Equivalent Fractions

These fractions are equivalent, meaning equal.

Hello,

In past posts, we have discussed fractions; we have learned how to add and subtract fractions, how to convert from improper fractions to mixed numbers, and how to convert from mixed numbers to improper fractions.  Today, we are going to learn about equivalent fractions.  Equivalent fractions represent the same part of something, such as a piece of pizza.  If you cut a piece of pizza in half, you have 2 pieces, while piece is 1 out of the two, or 1/2.  If you cut the pizza into 4 pieces, then 2 of the pieces represent 1/2, and so now you have 2 out of the total 4 pieces, or 2/4.  In other words, 1/2 = 2/4.  Common words to describe equivalent fractions other than 'equivalent to' are 'equal to' and 'congruent to.'  Basically, equivalent fractions multiply the same number to the numerator and denominator to get the new fraction.  1/2 = 2/4 because we can multiply 2 to our numerator, 1, and multiply 2 to our denominator, 2, to get 2/4.  1/2 is also congruent to 3/6 because we can multiply numerator and denominator by 3 to get 3/6.  If we multiplied 1/2 by 4 to the numerator and denominator, what would our equivalent fraction be? Our calculation is 1/2 x 4/4 = 4/8, since when you multiply fractions you just multiply straight across, (numerator x numerator) divided by (denominator x denominator), which we will learn in more detail in another post.

Hint: In order to find equivalent fractions, you must multiply by the same number to numerator and denominator to find your new, equivalent fraction, or you must divide by the same number to numerator and denominator to find your new, equivalent fraction.  Dividing numerator and denominator by the same number to get our equivalent fraction means that we are reducing the fraction, usually in lowest terms.

Let's do some examples of finding equivalent fractions and recognizing equivalent fractions.

1.) 1/3 = ?/6
2.) 5/9 = ?/18
3.) 2/6 = 1/?
4.) True or False. 3/4 = 12/16.
5.) 3/5 = 15/?
6.) 7/10 = 14/?
7.) 4/9 = ?/27
8.) True or False. 1/9 = 7/62.
9.) 4/12 = ?/3
10.) 2/7 = ?/49

Try these examples on your own, and then see the solutions attached here: Answer key to equivalent fractions questions 

For more help with equivalent fractions you can view the chart below, as well as the links below:

Website for understanding equivalent fractions , YouTube video describing equivalent fractions with pictures