“working with fractions” a review of addition and subtraction click here to begin
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““Working with Working with Fractions”Fractions”
A Review of A Review of Addition and SubtractionAddition and Subtraction
CLICK HERE TO BEGIN
Goals:Goals:
After finishing this activity you will be able to:After finishing this activity you will be able to:
Add fractions with Add fractions with likelike denominators denominators
Add fractions with Add fractions with unlikeunlike denominators denominators
Subtract fractions with Subtract fractions with likelike denominators denominators
Subtract fractions with Subtract fractions with unlikeunlike denominators denominators
Click to CONTINUE
FractionsFractionsLet’s review the parts of a fraction:Let’s review the parts of a fraction:
2
1Numerator
Denominator
Fractions have “Like Denominators” if both fractions have the exact same number in the denominator.
Fractions have “Unlike Denominators” if they have different numbers in the denominator.
Example
Example
Click to CONTINUE
““Like DenominatorsLike Denominators””
15
2
15
7The
same number for both fractions
RETURN to Lesson
““Unlike DenominatorsUnlike Denominators””
19
7
12
5Different numbers for each fraction
RETURN to Lesson
Adding Fractions with Adding Fractions with LIKE LIKE DenominatorsDenominators
Let’s say we wanted to solve the problem below:Let’s say we wanted to solve the problem below:
5
1
5
3
Since these fractions have the same number in Since these fractions have the same number in the denominator, all we have to do is add the the denominator, all we have to do is add the numerators!numerators!
WATCH it happen!
5
1
5
3
5
13
5
4
When adding fractions When adding fractions DO NOTDO NOT add the denominators together!add the denominators together!
Click to CONTINUE
Adding Fractions with Adding Fractions with UNLIKEUNLIKE DenominatorsDenominators
This time, let’s try to solve a problem that is slightly This time, let’s try to solve a problem that is slightly more challenging:more challenging:
4
1
3
2
Since the denominators are NOT THE SAME, the first thing Since the denominators are NOT THE SAME, the first thing we have to do is make them the same by finding the Least we have to do is make them the same by finding the Least Common Multiple or the LCM.Common Multiple or the LCM.
Click here to FIND the LCM.
Step #1: List the multiples of each denominator.Step #1: List the multiples of each denominator.
... 21 18, 15, 12, 9, 6, 3, :3 of Multiples... 28 24, 20, 16, 12, 8, 4, :4 of Multiples
Step #2: Find the SMALLEST number that is in BOTH lists.Step #2: Find the SMALLEST number that is in BOTH lists.
... 21 18, 15, 12, 9, 6, 3, :3 of Multiples... 28 24, 20, 16, 12, 8, 4, :4 of Multiples
This number is the LCM of the denominators!This number is the LCM of the denominators!Click here to find
out what to do now that we have
the LCM!
We want to make the denominators of both fractions to be equal to the We want to make the denominators of both fractions to be equal to the LCM we just found. We can use multiplication to make that happen!LCM we just found. We can use multiplication to make that happen!
12
8
3
2
4
4 Since
12
3
4
1
3
3 and
12
3
12
8
4
1
3
2 Becomes
Now that we have like denominators we can add the fractions like we did
last time!
12
3
12
8
12
38
12
11
12
11
4
1
3
2 So
Click to CONTINUE
Subtracting Fractions with Subtracting Fractions with LIKE LIKE DenominatorsDenominators
Let’s say we wanted to solve the problem below:Let’s say we wanted to solve the problem below:
7
3
7
4
Since these fractions have the same number in Since these fractions have the same number in the denominator, all we have to do is subtract the the denominator, all we have to do is subtract the numerators!numerators!
WATCH it happen!
7
3
7
4
7
34
7
1
When subtracting fractions When subtracting fractions DO NOTDO NOT subtract the denominators!subtract the denominators!
