Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Section 12 Variables and Expressions
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1 Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Please watch Section 12 of this DVD before working these problems. The DVD is located at: Page 1
2 1) Solve the following. 2) Solve the following. Page 2
3 3) Solve the following. 4) Solve the following. Page 3
4 5) Solve the following. 6) Solve the following. Page 4
5 7) Solve the following. 8) Solve the following. Page 5
6 9) Solve the following. 10) Solve the following. Page 6
7 11) Solve the following. 12) Solve the following. Page 7
8 13) Solve the following. 14) Solve the following. Page 8
9 1) Solve the following. Before we can solve the arithmetic we must first substitute the variable value into the problem. In this case we have the variable x which we know equals 4. We can now complete the arithmetic to find our answer. 2) Solve the following. Before we can solve the arithmetic we must first substitute the variable value into the problem. In this case we have the variable y which we know equals 4. We can now complete the arithmetic to find our answer. Page 9
10 3) Solve the following. Before we can solve the arithmetic we must first substitute the variable value into the problem. In this case we have the variable x which we know equals 2 and there are two places to substitute. We can now complete the arithmetic to find our answer. 4) Solve the following. Before we can solve the arithmetic we must first substitute the variable value into the problem. In this case we have the variable y which we know equals 5. We can now complete the arithmetic to find our answer. Page 10
11 5) Solve the following. Before we can solve the arithmetic we must first substitute the variable values into the problem. In this case we have the variables x and y. x equals -2 and y equals 5. We can now complete the arithmetic to find our answer. 6) Solve the following. Before we can solve the arithmetic we must first substitute the variable values into the problem. In this case we have the variables x and y. x equals 4 and y equals -1. We can now complete the arithmetic to find our answer. Page 11
12 7) Solve the following. Before we can solve the arithmetic we must first substitute the variable values into the problem. In this case we have the variable z which we know equals -1. Remember, a negative number squared becomes a positive number. We can now complete the arithmetic to find our answer. Page 12
13 8) Solve the following. Before we can solve the arithmetic we must first substitute the variable values into the problem. In this case we have the variable t which we know equals 2. We can now complete the arithmetic to find our answer. Page 13
14 9) Solve the following. Before we can solve the arithmetic we must first substitute the variable values into the problem. In this case we have the variables x and y. We know x equals -2 and y equals 3. Remember, a negative number cubed is multiplying a negative number by it s self an odd number of times, therefore the result is negative. We can now complete the arithmetic to find our answer. Page 14
15 10) Solve the following. Before we can solve the arithmetic we must first substitute the variable values into the problem. In this case we have the variables x and y. We know x equals 4 and y equals 2. We can now complete the arithmetic to find our answer. The first step is to simply the improper fraction which is easily done since 4/2 =2. Page 15
16 11) Solve the following. Before we can solve the arithmetic we must first substitute the variable values into the problem. In this case we have the variables x and y. We know x equals 2 and y equals 3. We can now complete the arithmetic to find our answer. Multiplying the numbers in the numerator yield a numerator of 6 and adding the numbers in the denominator yield a new denominator of 5. The answer is an improper fraction which can be simplified as shown the left and covered in previous lessons. Page 16
17 12) Solve the following. Before we can solve the arithmetic we must first substitute the variable values into the problem. In this case we have the variables x and y. We know x equals 4 and y equals 3. We can now complete the arithmetic to find our answer. Simplifying the problem yields two fractions that are to be added. Before we can add to fractions we need to find a common denominator. The lowest common multiple of 4 and 3 is 12. Thus we ll make each of the fractions have a denominator of 12 as shown to the left and covered in previous lessons. Now that the fractions have a common denominator, we can add them. The result is an improper fraction that can be simplified as shown. The answer cannot be further simplified so we are complete. Page 17
18 13) Solve the following. Before we can solve the arithmetic we must first substitute the variable values into the problem. In this case we have the variables x and y which we know equal 4 and -2 respectively. ( 1) (1+ 2) = We can now complete the arithmetic to find our answer. Simplifying the problem yields two fractions that are to be added. Before we can add to fractions we need to find a common denominator = -1i2 3i The lowest common multiple of 3 and 6 is 6. Thus we ll make each of the fractions have a denominator of 6 as shown to the left and covered in previous lessons. = Page 18
19 Now that the fractions have a common denominator, we can add them. The answer cannot be further simplified so we are complete. Page 19
20 14) Solve the following. Before we can solve the arithmetic we must first substitute the variable values into the problem. In this case we have the variables x and y. We know that x equals 3 and y equals -1. ( )(9 + 1) ( = )(10) 5 = = = 4 We can now complete the arithmetic to find our answer. Simplifying the problem yields a fraction but since the denominator, 5, divides evenly into -10, we can simply convert this to a whole number (-2). The answer cannot be simplified further so we are complete. 4 Page 20
Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Section 15 Dividing Expressions
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