Problems from Introduction to fractions

  1. Write as a fraction the coloured parts of the following rectangles:

    1.      
           
           
           
    2.          
               
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Development:

  1. We notice that the rectangle is divided into a grid of $$12$$ pieces, so the denominator of the fraction will be $$12$$. Of these there are seven blue pieces. Therefore the numerator of the fraction is $$7$$.
  2. This time, the rectangle is divided into $$10$$ parts, this means that the denominator of the fraction is the number $$10$$. Of these ten parts, we have exactly six green pieces, so the numerator of the fraction is the number $$6$$.

Solution:

  1. $$\dfrac{7}{12}$$
  2. $$\dfrac{6}{10}$$
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Draw as a rectangle, divided and coloured, the following fractions (to do this you can use a table and colour the cells with background color in the cell’s properties):

  1. $$\dfrac{7}{8}$$
  2. $$\dfrac{9}{5}$$
See development and solution

Development:

  1. To draw a fraction we begin with a rectangle and divide it in such pieces as indicated by the denominator, in this case $$8$$:
       
       

After that, we paint the number of pieces of the rectangle indicated by the numerator, that is, $$7$$.

       
       

To divide the rectangle, we can do the pieces in any order or direction that we want as long as we obtain exactly eight pieces and that all are of equal size. As a matter of fact, we can paint any of the pieces as long as we paint exactly seven.

  1. Doing it in the same way, we start with a rectangle and divide it into five different parts since this is what the denominator indicates:

             

From the five cells that we get, we must paint nine of some color, so we are going to need another rectangle divided into an equal number of pieces, since there are not enough cells to be painted as the numerator indicates:

         
         

Once we have both rectangles, we paint $$9$$ cells, as indicated by the numerator:

          
      <table border="1" cellpadding="1" cellspacing="1" height="40" width="200">
        <tbody>
          <tr>
            <td bgcolor="#339999">
              &nbsp;</td>
            <td bgcolor="#339999">
              &nbsp;</td>
            <td bgcolor="#339999">
              &nbsp;</td>
            <td bgcolor="#339999">
              &nbsp;</td>
            <td>
              &nbsp;</td>
          </tr>
        </tbody>
      </table>

Solution:

  1.        
           
  2.           
      <table border="1" cellpadding="1" cellspacing="1" height="40" width="200">
    <tbody>
      <tr>
        <td bgcolor="#339999">
          &nbsp;</td>
        <td bgcolor="#339999">
          &nbsp;</td>
        <td bgcolor="#339999">
          &nbsp;</td>
        <td bgcolor="#339999">
          &nbsp;</td>
        <td bgcolor="#339999">
          &nbsp;</td>
      </tr>
    </tbody>
  </table>
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