# Adding Fractions with Unlike Denominators

May I please seek your assistance with the concept of how to add the following fractions:

2/8 + 1/6

2/9 + 5/6

4/5 + 2/3

7/8 + 2/9

2/9 + 5/6

2/6 + 1/5

### Comments for Adding Fractions with Unlike Denominators

 Apr 10, 2012 Adding Fractions with Unlike Denominators by: Staff Question:May I please seek your assistance with the concept of how to add the following fractions:2/8 + 1/62/9 + 5/64/5 + 2/37/8 + 2/92/9 + 5/62/6 + 1/5Answer:2/8 + 1/6As you know, fractions cannot be added unless the denominators of both fractions are the same.Your primary task is to convert both fractions so that they both have the same denominator.Convert the fraction 2/8 to a fraction with a denominator of 12 2/8 = ¼To convert the fraction ¼ to a fraction with a denominator of 12, multiply the fraction ¼ by another fraction: 3/3. Note that 3/3 = 1, so you are actually multiplying by 1. The value of the fraction ¼ will not change.¼ * (3/3) = 3/12Convert the fraction 1/6 to a fraction with a denominator of 12 To convert the fraction 1/6 to a fraction with a denominator of 12, multiply the fraction 1/6 by another fraction: 2/2. Note that 2/2 = 1, so we are actually multiplying by 1. The value of the fraction 1/6 will not change.(1/6) * (2/2) = 2/12Since the two fractions now have the same denominator, they can be easily added. (Remember, only the numerators are added. The denominator of 12 remains the same)= 3/12 + 2/12= (3 + 2)/12= 5/12>>> 2/8 + 1/6 = 5/12------------------------------------2/9 + 5/6= (2/9) * (4/4) + (5/6) * (6/6)= (2*4)/(9*4) + (5*6)/(6*6)= (8)/(36) + (30)/(36)= 8/36 + 30/36= (8 + 30)/36= 38/36= 19/18This fraction cannot be reduced, but it can be converted into a mixed number.To convert 19/18 to a mixed number, divide 19 by 18= 19÷18= 1, remainder 1= 1 1/18>>> 2/9 + 5/6 = 1 1/18------------------------------------4/5 + 2/3= (4/5) * (3/3) + (2/3) * (5/5)= (4*3)/(5*3) + (2*5)/(3*5)= (12)/(15) + (10)/(15)= 12/15 + 10/15= (12 + 10)/15= 22/15This fraction cannot be reduced, but it can be converted into a mixed number.To convert 22/15 to a mixed number, divide 22 by 15= 22÷15= 1, remainder 7= 1 7/15>>> 4/5 + 2/3 = 1 7/15------------------------------------7/8 + 2/9= (7/8) * (9/9) + (2/9) * (8/8)= (7*9)/(8*9) + (2*8)/(9*8)= (63)/(72) + (16)/(72)= 63/72 + 16/72= (63 + 16)/72= 79/72This fraction cannot be reduced, but it can be converted into a mixed number.To convert 79/72 to a mixed number, divide 79 by 72= 79÷72= 1, remainder 7= 1 7/72>>> 7/8 + 2/9 = 1 7/72------------------------------------2/6 + 1/52/6 = 1/32/6 + 1/5 = 1/3 + 1/5= (1/3) * (5/5) + (1/5) * (3/3)= (1*5)/(3*5) + (1*3)/(5*3)= (5)/(15) + (3)/(15)= 5/15 + 3/15= (5 + 3)/15= 8/15>>> 2/6 + 1/5 = 8/15Thanks for writing. Staff www.solving-math-problems.com

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