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:
- 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
- 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 =
- 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:
- 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.
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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. 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.
back
no.1
The answer is 137 1/8.
back
no.2
The answer is 8/15.
back
no3.
the answer is 37 and 1/3.
back
no4.
The answer is ZERO dollars for you!
back
no 5.
The answer is 118 and 23/30. WAY TO GO if you got this one right!!
back
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