Equivalent Fractions

Equivalent fractions
What Equivalent fractions means?

Equivalent fractions are fractions that name the same amount.

a fraction can have many different appearances, these are called equivalent fractions

The word EQUIVALENT means the same as EQUAL or, more precisely, of equal value.

In the following picture we have ½ of a cake because the whole cake is divided into two congruent parts and we have only one of those parts.

But if we cut the cake into smaller congruent pieces, we can see that Or we can cut the original cake into 6 congruent pieces,

Now we have 3 pieces out of 6 equal pieces, but the total amount we have is still the same. Therefore,

If you don’t like this, we can cut the original cake into 8 congruent pieces,

Then we have 4 pieces out of 8 equal pieces, but the total amount we have is still the same. Therefore,

By looking at the pictures, each box has the same portion (or fraction)
filled, so these portions are called equivalent fractions.

We can generalize this to
 

Are they equivalent fractions?
 
Yes!
These fractions are equal. They are equivalent fractions.



1) To raise fractions make the denominator larger.

2) Multiply numerator and denominator (top and bottom) of the fraction by the same number.

3) This is the same thing as multiplying by 1.



Are sometimes called equal fractions: two or more fractions that name the same number.
Equivalent Fraction Models




To compare 1/2 and 3/7 we would multiply 1/2 by 3/3 to produce 3/6. Since 3/6 is not the same as 3/7, the fractions are not equivalent.

Fractions equivalent to 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12 ...

Fractions equivalent to 1/3 are 2/6, 3/9, 4/12, 5/15, ...

Fractions equivalent to 1/4 are 2/8, 3/12, 4/16, 5/20, ...

Fractions equivalent to 1/5 are 2/10, 3/15, 4/20, 5/25, ...

Fractions equivalent to 2/5 are 4/10, 6/15, 8/20, 10/25, ...