Explain Equivalent Fractions

Do you need someone to explain equivalent fractions?  This can be a confusing math concept, but the explanation below should help.

The word “equivalent” means that two fractions will have the same value.  Basically, that means that the fractions are the same.  For instance, ½ is the same as 50/100 because they are equivalent.  Let’s find out how you know whether they are equivalent or not.

• One way to explain equivalent fractions is to tell the person that whatever is done to the top of the fraction is also done to the bottom.  This refers only to multiplying and dividing.  So, looking at the previous example, if you multiply the top number 1 by 50, it equals 50.  If you multiply the bottom number 2 by 50, it equals 100.  Therefore the two fractions are equivalent because both numbers, top and bottom, have been multiplied by 50.  

• To further explain equivalent fractions, you might want to state that the top number is the numerator and the bottom number is the denominator.  Also, when you keep dividing the top and bottom numbers until they can no longer be divided, you have simplified the fraction.

Online Help for Equivalent Fractions

Following are some links to websites that have worksheets, calculators and tables to help you with equivalent fractions:

• Home School Math has a worksheet generator that will provide practice on equivalent fractions.  
• Dr. Mike’s Math Games for Kids has a calculator that will tell you if two fractions are equivalent and has links to worksheets and tests.
• Math A Tube has a table of equivalent fractions that goes up to 10/100.
• Cut the Knot  has a table that goes up to 16/16.

Uses of Fractions

Fractions are used in many places, like in money, time, measurements, and cooking, to name a few. 

• A “quarter after the hour” refers to a fraction of an hour
• Recipes call for ½ cup of this or 1/8 teaspoon of that
• Gas consumption is measured in miles per gallon, which is a ratio
• Fractions can represent a part of a whole, a division problem, or a ratio.  If three out of ten people buy a certain brand, it can be shown as a fraction 3/10. 
• Fractions can be used to solve complex mathematical equations.  In order to do this, you must understand how to add, subtract, multiply, and divide them and also how to make equivalent fractions. 

Adding and Subtracting Fractions

For those looking to explain equivalent fractions, you might also be interested in how to add and subtract fractions

• In order to add or subtract fractions, the denominator has to be the same.  This is where equivalent fractions are used. 
• Let’s say we want to add 1/3 and 2/5.  The denominators are 3 and 5 and need to become the same so you need to think of a number that is divisible by both 3 and 5. 
• The smallest number that would work is 15. 
• So now you make an equivalent fraction for each one with 15 on the bottom, remembering that you have to multiply the top and bottom numbers by the same number.  
• 1/3 will be multiplied by 5 to make 5/15 and 2/5 will be multiplied by 3 to make 6/15. 
• Now the equation is simple to solve: 5/15 + 6/16 = 11/15.  If the denominators are the same, all you do is add or subtract the numerators.

Fractions to Decimals

Sometimes in math it is necessary to change a fraction to a decimal.  That is really easy if you understand that a fraction represents a division problem.  For example, the fraction ¾ can be looked at as a division problem with 0.75 being the answer.  All you have to do to convert a fraction to a decimal is to divide the numerator (top number) by the denominator (bottom number).    

Another example is 2/5.  Simply divide 2 by 5 and you get 0.4 which is also an equivalent fraction when written as the fraction 4/10.  This is yet another example of equivalent fractions popping up while you are solving math problems.