Please share your best and simplest explanation for adding fractions

[dorothy]

with different denominators. DD is not understanding the way it is explained in Singapore. I want to make sure it makes sense to her. Thanks.

[Karenciavo]

convert fractions to lowest common denominator (LCD)
divide the LCD by the original denominator of each fraction
multiply the numerators by each answer
add
reduce

1/2 + 2/3

6 is the LCD

6/2 x 1 =3 so the first fraction is 3/6
6/3 x 2 = 4 and the second fraction is 4/6

3/6 + 4/6 = 7/6 = 1 1/6

[Elinor Everywhere]

with different denominators. DD is not understanding the way it is explained in Singapore. I want to make sure it makes sense to her. Thanks.

We do it much the same way as Karen. Here's what I would say:

1/2 + 1/3. I would ask my kids: Let's take the biggest denominator, which is 3. Find the first multiple of 3 that is also a multiple of 2. Is 3 a multiple of 2? (they say no). Is 6? (they say yes).

Okay, let's make the denominator 6. Using our first fraction of 1/2, what number times 2 (the denominator) equals 6? (they say 3). Good, so we multiply the 1 in our fraction by 3 also. Now we have 3/6.

The next fraction is 1/3. What do we multiply 3 by to reach 6? (they say 2). Yes, so let's multiple the one by 2 also. Now we have 2/6.

3/6 + 2/6 = 5/6.

HTH!

[Laura Corin]

with different denominators. DD is not understanding the way it is explained in Singapore. I want to make sure it makes sense to her. Thanks.

1/2 plus 1/3. Okay, how are we going to have each of these made up of the same size pieces? We are going to have to divide them both up into smaller pieces. What's the lowest number that both 2 and 3 go into? Okay, six. Each is now made up of sixth-pieces. (I draw pie pictures at this point to show how the thirds and halves become sixths)

Now, we have something sixths plus something sixths. If we want to write 1/2 as something sixths, what would it be? How many sixths is the same as one half? What's half of six? Okay, three sixths.

How many sixths is the same as one third? What's one third of six? Okay two sixths. Now you have three sixths plus two sixths. Remember that the 'sixth' means sixth-pieces, so you are going to add three sixth-pieces to two sixth-pieces and get five sixth-pieces, which is five sixths.

The reminder at the end is to stop them suddenly deciding that the answer is five twelfths!

(Calvin just read over my shoulder and said, "You're raving about fractions. No-one will listen to you.")

Laura

[dorothy]

:)

[dorothy]

I am sure it will help.

[OhElizabeth]

Dorothy, not an explanation, but RightStart makes a hardwood fractions puzzle that will help her greatly. It allows them to pick the pieces up, move them around, and see how they relate (that 4/8 really does equal 1/2, etc.). http://www.activitiesforlearning.com/index.asp?PageAction=VIEWCATS&Category=33 It also comes as a magnet or paper version in the card games kit. You might also like to get the Fractions Games kit. It has just the fractions deck from the games kit and instructions for a good number of games you can play. When you play these games, your dc will build their understanding of how fractions work. Sometimes kids do things by rote and don't really GET how they work. When you play the fractions games, let her use the puzzle as needed to figure things out. The games are simple to learn but very effective, and this process will clarify things in her mind.

[Lorna]

Show 1/2 +2/4
She will hopefully be able to see that 2/4 of a cake is the same as 1/2
Keep it to numbers she can visualise (or you can demonstrate easier)
I also recommend the Key to series for supplementing fractions with Singapore. It is a real confidence booster and she will whizz through it. It demonstrates fractions is a much more gradual manner. Both our two did a couple of these books and have a great grasp of fractions.

[Jenny in Atl]

I love using food... pies and apples. M&M's also work great with both fractions and percents. At least it keeps them interested. :D

[Testimony]

1/2 + 1/3=?

You cannot add different fractions with different denominators. We must make the bottom part the same.

Look in Singapore Textbook where it talks about common multiples. 12 is a common multiple of 4 and 6 on page 26.

If you notice 6 is the common mulitple of 2 and 3 in your fraction problem or multiply 2x3=6.

So, the denominator must be 6 for both fractions. Half of 6/6 is 3/6 and 1/3 of 6/6 is 2/6.

Another way to show this is:

[-][-][-]/[-][-][-]

Half of this bar is 3/6. You can count to 3 to see this.
To see 1/3, circle 3 groups.
[-][-]/[-][-]/[-][-]

1/3 of that group is 2.

Therefore 3/6 + 2/6= 5/6

I hope that that helps.

Blessings,
Karen and her son
www.homeschoolblogger.com/testimony
www.homeschoolblogger.com/thegenius

[katilac]

This is much, much easier to see if you use fraction tiles. I highly recommend a set; you can get them at teacher education stores or many places online.

I suppose you could make them as well, but they only cost a few dollars.

[Eliana]

Is it that she understands the *concept*, but doesn't get Singapore's technique, or that the underlying concept doesn't make intuitive sense to her?

If the concept is the problem, then I'd add my vote to Lorna and Katilac's and Jenny's: start really simply and make it as concrete as possible. (and, yes, food always goes over well here too!) I'd start with real objects (pizza!), then fraction tiles and pattern blocks - I *love* manipulatives, it comes of being a Montessori kid I think - then drawings. Doing it with real objects makes the number really real for most kids - and they carry that belief into the abstractions they get later.... and it really, really, really helps if they feel intuitively comfortable with fractions *before* you start them doing stuff it hard to illustrate tangibly. (I found this to be true with negative numbers too - my kids start out thinking of it as how much money they have vs how much money they owe, and by the time we get into more sophisticated things, they already feel at home with the ideas.)

To introduce how to do it numerically, I start with something my child understands intuitively - and talk her (or him) through it on paper, using her method as she describes it to me. (for example: adding 1/2 + 1/4, the answer is very intuitive for a kid who's played with fraction tiles or helped a lot in the kitchen, but she probably doesn't realize that she's doing a conversion, once she sees that that is what she is doing - and you do it with a few more really obvious examples, ones she can test easily with real objects, then you can move on to purely paper processes... at least until the first time she gets confused, and then you can break out the pizza or the tiles again.)

Eliana