Addition of fractions
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   1.- Addition of fractions with the same denominator.

   We have one piece of cake (1/5) and we add 2 pieces (2/5). Finally we have three pieces (3/5).

   To add fractions with the same denominator, we must add the numerators, keeping the same denominator.

   Examples: 2/7 + 3/7 + 1/7 = 6/7; 5/9 + 8/9 = 13/9

   Solve these sums:

2/7 + 3/7 =

 

3/5 + 1/5 =

 

1/4 + 3/4 =

 

3/8 + 1/8 + 2/8 =

 

      2.- Addition of fractions with different denominators.

      First, we must reduce the two fractions to a common denominator: 1/2 + 1/4 = 4/8 + 2/8
      Then, we sum 4/8 + 2/8 = 6/8

      To add fractions with different denominators, we must reduce them to a common denominator and then, we must apply the previous rule.

     Do these sums:

1/2 + 1/3 =

 

1/3 + 1/4 =

 

1/2+2/3+3/4=

 

1/3 + 1/6 =

 

   3.- Addition of mixed numbers

   To add mixed numbers, we add the whole numbers and the fractional parts.

   Examples 3 1/3+ 2 1/3 = (3 +2) and (1/3 + 1/3) = 5 2/3 1 1/4 + 2 1/3 = (1 +2) + (1/4 +1/3 = 3/12 + 4/12) = 3 7/12.

   Do these sums of mixed numbers. Do it on paper and check it.

3 y 3/5 + 2 y 1/3 =

 

2 y 1/3 + 1 y 1/5 =

 

7 y 1/4 + 6 y 1/3 =

 

3 y 1/9 + 2 y 1/7 =

 

   4.- Simplified fractions.

   If we divide the numerator and the denominator of a fraction by the same number, we obtain a simplified fraction.

   Examples: 6/15 = 6:3 / 15:3 = 2/5; 8/12 = 4/6 = 2/3, 9/12 = 3/4.

   Simplify these fractions:

6/8 =

 

3/12 =

 

9/18 =

 

3/18 =

 

    5- Add these fractions and simplify the result. 

    Do these operations on a paper.
 
   Recuerda que 2/2 = 3/3 = 4/4 = 1

1/4 + 3/4 =

 

3/8 + 1/8 =

 

1/2 + 1/4 =

 

1/6 + 1/6 =

 

    6- Do these problems 

    Do it on a paper and check it:

1. On Monday a worker won 8 1/3 euros and on Tuesday he won 9 2/5 euros. How much money did he win on both days?

 

2. John has 1/3 of a cake and Montse has 1/5. How many pieces of cake did they have in total?

 

3. Ana has 5 2/5 euros and Arturo has 6 1/4 euros. How much money do they have in total?

 

4. A boy drinks ½ sip of a bottle and then he drinks 1/3. How much did he drink in total?

 






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®Arturo Ramo García.-Record of intellectual property of Teruel (Spain) No 141, of 29-IX-1999
Plaza Playa de Aro, 3, 1º DO 44002-TERUEL