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Equivalent Fractions:
On The Number Line
We have already had a look at equivalent fractions using shapes. Now we will put some simple equal fractions on number lines to prove that they have the same numerical value as each other.
The first fraction we will look at is 4 and one half. As shown previously, the fraction part of this number can be changed into different forms like this:
So we can see that 4 1/2 can also be written in several ways, as shown below. Only three equivalent values are used here, but you can make as many as you like.
Now let's put those fractions on three identical number lines.
Just as all those fraction parts mean one half, so you can convert any fraction into an equivalent version of the fraction by multiplying or dividing the top and bottom of the fraction by the came number:
This is an ideal method of inspiring confidence in the equal values of equivalent whole number and fraction parts. Once this confidence is gained, the student can move off the number line and proceed to just use the method with confidence.Here are some other fractions you may wish to apply this method to:
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