Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Section 15 Dividing Expressions
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1 Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Please watch Section 15 of this DVD before working these problems. The DVD is located at: Page 1
2 1) Simplify. 2) Simplify. Page 2
3 3) Simplify. 4) Simplify. Page 3
4 5) Simplify. 6) Simplify. Page 4
5 7) Simplify. 8) Simplify. Page 5
6 9) Simplify. 10) Simplify. Page 6
7 11) Simplify. 12) Simplify. Page 7
8 13) Simplify. 14) Simplify. Page 8
9 1) Simplify. Anything that is in the denominator and the numerator can be canceled. x is in the top and the bottom of the equation so we can cancel x from both. Both 9 and 3 contain a factor of 3, so we can simplify those as well by dividing top and bottom by 3. The answer cannot be simplified further so we are complete. Page 9
10 2) Simplify. Anything that is in the denominator and the numerator can be canceled. m is in the top and the bottom of the equation so we can cancel m from both. Both 18 and 6 contain a factor of 6, so we can simplify those as well by dividing top and bottom by 6. The answer cannot be simplified further so we are complete. Page 10
11 3) Simplify. Anything that is in the denominator and the numerator can be canceled. Since y 2 is really y*y, we can cancel the y from the top with one of the y s from the bottom. Both 8 and 4 contain a factor of 4, so we can simplify those as well by dividing top and bottom by 4. The answer cannot be simplified further so we are complete. Page 11
12 4) Simplify. The easiest way to simplify this fraction is to divide it up such that each numerator term is its own fraction. Since the numerator has a subtraction, the resulting two fractions are subtracted. The resulting two fractions are easily simplified since the denominator divides easily into the numerators. The answer cannot be simplified further so we are complete. Page 12
13 5) Simplify. The easiest way to simplify this fraction is to divide it up such that each numerator term is its own fraction. Since the numerator has a subtraction, the resulting two fractions are subtracted. The resulting two fractions are easily simplified since the denominator divides easily into the numerators. The answer cannot be simplified further so we are complete. Page 13
14 6) Simplify. The easiest way to simplify this fraction is to divide it up such that each numerator term is its own fraction. Since the numerator has an addition, the resulting two fractions are added. From the first fraction we can cancel a factor of 4 from the numerator and the denominator as well as a single factor of x. From the second fraction we can cancel a factor of x. The answer cannot be simplified further so we are complete. Page 14
15 7) Simplify. The easiest way to simplify this fraction is to divide it up such that each numerator term is its own fraction. Since the numerator has a subtraction, the resulting two fractions are subtracted. From the first fraction, we can cancel a factor of i as well as simplify 6/2 which is 3. For the second fraction, we can cancel a single factor of i as well simplify 10/2 which is 5. The answer cannot be simplified further so we are complete. Page 15
16 8) Simplify. The easiest way to simplify this fraction is to divide it up such that each numerator term is its own fraction. Since the numerator has an addition, the resulting two fractions are added. We can cancel a factor of j 2 from each fraction. We can also simplify 21/3 which is 7. The answer cannot be simplified further so we are complete. Page 16
17 9) Simplify. The easiest way to simplify this fraction is to divide it up such that each numerator term is its own fraction. Since the numerator has a subtraction, the resulting two fractions are subtracted. We can cancel a factor of x from each fraction. -1/-1=+1. Since x/-1=-x, the negative sign of the second term will cancel with the subtraction sign turning this into an addition problem. The answer cannot be simplified further so we are complete. Page 17
18 10) Simplify. The easiest way to simplify this fraction is to divide it up such that each numerator term is its own fraction. Since the numerator has a subtraction, the resulting two fractions are subtracted. In the first fraction, we can cancel both 4 and a single factor of i. In the second fraction, a single factor of i cancels and we can simplify 12/-4, which is 3/-1. Further simplifying, i/-1=-i. Also, 3/-1=-3. The answer cannot be simplified further so we are complete. Page 18
19 11) Simplify. The easiest way to simplify this fraction is to divide it up such that each numerator term is its own fraction. 142mn /2 7 n + 213mn 7 n + 355n 7 n = 2mn + 3m + 5 We can cancel a single factor of n from each fraction. Additionally, 14/7 simplifies to 2, 21/7 is 3, and 35/7 is 5. The answer cannot be simplified further so we are complete. Page 19
20 12) Simplify. The easiest way to simplify this fraction is to divide it up such that each numerator term is its own fraction. 9x 2 y 2 xy xy 32 xy + xy xy = 9xy y2 + 1 We can cancel both a single factor and x and y from each fraction. The answer cannot be simplified further so we are complete. Page 20
21 13) Simplify. One way to begin simplification is to first multiply the 12x into the numbers in the parenthesis and then simplify by dividing in the bottom of the fraction. However, in certain situations, if we do some initial simplification, it will make the problem much easier. We can cancel a single factor of x in the top and bottom as well as simplify 12/3 which is 4. 4i9x + 4i6x 2 x 36x + 24x 2 x Next, let s multiply the 4 into the parenthesis. We then complete the multiplication. 36x x + 24x2 x Now we can divide up the fraction by dividing each of the numerators by the denominators. Page 21
22 36 x x + 24x 2 x = x We can cancel a single factor or x from both equations and further simplify. The answer cannot be simplified further so we are complete. Page 22
23 14) Simplify. The easiest way to simplify this fraction is to divide it up such that each numerator term is its own fraction. 16x 2 y 2 4xy 2 40xy3 + 4x3 y 2 4xy 2 4xy 2 = 4x 2 y i xy + 4 x 32 y 2 1xy 2 1xy 2 4 xy 2 = 4x 10y + x 2 For the first fraction, 16/4 simplifies to 4 and we can cancel a single factor of x and 2 factors of y (y 2 ). For the second fraction, 40/4 simplifies to 10 and we can cancel a single factor of x and 2 factors of y (y 2 ). We can cancel a factor of 4xy 2 from each fraction. For the third and final fraction, a 4 on the top and bottom cancel and we can cancel a single factor of x and 2 factors of y (y 2 ). Page 23
24 16x 2 y 2 40xy 3 + 4x 3 y 2 4xy 2 = 4x 10y + x 2 The answer cannot be simplified further so we are complete. 4x 10y + x 2 Page 24
Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 2 Section 12 Variables and Expressions
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: http://www.mathtutordvd.com/products/item67.cfm
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