Division of fractions
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   1.- Division of fractions.

   A farmer has divided his field into 8 equal plots. How many plots contain ¾ of the field? Each plot is 1/8 of the field. We just see how many times 1/8 is contained in 3/4. For that, we do that division 3/4: 1/8

   To solve this division, we multiply 3 x 8 and it will be the numerator. Then 4 x 1 and it will be the denominator. 

   So 3/4: 1/8 = (3 x 8) / (4 x 1) = 24/4 = 6. In ¾ of the field there are 6 plots of 1/8.

   Remember: to divide two fractions, we multiply in cross, that is, the numerator of the first by the denominator of the second (for the numerator) and the denominator of the first by the numerator of the second (for the denominator) a / b: c / d = a x d / b x c.

   Examples: 2/3: 1/9 = 18/3 = 6; 7 /2: 4/5 = 35/8, 5 /3: 2/7 = 35/6.

   Solve these divisions:

2/3 : 1/2 =

 

4/3 : 1/5 =

 

3/8 : 2/5 =

 

1/5 : 4/7 =

 

   2. Divisions of fractions by a whole number.

   First we convert the whole number in a fraction, putting as denominator the number 1. 
   
   Examples: 7 = 7/1; 8 = 8/1; 2 = 2/1.
   
   Then we divide the two fractions as in the previous question.

   2/3: 5 = 2/3: 5/1 = 2/15;  
                 3/5: 8 = 3/5: 8/1 = 3/40;  
                 3/8 : 4 = 3/8 : 4/1 = 3/ 32

   Do these exercises:

2/11 : 4 =

 

3/13 : 3 =

 

8/17 : 4 =

 

6/19 : 7 =

 

   3.- Do these problems

1. How many euros cost 125 liters of milk to 1/5 euros per liter?

 

2. We measure a street of 257 ¼ meters with a cane of 7/8 meters. How many times does the cane fit?

 

3. John received an inheritance of 2/7 from a farm and then he bought 3/8. What fraction of the farm does he have now?

 

4. A cyclist has traveled 1375 ¼ meters with a bicycle in which a wheel is 2 1/3 meters in circumference. How many stages did the wheel do?

 

5. A bricklayer does 6 2/7 meters of wall daily. How many meters will he do in 3 1/2 days?

 

6. A man left 162 000 euros and ordered that 5/6 of that heritage is shared equally among his three sons. How many euros receive each one?

 

7. How many pesos cost one meter of cloth if 5 2/3 meters cost 275 2/5 pesos?

 

8. A worker earns daily 47 1/4 euros and he spends 41 3/4 euros. How much money does he save per day?

 






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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