 ## Is a Step by Step processss

Adding fractions is a detailed process that sometimes requires multiplication.  For this section I assume that your child is comfortable with the Concepts of Fractions and with multiplication of whole numbers.

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This is very important for your child to know, and it is the basis of fractions.  You cannot add apples and oranges!

For example: What is three apples plus two oranges?  The answer is three apples plus two oranges!

Do we stop here?  No.

We could re-write the question to read ..

What is three pieces of fruit plus two pieces of fruit?  The answer ... five pieces of fruit!

Do you tell what we just did here?  We altered the question using equivalent values.

Equivalent Fractions

Equivalent Fractions are fractions expressed in different forms - that is have different denominators, but have the same value.

If you need to brush up on this concept, I have equivalent fractions explained in detail here.

## Adding Fractions - The Facts

It is a good idea for you to have a set of Fraction Circles, or when checking out our manipulatives area, you may decide on Fraction Bars - whichever your kid prefers using, is just fine.

Let's take a look at some worked examples.

### Example 1 As you can see our Denominators are the same.  We are adding halves to halves.  Encourage your child to read this question out loud.

One half plus three halves equals what?

This is pretty much the same as saying - one apple plus three apples equals what?

We can say 1 + 3 = 4 so ...

1 half + 3 halves = 4 halves. ### Example 2 Again, have your child read this out loud.  One half plus three quarters equals what?

Can we add these?  Nope.  We are trying to add apples and oranges, and that just can't be done!

Not unless we express them as the same type of fraction.

Give your child a half circle and some quarter chircles.  Encourage them to find a way of representing the half with quarters or the quarters with halves.

The should come up with the half is equivalent to two quarter pieces.

So now we can re-write the question as ... 2 + 3 = 5, so 2 quarters + 3 quarters = 5 quarters. ## No Circles, No Equivalent Fractions, No Problems!

What happens if your child draws a blank on remembering the equivalent fractions, and they don't have their fraction circles.  What then?  Are they stumped?

Of course not.  Let's look at the mathematical way of solving this problem, which  works for all fractions, all the time!

## Example 3 Step 1: Multiply the denominators - 2 x 4 = 8 Step 2: Multiply Numerator of 1st fraction by denominator of 2nd fraction.  In this case 1 x 4 = 4 Step 3: Multiply Numerator of 2nd fraction by denominator of 1st fraction.  In this case 1 x 2 = 2

Rewrite the equation and solve  