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division , addition

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3 Answers

We can add or subtract fractions only with the same denominators.
If denominators are different, first, we have to find the least common denominator (LCD).
In our case 67 and 89 are prime numbers, therefor
LCD(67, 89) = 67 × 89 = 5963
If we multiply denominator by some number, we must multiply numerator by the same number.
  45 * 89        77 * 67    
————— + ————— =
    5963            5963  
          
    4005           5159     
  ————  +  ————  = 
    5963           5963      

  4005 + 5159 
 ———————  = 
       5963 

 9164            3201
———  =  1  ———  
 5963            5963  

1. Multiply the denominators

2. Multiply first numerator by second denominator.

3. Multiply second numerator by first denominator.

4. Add the products of Steps 2 and 3 in the numerator

45/67 + 77/89 = (45*89 + 67*77)/(67*89)

Comments

Martin did a great job of breaking this down step by step. The idea with fractions is to get a common denominator. In other words you want both fractions written over a single divisor.

Martins process accomplishes this in the most efficient way possible. If you don't already have a good calculator there are several that can help you do this, such as my go to calculator the TI 36X Pro, or you can try plugging your problems into the WolframAlpha website at

http://www.wolframalpha.com

Type fraction questions in there, it will present you with a solution in the lowest terms.

Comment

Just divide each fraction to get two decimal numbers, then add them:

45/67 = 0.6716

77/89 = 0.8652

0.6716 + 0.8652 = 1.5368

Comments

I originally wrote an answer that showed how to add these numbers as fractions.  Then I noticed that it is labeled as a division and addition problem, so the answer above is more appropriate.

Comment