Transcript Adding and Subtracting Fractions

3
8
Adding and Subtracting
Fractions
Adding Fractions with common
denominators
3 4
7


8
8 8
Adding Fractions with different
denominators
Problem:
You can’t add fractions with different denominators
without getting them ready first. They will be ready to
add when they have common denominators
Solution:
Turn fractions into equivalent fractions with a
common denominator
that is find the Lowest
Common Multiple (LCM) of the two denominators
Finding the
Lowest Common Denominator
• The lowest common multiple of two numbers is
the lowest number in BOTH lists of multiples
1 1

2 3
Multiples of 2 are 2, 4, 6, 8, 10……
Multiples of 3 are 3, 6, 9, 12, ………
What is the lowest common
multiple?
Finding the
Lowest Common Denominator
• The lowest common multiple of two numbers is
the lowest number they will BOTH divide into
1 1

2 3
2 divides into 2, 4, 6, 8…..
3 divides into 3, 6, 9….
What is the lowest number 2 and 3
both divide into?
1 1

2 3
You can’t add fractions with
different denominators
+
The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths
1 3 1 2 3 2 5
     
2 3 3 2 6 6 6
Special form of 1
1
2

2
5
Lowest common denominator is 10 so make all fractions tenths
5 4 9
 
10 10 10
1
1

3
4
Turn both fractions into twelfths
4 3
7
 
12 12 12
?
?
3 3 2 7
2
9 14 23
   




1
3 7 3 7
21 21 21 21 21 21
It is 3/3
It is 7/7
So I multiply
So I multiply
3/7 by 3/3
2/3 by 7/7
Finally the fractions are READY to
add. I just have to add the
numerators
9+14=23
What
is special
the
lowest
What
What
special
form
formnumber
3 and
77divide
ofBOTH
1 of
will1 change
will
change
3 into?
to 21.
to 21.
Hmmmm?
Hmmmm?
It is 21.
So
that is my
Hmmmmm??????
common denominator
Now 3x3=9 and 2x7=14
Now I know the new
numerators
Adding Mixed Numbers
• Separate the fraction and the whole number sections,
add them separately and recombine at the end
22
11
22

