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How to add and subtract unlike fractions

This week we are learning how to add and subtract fractions with unlike denominators.  Watch the video below to get you started.

How to Video:

 

Step 1:  Find a common denominator.

1  +   2

4       3

Before we can add or subtract the fractions, we need to write them so they have the same denominator (a "common denominator") that is divisible by both numbers.  Therefore, we must list the multiples (skip count by 3 and 4) of each denominator and find the smallest one that they have in common.  

List the multiples

3: 3, 6, 9, 12, 15, 18, 21, 24

4: 4, 8, 12, 16, 20, 24

The numbers 3 and 4 have 12 and 24 in common, but we want to use the smallest or "Least Common Multiple" as our denominator.  Although we can use any number they have in common, the smallest is the easiest to deal with and reduces our need to simplify our fraction later.  Therefore, we will use 12 as our new denominator.

Step 2:  Make an equivalent fraction of the first fraction by using the new denominator.

Remember: we can't just change the denominator without multiplying the numerator by the same amount as well. Here's how we turn it into an equivalent fraction:

1  x 3    =     3                                2 x 4   =       8

4  x 3    =    12                               3 x 4    =   12

  • We know 4 x 3 = 12.
  • Multiply both the numerator and the denominator by the same number to get the result:
  • (1 x 3 ) / (4 x 3) = 3/12                                                                            

Step 3:Do the same process to the other fraction (see example above)

  • We know 34 = 12.
  • Multiply both the numerator and the denominator by the same number to get the result:
  • (2 x 4 ) / (3 x 4) = 8/12

Step 4: Add or subtract the numerators of each fraction to get the answer.   Keep the denominators the same.

 

    3     +        8      =       11                              

   12            12              12

  • We know 3 + 8 = 11
  • Remember:  Keep the denominators the same.  

 

Step 5: Simplify the fraction: Simplifying a fraction means writing it in its smallest equivalent form, to make it easier to use. Do this by dividing the numerator and denominator by the same number (Use the Greatest Common Factor; it is faster). 

  • There are no numbers that divide evenly into both 11 and 12, so this is our final, simplified answer.   Remember: when numbers are back to back on the number line, then they are reduced.

 

But, sometimes we need to Convert improper fractions into Mixed Numbers before we can simplilfy.   

 

 

If needed:  If the numerator ends up larger than the denominator, you have a fraction larger than 1 (an "improper fraction). You can make these into a mixed number, which is easier to read, by dividing the numerator by the denominator, and keeping the remainder as a fraction.

 

For example, using the fraction      58

                                  44

 

We get 58 ÷ 44 = 1, with remainder 14 left over. This means our final mixed number is 1 and 14/44.

 

If you're not sure how to divide the numbers, you can keep subtracting the bottom number from the top, writing down how many times you've subtracted.

 

For example, convert 317 / 100 like this:

317 - 100 = 217 (subtracted 1 time). 217 - 100 = 117 (subtracted 2 times). 117 - 100 = 17 (3 times). We can't subtract any more, so the answer is 3 and 17/100

 

 
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