchell

## Algebraic Expressions Worksheet #2.1

For each phrase below, pick variables to represent the unknowns. State what the variables represent, and then write the phrase as an algebraic expression.

Example:     One dollar less than twice the cost of an apple
Solution:      a = the cost of an apple; 2a - 1

1. Twice the sum of two numbers

2. The sum of a number and half that number

3. The product of the width and two more than the width

4. Four more than a number, times three less than a number

5. Two more than half the number of marbles

6. Six times two more than a number

7. Two dollars less than the value of n nickels

8. Twice the value of some dimes

9. Three less than four more than a number

10. A microwave's price is decreased by \$30, and then doubled

11. One third of two more than a number

12. Twice the sum of the length and the width

13. The value of some pennies and the value of some nickels combined

14. Six less than twice the sum of two numbers

15. Two thirds of twice my age, decreased by seven

## Algebraic Expressions Worksheet #2.1: Answer Key

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## Algebraic Expressions Worksheet #2.2

For each phrase below, pick variables to represent the unknowns. State what the variables represent, and then write the phrase as an algebraic expression.

Example:     Twice the cost of an item which has been discounted by \$19
Solution:      p = the original price; 2(p - 19)

1. Half the difference between 7 and the current day of the month

2. The product of a number and one more than that number

3. Two thirds of the five less than Harold's age

4. The ratio of a number to that number reduced by three

5. The number of miles per gallon during a 500 mile trip, if I used three full gas tanks

6. The difference in price between three widgets and two fidgets

7. The number of seconds in h hours and m minutes

8. The product of the sum of two numbers with their difference

9. Four less than seven times the product of Nan's and Van's ages

10. The sum of Andy's and Randy's ages five years ago

11. The sum of Paul's age seven years ago, and Paul's age in eight years

12. The sum of the product of the length and width of a rectangle and seventeen

13. One third of eighteen minus a number

14. Half of a third of all my teachers

15. Half of a price which has already been discounted by \$7

## Algebraic Expressions Worksheet #2.2: Answer Key

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