 55
11
33



7

5
6
7

5
6

Let’s Review Adding and
Subtracting
FRACTIONS!!!!
First of all,
what makes up a Fraction?
• A fraction has two parts to it:
• A Numerator (the top number)
• And a Denominator (the bottom number)
Which section do you need help
with? Select an area to learn.
Adding Fractions
Subtracting Fractions
How do you ADD FRACTIONS?
• First of all, you need a
“common
denominator”. This
means the bottom
numbers of each
fraction must be the
same.
½+¾
Cannot be added
together... Yet.
2/4 + ¾
Can be added because
the denominators are
“common” (the same)
Test Time!!!!
See if you can get these
correct, and you will be
on your way!
Can These Be Added?
A. ¾ + ¼
B. ½ + 5/8
C. 3/16 + 5/16
A. YES
B. NO
C. YES
D. 1 ½ + 3 ½
E. 10 3/16 + 3 5/8
F. 15/16 + 3 3/8
G. 2 7/8 + 2 3/8
D. YES
E. NO
F. NO
G. YES
How did you do?
To start any problem, you first need to
determine if you CAN add them together
as they are.
Or…if you need to change them somehow
to add them.
Making a Common
Denominator
How to make a common
denominator.
Here’s what you do if
the denominators are
different:
You first need to find a
number that BOTH
denominators can
divide into evenly.
• Find the common
denominator for:
• 2 and 4
• ANSWER: 4
• 16 and 4
• ANSWER: 16
• 4 and 8
• ANSWER: 8
HINT
• Did you notice that the common
denominator was ALWAYS the bigger of
the two denominators?
• Just remember that this rule ONLY applies
in woodworking. Not in your math class.
Converting the
Fractions
Step #1
Converting the Fraction
Step #1
• Let’s try an example together!
½+¾
• The ½ needs to be converted to match the
bigger denominator.
• So…(what number) x 2 = 4?
• Answer: 2
• Simple huh?
Converting the
Fractions
Step #2
Converting the Fraction
Step #2
• Take the answer (2) and multiply it by both the
numerator and denominator.
2x½
(OR) 2 x 1 = 2
2x2 = 4
Do you agree that ½ = 2/4?
So now…2/4 + 1/4 can be added together.
Adding the Fractions
Adding the Converted Fraction
• Now…what do we do with 2/4 + 1/4?
• All that’s left is adding ONLY the
numerators. The denominator IS NOT
added. It stays the same.
• So… 2/4 + 1/4 = 3/4 THE ANSWER!!!
Conclusions
• All addition problems take the same steps
to solve.
• The common denominator will ALWAYS
be the bigger denominator of the two.
• Don’t be afraid of the problem if it has big
numbers. It’s easy!
Click here to go back to the
beginning of the slide show.
Subtracting
Fractions
Learn to Borrow
Subtraction
• Subtracting fractions begins exactly the
same way as adding fractions.
• The first thing you have to do is figure out
if you CAN subtract them as they are.
• If not, you will need to convert a
denominator so you can.
Test Time!!!
This should be a breeze.
Can these be subtracted?
• 1½-¾
• NO
• 15/16 – 3/16
• YES
•
•
•
•
•
•
•
•
•
•
3 5/8 – 1 ½
5 2/4 – 3 ¼
10 5/8 – 7 15/16
3¼-1¼
7 7/8 – 3 13/16
NO
YES
NO
YES
NO
How did you do?
• Remember that all you need to know is if
they are able to be subtracted.
• If not, we need to convert one of the
fractions.
Make a common
denominator
Let’s do one together
• 1½-¼
• You can see that one of them needs to be
converted so you can subtract them.
• What will the common denominator be?
• ANSWER: 4
Step #1
• Identify the common
denominator.
• 1½-¼
• ANSWER: 4
Step #2
• Since ¼ already has
a denominator of 4
you don’t need to
change it.
• But ½ needs to be
converted to 4’ths.
Step #2 (continued)
•
•
•
•
How do you convert ½ into 4ths?
(what number) x 2 = 4?
ANSWER: 2
Now, multiply both the numerator (top
number) and the denominator (bottom
number) by 2.
• 1x2=2
2x2=4
Step #3
• So now ½ has been converted to 2/4.
• Now we have: 1 2/4 – ¼
• Go ahead and subtract ONLY the
numerators. What did you get?
• ANSWER: 1 ¼
Go again
Did you get the right answer?
If so, good job!!!
If not, you had better go over it
again.
BORROWING!!!
• Generally, borrowing is the most difficult
thing to do in subtracting fractions.
• There are 4 simple steps to follow and it
works for ANY fraction in ANY problem.
• Don’t worry, it’s easy once you learn the
steps.
Here is the problem
• Let’s say that you got a problem like this:
• 3 ¼ - 15/16
• First step: They can’t be subtracted as
they are.
• Second step: What is the common
denominator? ANSWER: 16
• Third step: Convert a fraction.
Let’s go through it
• With a common denominator of 4 we need
to figure out: (what number) x 4=16?
• ANSWER: 4
• SO: 4 x 1 = 4
4 x 4 = 16
Oops! What’s this?
• The problem now
reads like this:
3 4/16 – 15/16
• Normally you would
now subtract. The
problem is that 4 – 15
would be a negative
number. We can’t
have that!
• THUS, BORROWING
IS NEEDED!
Borrowing
• In this problem:
3 4/16 – 15/16
• Borrowing is having to increase the value
or amount of 4/16 so that it’s bigger than
15/16.
• In other words, we need to make 4/16
bigger so that we CAN subtract.
Here’s how to do it
• 3 4/16 needs to be changed somehow.
• We’re going to take 1 whole number from the 3
and add it to 4/16.
• Would you agree that:
2 + 1 4/16 = 3 4/16?
• NOW COMES THE TRICKY PART.
The tricky part
• 2 + 1 4/16 needs to
be changed a bit
before we can
subtract from it.
• Lets take 1 4/16 and
“fix” it.
• Because 16 is the
common denominator
we need to write 1 in
16ths.
• We can write 1 as:
2/2 = 1
3/3 = 1
4/4 = 1
• And so forth up to:
16\16 = 1
SO NOW:
16 + 4 = 20
16 16 16
Recap
• 3 ¼ -15/16 =
• 3 4/16 – 15/16 =
• (2 +1 + 4/16) – 15/16 =
• (2 + 16/16 + 4/16) – 15/16 =
• (2 + 20/16) – 15/16 =
• All of these expressions are equal to each
other.
Let’s pause and try a
couple problems.
Ready for an easy
test?
What fraction would you turn 1 into
to complete the problem?
•
•
•
•
•
•
1 + 3/16
1 + 1/8
1 + 9/16
1+½
1+¾
1 + 5/8
•
•
•
•
•
•
16/16
8/8
16/16
2/2
4/4
8/8
Back to the problem
• Now, instead of:
2 + 1 4/16 we have: 2 20/16
• If we rewrite the problem now we have:
2 20/16 – 15/16
• Now it’s just a simple subtraction problem!
Don’t forget
2 20/16 – 15/16
• Remember that you only subtract the
numerator, not the denominator.
• The answer:
• WHEW!
2 5/16
If you’re not sure yet about
how to borrow, click below to
go through it again.
Borrowing
The End
Has your brain turned
into mush yet?