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How To Find The LCD & Add Or Subtract fractions With Unlike denominators ( PRE Algebra )

How To Find The LCD & Add Or Subtract fractions With Unlike denominators ( PRE Algebra ) post thumbnail image

The lowest common denominator (LCD) of two fractions is the smallest number that is a multiple of both denominators. This is important because it allows you to compare and add or subtract fractions with different denominators. In order to find the LCD, you will need to use the least common multiple (LCM). The LCM is the smallest number that is a multiple of two or more numbers.

How To Find The LCD Of Fractions

To find the LCD of two fractions:

  1. List the multiples of the first denominator. Start with the number itself and keep going until you find a multiple that is also a multiple of the second denominator. 
  2. Do the same thing with the second denominator. 
  3. The smallest number that appears on both lists is the LCD!

Let’s try it out with an example. Say we want to find the LCD of 4/7 and 3/8.

 We would list out the multiples of 7: 7, 14, 21, 28, 35, 42, 49,56 

And then we would list out the multiples of 8: 8, 16, 24, 32, 40, 48,56… As you can see, 56 appears on both lists, so 56 is our LCD! 

Now let’s add both fractions:

Let’s list them out with their new found denominators:

Let’s start with {4 \over 7} , we need to turn the 7 into the new LCD that is 56. To do that we have to multiply the denominator by 8. But we need to remember that anytime of the members of the fraction is changed, all are changed. So the numerator is also going to be multiplied by 8

{4*7 \over 7*8}

And we’ll repeat the same process with {3 \over 8}

{3*8 \over 8*7}

Now we can add both fractions

So {4 \over 7} + {3 \over 8}  has become 

{32 \over 56} + {24 \over 56}

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