Guess and add  fractions
(with a splash of algebra to keep your brain strong)


*Today we are going to sharpen our fraction and equation solving skills,
the ones involving addition of fractions.

We like to start any discussion of fraction adding with good old common sense estimating.  It really helps if you can look at a fraction and tell whether  it is closer to zero, 1/2, or 1

Here is a list of fractions.  Take a guess which number they are closest to 0 , 1/2, or 1. Then move your mouse over the number and we will tell you if you are right.  If your mouse fails to work, use a calculator.

14/15 32/68 3/8 1/98 34/80
Now let's do some common sense estimating of sums.

Look at each addition problem take a guess on it's answer then move your mouse over the problem to find out how close you were.

1/5 + 3/4 = ?

6/8 + 9/10 + 1/4 = ?

3 3/5 + 19 5/6 = ?

In real life, often being able to get a reasonable estimate is more important than getting the actual answer.   A fraction capable calculator will give you the exact answer (assuming you enter the problem correctly), but if you don't have a "feel" for what the answer should be you can end up looking foolish if the data is entered incorrectly and you do not catch it.

For example, there was a student who took 3/8 + 1/2 and got -1/8, and didn't think anything of it. The student pressed the (-)sign instead of the (+) sign on the calculator. (real answer is 7/8)

Be sure to practice your estimating skills.

This brings us now to ACTUAL addition and subtraction of fractions by hand.

It may have been a while since you have done this.  So here are a few tips to remember:

  1. When the denominators (bottom numbers) are the same, DO NOT ADD THEM TOGETHER!  Just add the numerators, (top numbers)
    EX: 3/5 + 4/5 = 7/5 or 1 2/5
  2. Always reduce your answers:
    EX: 3/6 is really 1/2 so call it that.
    EX: 13/8 is improper. That means the top is bigger than the bottom, and that is uncool most of the time, people don't say, "I have 13/8 pizzas. You reduce it by dividing and say, "I have 1 5/8 pizzas."


    You try these: (move your mouse over the problem to check your answer)

    5/8 + 5/8 =

    1/3 + 1/3 + 2/3 =

    5/16 + 7/16 =
  3. Remember if the denominators are DIFFERENT, you need to find a COMMON DENOMINATOR and corresponding numerators before you can add.
    EX: 3/4 + 2/5 = (multiplying the denominators will always give a common denominator)
    4 x 5 = 20; so I must find the corresponding numerators that will match the denominator of 20.
    3/4 x 5/5 = 15/20 and
    2/5 x 4/4 = 8/20...............so these two are what we add getting 23/20 or 1 3/20

 

Now comes the ALGEBRA:

Let's play a game of I'M THINKING OF A NUMBER.

Here is how it works:         brain2.wmf (3254 bytes)
  • I'll tell you a hint about the number I have in my mind.
  • Then you do some mental calculation, or use a piece of paper to undo my hint  and reveal  my number.
  • When you think you know the answer, just click on the answer button to check it.

 

HERE TRY A SAMPLE!

I'm thinking of a number, and if  I take 1/2 away from it, I will still have 22 and 1/2.  What is my number?

answer

NOW LET'S TRY SEVERAL SOLO!
Be sure not to click on the answer until you figure it out yourself.

I'm thinking of a big number,  If I take away 3/8, I will still have 136 and 3/4.  What is my number?

answer

I'm thinking of a small number.   If I take away 1/3, I will only have 1/5 left.  What is my number? answer
I have a number in my mind.  Now if I take 4 away and then take 5/6 more away, I will still have 32 and 1/2.  So what number is in my mind? answer
Hello.  I have a number locked in my safe.   If you are smart enough to figure it out, I'll give you this number in dollar bills. dollar.jpg (12374 bytes) Give it a try.

If we take away 7/8 from this number and then take away 1/3 more we will end up with -29/24.   What is my number?

answer
Well howdy, I've got this here number in ma head.  

If I take away 17, and then take away a half, and then take away 2/3, and then take away 3/5 more,
well by George, I'll still have 100.  

Can you tell me my number?

answer

YOUR TURN:

Make up and solve some problems like this to share with someone.

These kind of problems are a great way to practice adding fractions.  You can make up a complete MAGIC Show if you are creative.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANSWERS:

SAMPLE: The answer here is 23. 

You see it said, "If I take 1/2 AWAY I will still have 22 1/2. 

So I took the 22 1/2 and I just added the 1/2 BACK ON to get the original number.  22 1/2 + 1/2 = 23.

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no.1
The answer is 137 1/8.

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no.2
The answer is 8/15.

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no3.
the answer is 37 and 1/3.

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no4.
The answer is ZERO dollars
dollar.jpg (12374 bytes) for you!

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no 5.
The answer is 118 and 23/30.   WAY TO GO if you got this one right!!

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