Click to CONTINUE
Subtracting Fractions with Subtracting Fractions with UNLIKEUNLIKE Denominators Denominators
This time, let’s try to solve a problem that is slightly This time, let’s try to solve a problem that is slightly more challenging:more challenging:
4
1
6
5
Since the denominators are NOT THE SAME, the first thing Since the denominators are NOT THE SAME, the first thing we have to do is make them the same by finding the Least we have to do is make them the same by finding the Least Common Multiple or the LCM.Common Multiple or the LCM.
Click here to FIND the LCM.
Step #1: List the multiples of each denominator.Step #1: List the multiples of each denominator.
... 36 30, 24, 18, 12, 6, :6 of Multiples
... 24 20, 16, 12, 8, 4, :4 of Multiples
Step #2: Find the SMALLEST number that is in BOTH lists.Step #2: Find the SMALLEST number that is in BOTH lists.
This number is the LCM of the denominators!This number is the LCM of the denominators!Click here to find
out what to do now that we have
the LCM!
... 36 30, 24, 18, 12, 6, :6 of Multiples
... 24 20, 16, 12, 8, 4, :4 of Multiples
We want to make the denominators of both fractions to be equal to the We want to make the denominators of both fractions to be equal to the LCM we just found. We can use multiplication to make that happen!LCM we just found. We can use multiplication to make that happen!
12
10
6
5
2
2 Since
12
3
4
1
3
3 and
12
3
12
10
4
1
6
5 Becomes
Now that we have like denominators we can add the fractions like we did
last time!
12
3
12
10
12
310
12
7
12
7
4
1
6
5 So
Click to CONTINUE
Let’s Review:Let’s Review:To Add or Subtract fractions with “To Add or Subtract fractions with “Like Like
DenominatorsDenominators:” all you have to do is add or :” all you have to do is add or subtract the numerators.subtract the numerators.
To Add or Subtract fractions with “To Add or Subtract fractions with “Unlike Unlike DenominatorsDenominators:” :” First find the LCM of the denominators.First find the LCM of the denominators. Second, multiply each fraction on make the Second, multiply each fraction on make the
denominators equal to the LCMdenominators equal to the LCM Finally, add or subtract the numeratorsFinally, add or subtract the numerators
Time to PRACTICE
Problem #1Click on the letter of the correct answer:
11
2
11
511
10 A.)
11
7 B.)
22
7 C.)
That is Correct!
11
7
11
2
11
5
Go to Problem #2
Sorry that is Incorrect…
Remember, when adding fractions with the same denominator:
Add the numerators DO NOT add the denominators Simplify the fraction when needed
Go to Problem #2
Problem #2Click on the letter of the correct answer:
5
3
7
412
7 A.)
35
7 B.)
35
41 C.)
That is Correct!
35
41
5
3
7
4
Go to Problem #3
Sorry that is Incorrect…
Remember, when adding fractions with the different denominators:
Find the LCM of the denominators Use multiplication to change the
denominators Add the “new” numerators, but NOT the
“new” denominators
Go to Problem #3
Problem #3Click on the letter of the correct answer:
21
2
21
1008
A.)
21
12 B.)
218
C.)
That is Correct!
21
8
21
2
21
10
Go to Problem #4
Sorry that is Incorrect…
Remember, when subtracting fractions with the same denominator:
Subtract the numerators DO NOT subtract the denominators Simplify the fraction when needed You can NEVER have a zero in the
denominator!
Go to Problem #4
Problem #4Click on the letter of the correct answer:
11
6
5
3553
A.)
63
B.)
55-3
C.)
That is Correct!
55
3
11
6
5
3
Click here to FINISH this lesson
Sorry that is Incorrect…
Remember, when subtracting fractions with the different denominators:
Find the LCM of the denominators Use multiplication to change the
denominators Subtract the “new” numerators, but NOT
the “new” denominators
Click here to FINISH this lesson
Congratulations!Congratulations!
You have finished this review lesson.You have finished this review lesson.
Please see your teacher to receive Please see your teacher to receive your homework assignment where your homework assignment where
you will practice these skills.you will practice these skills.
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