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Adding and Subtracting Fractions
8
3
Adding Fractions with common denominators
8
4
8
3
8
7
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
3
1
2
1
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
3
1
2
1
2 divides into 2, 4, 6, 8…..3 divides into 3, 6, 9….
What is the lowest number 2 and 3 both divide into?
+The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths
6
5
6
2
6
3
2
2
3
1
3
3
2
1
You can’t add fractions with different denominators
Special form of 1
3
1
2
1
10
9
10
4
10
5
5
2
2
1
Lowest common denominator is 10 so make all fractions tenths
4
1
3
1
Turn both fractions into twelfths
12
7
12
3
12
4
3
2
7
3
What is the lowest number BOTH 3 and 7 divide into?
Hmmmmm??????It is 21. So that is my common denominator
21
?
21
?
What special form of 1 will
change 7 to 21. Hmmmm?
It is 3/3So I multiply 3/7 by 3/3
3
3
What special form of 1 will
change 3 to 21. Hmmmm?
It is 7/7So I multiply 2/3 by 7/7
7
7
Now 3x3=9 and 2x7=14Now I know the new
numerators
21
14
21
9
Finally the fractions are READY to add. I just have to add the
numerators 9+14=23
21
21
21
23
Adding Mixed Numbers
• Separate the fraction and the whole number sections, add them separately and recombine at the end
2
2
13
15
6
57
7 65
2 2
13
15
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 + ¼B. ½ + 5/8C. 3/16 + 5/16
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
A. YESB. NOC. YES
D. YESE. NOF. NOG.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 CommonDenominator
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 FractionStep #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 FractionStep #2
• Take the answer (2) and multiply it by both the numerator and denominator.
2 x ½
(OR) 2 x 1 = 2
2 x 2 = 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 thebeginning 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?• 1 ½ - ¾• 15/16 – 3/16
• 3 5/8 – 1 ½
• 5 2/4 – 3 ¼
• 10 5/8 – 7 15/16
• 3 ¼ - 1 ¼
• 7 7/8 – 3 13/16
• NO• YES
• 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
• 1 ½ - 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 Step #2
• Identify the common denominator.
• 1 ½ - ¼ • ANSWER: 4
• 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.
• 1 x 2 = 2
2 x 2 = 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
Did you get the right answer?
If so, good job!!!
If not, you had better go over it again.
Go 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 forget2 20/16 – 15/16
• Remember that you only subtract the numerator, not the denominator.
• The answer: 2 5/16
• WHEW!
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?
