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© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 7 – Finding the Common Denominator

Supplemental Worksheet Problems To Accompany:

The Pre-Algebra Tutor: Volume 2

Section 7 – Finding the Common Denominator

Please watch Section 7 of this DVD before working these problems.

The DVD is located at:

http://www.mathtutordvd.com/products/item67.cfm


1) Express both fractions in terms of a common denominator.



9) Fill in the appropriate symbol (<, >, =).



Question

Answer


Begin.

The first step is to find a common denominator we can start working to. In this case, we know that 3 times 3 is 9. So if we use 9 as the common denominator, we only have to transform the first fraction.

In order to arrive at 9 for our common denominator, we need to multiplly the denominator of 2/3 by 3, to arrive at 9.

Anything we do to one half of a fraction (either top or bottom), we need to do to the other half. In this case, since we multiplied the denominator by 3, we also need to do the same to the numerator.

We next complete the arithmetic and arrive at 6/9. This is equivalent to the original 2/3.

Since 2/3 is the same as 6/9, we substitute it in and arrive at our answer. Now both fractions have 9 as the common denominator.

Ans:


Question

Answer


Begin.

The first step is to find a common denominator we can start working to. In this case, we know that 5 times 4 is 20. So if we use 20 as the common denominator, we only have to transform the first fraction.

In order to arrive at 20 for our common denominator, we need to multiply the denominator of 4/5 by 4, to arrive at 20.




Ans:


Question

Answer


Begin.

The first step is to find a common denominator we can start working to. In this case, we know that 10 times 2 is 20. So if we use 20 as the common denominator, we only have to transform the second fraction.





Ans:


Question

Answer


Begin.

The first step is to find a common denominator we can start working to. In this case, we know that 4 times 2 is 8. So if we use 8 as the common denominator, we only have to transform the second fraction.





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Question

Answer


Begin.

The first step is to find a common denominator we can start working to. In this case, we know that 3 times 2 is 6. We will have to transform both fractions such that the denominators are 6, the lowest common multiple of 2 and 3.

Let’s start with the first fraction, -2/3. In order to arrive at 6 for our common denominator, we need to multiply the denominator of -2/3 by 2. Whatever we do to the denominator, we must also do to the numerator. Don’t forget to take into account the negative sign in the numerator arithmetic.

Now let’s work with the second fraction (1/2). In order to make the denominator 6, we must multiply it by 3. Whatever we do to the denominator, we must also do to the numerator.

We now have both fractions in terms of a common denominator, 6.

Ans:


Question

Answer


Begin.

The first step is to find a common denominator we can start working to. In this case, we know that 3 times 4 is 12 and 2 times 6 is 12. We will have to transform both fractions such that the denominators are 12, the lowest common multiple of 6 and 4.

Let’s start with the first fraction, 1/6. In order to make the denominator 12, we must multiply it by 2. Whatever we do to the denominator, we must also do to the numerator.

Now let’s work with the second fraction, -3/4. In order to arrive at 12 for our common denominator, we need to multiply the denominator of -3/4 by 3. Whatever we do to the denominator, we must also do to the numerator. Don’t forget to take into account the negative sign in the numerator arithmetic.

We now have both fractions in terms of a common denominator, 12.

Ans:


Question

Answer


Begin.

The first step is to find a common denominator we can start working to. In this case, we know that 3 times 2x is 6x and 2x times 3 is 6x. We will have to transform both fractions such that the denominators are 6x, the lowest common multiple of 3 and 2x.

Let’s start with the first fraction, 2/3. In order to make the denominator 6x, we must multiply it by 2x. Whatever we do to the denominator, we must also do to the numerator.

Now let’s work with the second fraction, 1/2x. In order to arrive at 6x for our common denominator, we need to multiple the denominator of 1/2x by 3. Whatever we do to the denominator, we must also do to the numerator.

We now have both fractions in terms of a common denominator, 6x.

Ans:


Question

Answer


Begin.

The first step is to find a common denominator we can start working to. In this case, we know that 2a times 3 is 6a. Thus we only need to manipulate the second fraction.

In order to make the denominator of 1/2a equal to 6a, we must multiply it by 3. Whatever we do to the denominator, we must also do to the numerator.

We now have both fractions in terms of a common denominator, 6a.

Ans:


Question

Answer


Begin.

The easiest way to compare the fractions to know if they are equal or not is to express them with a common denominator. In this case, we know that 8 times 2 is 16. Thus we only need to manipulate the first fraction.

In order to make the denominator of 7/8 equal to 16 we must multiply it by 2. Whatever we do to the denominator, we must also do to the numerator.

Now that we have both fractions with a common denominator we can compare the numerators. Since 14 is less than 15 we know the left fraction is smaller.

Since the left fraction is smaller we can place the “<” symbol inside the box.

Ans:


Question

Answer


Begin.

The easiest way to compare the fractions to know if they are equal or not is to express them with a common denominator. In this case, we know that the least common denominator of 6 and 9 is 18 thus we can express both fractions with a common denominator of 18.





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Question

Answer


Begin.






Ans:


Question

Answer


Begin.

The easiest way to compare the fractions to know if they are equal or not is to express them with a common denominator. In this case, we know that the 3 times 7 equals 21 so we only need to manipulate the first fraction.

In order to make the denominator of -2/3 equal to 21 we must multiply it by 7. Whatever we do to the denominator, we must also do to the numerator.

Now that we have both fractions with a common denominator we can compare the numerators. Since -14 equals -14 we know the fractions are equal.

Since the left fraction is smaller we can place the “=” symbol inside the box.

Ans:


Question

Answer


Begin.


Let’s start with the first fraction, 11/9. In order to make the denominator equal to 18 we must multiply it by 2. Whatever we do to the denominator, we must also do to the numerator.

Now for the second fraction 7/6. In order to make the denominator equal to 18 we must multiply it by 3. Whatever we do to the denominator, we must also do to the numerator.

Now that we have both fractions with a common denominator we can compare the numerators. Since 22 is greater than 21 we know the left fraction is greater.

Since the left fraction is smaller we can place the “>” symbol inside the box.

Ans:


Question

Answer


Begin.

The easiest way to compare the fractions to know if they are equal or not is to express them with a common denominator. In this case, we know that the least common denominator of 5x and 8x is 40x thus we can express both fractions with a common denominator of 40x.

Let’s start with the first fraction, 2/5x. In order to make the denominator equal to 40x we must multiply it by 8. Whatever we do to the denominator, we must also do to the numerator.

Now for the second fraction 5/8x. In order to make the denominator equal to 40x we must multiply it by 5. Whatever we do to the denominator, we must also do to the numerator.


Since the left fraction is smaller we can place the “>” symbol inside the box.

Ans:

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