1: Equivalent Fractions

Fractions are equivalent if they represent the same amount. They're equal

For example, here are some equivalent (equal) fractions:



In picture form, you can see why they're equal:



You can also recognize equivalent fractions numerically:

If you can divide the numerator and denominator by the same number, you will get a new fraction that's equivalent:

  

Similarly, if you can multiply both the numerator and denominator by the same number to get a second fraction, that new fraction will be equivalent.



In either case, the pairs of fractions are equivalent; they're equal, and represent the same amount.


Let's look at another example:



The segments are clearly the same size. The three fractions represent the same amounts.

Here are the three equivalent fractions:



Can you see that:
  • The second fraction is a multiple of 2 of the first fraction
  • The third fraction is a multiple of 2 of the second fraction
  • The third fraction is a multiple of 4 of the first fraction
The fact that they're multiples makes them equivalent, or equal.


Now let's look at reducing a fraction ...


Equivalent Fractions | Reducing a Fraction | Practice



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