Transcript 4NF3cd - Polk School District

I can add and subtract mixed numbers with the same
denominators.
I can solve word problems with addition and subtraction of
fractions that refer to the same whole and have the same
denominators.
What you already know…
 That fractions are ways of representing parts of a
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whole (the same whole)
The numerator goes on top
The denominator goes on bottom
Fractions with the same denominators are called like
fractions
You know how to decompose fractions (you’d better)
You know that the kid next to you has been picking his
nose for the past half hour
Moving on…
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Okay, so you can probably add ¾ + ¾
3 + 3 = 6, so ¾ + ¾ = 6/4
Well now… It appears we have an improper fraction.
We can convert improper fractions (fractions with a bigger
numerator than denominator) into a mixed number (whole
number – fraction combo) by decomposing.
All right, 4/4 is equal to 1 whole…
6 can be decomposed into 4 + 2, so
6/4 can become 4/4 + 2/4
Since 4/4 = 1, 6/4 = 1 & 2/4
You don’t have to use the ampersand like I do.
On paper…
 The problem should look something like this in math class:
 3
3
6
 --- + --- = -- 4
4
4
 6
4
2
 --- = --- + -- 4
4
4
 Which equals…
 2
 1 -- 4
Model It!
 A 4th grader must be able to solve these problems using
numbers, but it is always helpful to draw a picture.
Here’s ¾ + ¾ = 6/4 = 1 & 2/4
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You may have noticed…
 After adding the 2 fractions in the model, we went
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ahead and regrouped the totals.
We filled up one of the models.
This is because 3 + 3 = 4 + 2
This is what I noticed…
It’s a picture of your mother driving home from school
So now what?
 Now that we’ve been introduced to mixed numbers…
 It’s time to work with them.
 First, let’s add some mixed numbers with like
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denominators.
Step 1: Add the fractions
Step 2: Add the whole numbers
Step 3: Rewrite the solution as an addition problem.
Step 4: Decompose the improper fraction (if necessary)
Step 5: Add up all the parts to get a final mixed number.
Easy for you to say!
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Okay, let’s try an example:
2 and 2/3 + 1 and 2/3
2/3 + 2/3 = 4/3
2+1=3
So…
2 and 2/3 + 1 and 2/3 = 3 and 4/3
That’s…
3 + 3/3 + 1/3
Which is…
3 + 1 + 1/3
Which is
4 + 1/3
AKA
4 & 1/3
On paper…
 The problem should look kind of like this in math class?
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2
2
4
 2--- + 1--- = 3-- 3
3
3
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--- = 1
3
 3+1=4
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 4 -- 3
Now subtraction:
 4 & 7/8 – 2 & 5/8
 Step 1: subtract the fractions
 7/8 – 5/8 = 2/8
 Step 2: subtract the whole numbers
 4 – 2 = 2, so…
 4 & 7/8 – 2 & 5/8 = 2 & 2/8
 Easy!!!
But what about regrouping?
 Yup, sometimes you have to borrow.
 This is where decomposing comes in again.
An example with borrowing:
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4 & 1/8 – 1 and 3/8
Can’t subtract 3 from 1, so you must borrow from the 4.
The 4 becomes 3 + 1
The 1 becomes 8/8.
Add the 8/8 to the 1/8 to get 9/8.
Now you can subtract 3 & 9/8 – 1 & 3/8
9 – 3 = 6; 3 – 1 = 2; so…
4 & 1/8 – 1 & 3/8 = 2 & 6/8
I know it sounds like a lot…
But it gets easier with practice.
Your turn!
Solve these 2 word problems…
 Joe ate 2 & 3/5 cups of ice cream. Jess did too. How
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much ice cream did they eat all together?
Emma had 3 & 1/3 cups of sugar. She use 1 & 2/3 cups
for a cookie recipe. How much sugar did Emma have
left.
You take your time, I’ll just wait here…
I’m sure you’ll make short work out of it…
At least, I’m pretty sure…
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How did you do?
 2 & 3/5 + 2 & 3/5 = 4 & 6/5 = 4 + 5/5 + 1/5 …
 = 4 + 1 + 1/5
 = 5 + 1/5, AKA
 5 & 1/5 cups
 That’s a lot of ice cream!
How about Emma?
 3 & 1/3 – 1 & 2/3; You have to borrow from the 3
 2 + 1 = 3; 2 + 3/3 = 3; Add the 3/3 to the 1/3 to get…
 2 & 4/3 – 1 & 2/3 = 1 & 2/3 cups of sugar.
 SWEET!
In Closing…
 Remember to decompose when you have to borrow or
convert an improper fraction into a mixed number
 Remember that the grass is always greener on the
other side.
 Remember that you can’t help being ugly, but you
could stay home.
 Peace Out!