Equivalent Fractions Made Simple
Equivalent fractions can be easily mastered with a small amount of practice. The term "equivalent" simply means "of equal value". An example of two things being equivalent is 300 cents and 3 dollars. They are not the same, but they are worth the same. In terms of two fractions, the term equivalent means that they have the same amount of the object coloured in, regardless of how many parts the object is split into. The image to the right shows this clearly: In each picture half of the cookie is coloured in. The fractions given next to the cookies show us number of pieces coloured (numerator) over the TOTAL number of pieces (denominator). We can also see that there is a pattern to these numbers. In fact, the only difference between the three cookies is the number of lines used to break them up. It is important to note once again that when dividing a whole object into parts, all the parts must be exactly the same size. Using Rectangular Objects For Fractions To demonstrate equivalent fractions effectively we will need to use rectangular objects. If your child has not yet understood the basics of fractions, she should start with the round objects given in these basic fraction worksheets. The method for making a series of equivalent fractions from a rectangular object is simple. First draw a rectangle, cut it into even size pieces using vertical lines and colour in some of the pieces. The image below shows a rectangle cut into 4 pieces. One of the pieces has been coloured in, giving the fraction 1/4.
Second draw a horizontal line through the centre of the rectangle. This cuts the rectangle into twice as many pieces as before:
Again, we count the number of coloured pieces and put that over the total number of pieces. It is clear that nothing has changed in this fraction except the numbers used to describe it. The first and second rectangles both have the same amount coloured in. We can push this example a little further by using more horizontal lines. In the below example a total of three horizontal lines have been used. All we need to do is remember to keep all the pieces the same size, which means space the horizontal lines evenly:
These three fractions are all exactly the same. It makes absolutely no difference how many horizontal lines we add to the original fraction picture. The amount coloured in does not change, and so they are all equal.
Multiplying The Numbers 
Clearly the numbers used in the three equivalent fractions shown above are related, but how? Adding the same amount to the top and bottom of the fraction does not work, but multiplying does. This is true for any fraction. This works if we multiply the top and bottom by the same amount, as shown to the right. This method works regardless of the value of the numerator (top number) or denominator (bottom number).Another example with different numbers confirms this point:
This is worth practicing using rectangles, colouring pencils and a ruler. After a while it becomes clear that making equivalent fractions is simply a times tables exercise. Division It also makes sense that this works in reverse. If we can divide a fraction by the same number on the top and bottom its value will not change. This is called simplifying fractions. Return from Equivalent Fractions to Free Math Worksheets or return to the Green Planet home page for Solar Power Facts.
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