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I do not like fractions. At. All!

My son has fraction homework and some of the answers look wrong to me. I need help

1 example

3 1/4 + 2 1/4 = 5 2/4 (his answer)

My question. Wouldn't the answer be 5 1/2 since 1/4 & 1/4 equal a half?

If he's right, great! I just need to understand this. It's been so long since I was in 4th grade, I didn't like fractions then. Ugh...

You're right.

Two quarters make a half.

Just like football.

AJ's MOM

I believe the answer is 5 1/2

Yes the final step in any math process that results in a fraction is to reduce the fraction to the smallest representation (ie all common factors from the numerator and denominator are removed)

That's how I explained it to him. I said if I have a 1/4 cup of something and I add another 1/4 cup that will give me half a cup.

He has another one

7 1/2 + 2 1/2 = 9 2/2 (his answer.

I told him that the answer might be 10 because a half and a half equal a whole.

I found a fraction calculator online and it did the math like he did, only adding the numerator because the denominators are the same.

Changing 2/4 to 1/2 is reducing to lowest terms and they may not have learned that yet.

Yes the final step in any math process that results in a fraction is to reduce the fraction to the smallest representation (ie all common factors from the numerator and denominator are removed)

Ok, what?

Yup my son was also taught to look at the answer and see if you can reduce the fraction further to the lowest possible common denominator.

So 2/4 can be simplified to 1/2

6/9 can be simplified to 2/3

Etc.

Assuming he hasn't learned reducing yet, should he leave the answers as is?

I was going to say they may have not yet reached the reduce to the simpilest form yet. In which case 2/4 would be correct.

2/2 would not be right, they should know that 2 1/2's make a whole already.

I asked him during dinner if they learned how to reduce. He said yes, but his teacher doesn't call it that.

So I'm going to go over his home work again with him. I also want to find out if her instructions were to reduce or leave it as is which sounds odd to me. She had them cross out some examples because she said you couldn't do the math right.

Fractions are all about taking a whole thing and breaking it apart into equal sized sections.

Say, you have one cake and cut it into 32 equal pieces. You can eyeball the cake and see half. You can count up the pieces in the half and find 16 out of the 32 are half (16/32...top number indicates amount you want, bottom number shows the total number of pieces...in this case you need 16 out of the 32 to show half. Top number is called the numerator, bottom number is the denominator...think "down-ominator")

I call this fraction 16/32 the "complicated form" because it is hard to picture it in my head. I cannot visualize 16 out of 32 pieces easily. It is also very time consuming and hard to draw.

But, I do know if I had another identical cake sitting next to the one I cut up into 32 pieces, I could easily show 1/2 by just cutting the cake one time into 2 equal parts. I could point to the half that would be the same size as the 16 parts I needed for half of the other cake.

This cake would be the "simple" example to show half, or form...get it "simplest form".

Both cakes show me one half (1/2 or 1 of the two equal pieces). Which one is easier to visualize?

Both halves are the same, they are equal or equivalent. They are called equivalent fractions.

1/2 = 16/32 or 16 out of the 32 pieces

1/2 = 2/4 or 2 out of the 4 pieces

In math, people prefer to use the simpler form of a fraction because it is easier to work with than the complicated form. It is easier to visualize, and easier to do arithmetic on.

So, when you have the fraction 2/2 what does that mean?

It means you have 2 of the 2 parts....wait a sec...

If you have 2 of 2 parts of a candy bar, don't you have all of it?

When the top and bottom number match, it means you have the entire object.

It means you have ONE of the object, because you have all of the parts. It is exactly like having 1 all dressed up in a costume. It is still 1, just an equivalent that looks different.

3/3 = 1

11/11 = 1

999/999 = 1

1/1 = 1

Her's a quiz:

3/3 + 1 = ?

learned how to reduce

This is not called reducing any more. It is simplifying.

"Reducing" seems to imply a different value. The value stays the same and is not "reduced" but the answer should be in simplest terms, so yes 2/4 should be written as 1/2.

Thank you all for help with this. I appreciate very much. He's handing it in today and I told him I want to see as soon as she corrects it and hands it back.

We'll see.

Thanks again!