DrDelMath

Elementary Algebra Exercises Section 1.1

As you study these exercises, move your cursor over the
light bulbs, highlighted words, equal symbols, arrows, and other graphic items.
Study with an active cursor.

The definition that pops up when you move the cursor over a highlighted word is what should pop into your mind when you read, hear, or speak that word. The material that pops up when you move the cursor over a light bulb is a suggested strategy for solving the problem. You should always formulate a similar strategy when you attempt to solve a problem. When you move the cursor over an explanation of a step in a solution, the property that pops up is the mathematical justification for taking that action. You must always be able to provide such a justification for every step you take in mathematics.

10. Is 18 + m an algebraic expression or an equation ?
Solution:   18 + m is an algebraic expression. (because it is a sum of terms)

12. Is y - 1 = 2 an algebraic expression or an equation ?
Solution:    y - 1 = 2 is an equation. (because it contains an = symbol)

14. Is t = 16b algebraic expression or an equation ?
Solution:    t = 16b is an equation. (because it contains an = symbol)

16. Is algebraic expression or an equation ?
Solution:   is an algebraic expression. (because it is a quotient of a sum of terms divided by a term)

18.  What operations does the expression contain ?
Solution:   The algebraic expression contains the operations of addition and division.

20.  What operations does the expression y + 14 = 5(6) contain ?
Solution:    The equation y + 14 = 5(6) contains the operations of addition and multiplication.

30. Write without using a multiplication symbol or parenthesis.
Solution:   may be written as 5y. (because juxtaposition causes no confusion)

32. Write without using a multiplication symbol or parenthesis.
Solution:   may be written as 22qs. (because juxtaposition causes no confusion)

34. Write without using a multiplication symbol or parenthesis.
Solution:   may be written as bh. (because juxtaposition causes no confusion)

38. Write without using a multiplication symbol or parenthesis.
Solution:   may be written as . (because juxtaposition causes no confusion)

38. Write (r)(t) without using a multiplication symbol or parenthesis.
Solution:  (r)(t) may be written as rt. (because juxtaposition causes no confusion)

42. Write using a fraction bar.
Solution:   may be written as .

44. Write using a fraction bar.
Solution:   may be written as .

46.    is read as the product of 45 and 12.

47.   11 - 9 is read as the difference of 11 minus 9.

48.   65 + 89 is read as the sum of 65 and 89.

50.   16t is read as the product of 16 and t.

51.    is read as the quotient of 66 divided by 11.

52.    is read as the quotient of 12 divided by 3.

       

57.  Translate the following verbal statement into an equation.
The amount of sand that should be used is the product of 3 and the amount of cement used.
Solution:
Let the variable s represent the amount of sand to be used.
Let the variable c represent the amound of cement used.
The problem states that the amount of sand must be 3c.
We now have two algebraic expressions for the amount of sand to be used (namely s and 3c)
Since the two algebraic expressions represent the same quantity, they must be equal and we get the equation s = 3c.

58.  Translate the following verbal statement into an equation.
The number of waiters needed is the quotient of the number of customers divided by 10.
Solution:
Let the variable w represent the waiters required.
Let the variable c represent the number of customers.
The problem states that the number of waiters must be .
We now have two algebraic expressions for the waiters required (namely w and )
Since the two algebraic expressions represent the same quantity, they must be equal and we get the equation .

59.  Translate the following verbal statement into an equation.
The weight of the truck is the sum of the weight of the engine and 1200.
Solution:
Let the variable w represent the weight of the truck.
Let the variable e represent the weight of the engine.
The problem states that the weight of the truck is e + 1200.
We now have two algebraic expressions for the weight of the truck (namely w and e + 1200)
Since the two algebraic expressions represent the same quantity, they must be equal and we get the equation w = e + 1200.

60.  Translate the following verbal statement into an equation.
The number of classes that are still open is the difference of 150 minus the number of classes that are closed.
Solution:
Let the variable n represent the number of classes that are open.
Let the variable c represent the number of classes that are closed.
The problem states that the the number of classes that are open is 150 - c.
We now have two algebraic expressions for the number of classes that are open (namely n and 150 - c)
Since the two algebraic expressions represent the same quantity, they must be equal and we get the equation n = 150 - c.

61.  Translate the following verbal statement into an equation.
The profit is the difference of the revenue minus 600.
Solution:
Let the variable p represent the profit.
Let the variable r represent the revenue.
The problem states that the profit is r - 600.
We now have two algebraic expressions for the profit (namely p and r - 600)
Since the two algebraic expressions represent the same quantity, they must be equal and we get the equation p = r - 600.

62.  Translate the following verbal statement into an equation.
The distance is the product of the rate and 3.
Solution:
Let the variable d represent the distance.
Let the variable r represent the rate.
The problem states that the distance is 3r.
We now have two algebraic expressions for the distance (namely d and 3r)
Since the two algebraic expressions represent the same quantity, they must be equal and we get the equation d = 3r.

63.  Translate the following verbal statement into an equation.
The quotient of the number of laps run divided by 4 is the number of miles run.
Solution:
Let the variable k represent the number of laps run.
Let the variable m represent the number of miles run.
The problem states that the number of miles is .
We now have two algebraic expressions for the distance (namely m and )
Since the two algebraic expressions represent the same quantity, they must be equal and we get the equation .

64.  Translate the following verbal statement into an equation.
The sum of the tax and 35 is the total cost.
Solution:
Let the variable t represent the tax.
Let the variable C represent the total cost.
The problem states that the total cost is 35 + t.
We now have two algebraic expressions for the total cost (namely C and 35 + t)
Since the two algebraic expressions represent the same quantity, they must be equal and we get the equation C = 35 + t.