““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.