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Adding Fractions is a Step-by-Step Process



KNOWLEDGE THAT IS ASSUMED FOR THIS SECTION


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

If your child is happy with both these areas, lets move on!



WHEN ADDING FRACTIONS YOU CAN ONLY ADD LIKE WITH LIKE!


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 see what we just did?

We altered the question using equivalent values.



EQUIVALENT FRACTIONS


Please read this page first if you want a detailed explanation of equivalent fractions.

In summary, these are fractions that are expressed in different forms, but have the same value.



ADDING FRACTIONS - THE FACTS!


Now is the time to take out your circle fractions that you saved from our first lesson.

Here we are going to work through some specific examples so that you can see exactly what is happening, in a step-by-step process.

adding fractions

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.

adding fractions

Our next example.

adding fractions

Again, have your child read this out loud. One half plus three quarters equals what?

Can we add this? 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 ...

adding fractions

What is 2 + 3; the answer is five so ....

adding fractions



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?

There is another way, that works for all fractions, all the time!

Our next example:

adding fractions

  • Step 1 Multiply the numbers below the line. In this case 2 x 4 = 8


    • adding fractions

  • 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.

    adding fractions



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