Fraction XI Adding Mixed Numbers With Unlike Denominators By Monica Yuskaitis

Fraction XIFraction XIAdding Mixed Numbers Adding Mixed Numbers

With Unlike With Unlike DenominatorsDenominatorsBy Monica YuskaitisBy Monica Yuskaitis

Common MultipleCommon Multiple

A number that is a A number that is a multiple of two or more multiple of two or more numbers.numbers.

Some multiples of 3 & 4

12, 24, 36, 48,

Least Common MultipleLeast Common Multiple

The smallest common The smallest common multiple of a set of two or multiple of a set of two or more numbers.more numbers.

5 = 5, 10, 15, 20, 25, 30 4 = 4, 8, 12, 16, 20, 24, 28

Mixed NumbersMixed Numbers

Mixed numbers are whole Mixed numbers are whole numbers and fractions numbers and fractions together.together.

123

Shortcut for Finding the Least Shortcut for Finding the Least Common Denominator or Least Common Denominator or Least

Common MultipleCommon Multiple

1218+

Check to see if the smaller denominator divides evenly into the larger denominator.If it does, use the larger denominator for your LCD or LCM.

2 will divide evenly into 8, so 8 is your LCD or LCM.

3

1

To Add Fractions Mixed To Add Fractions Mixed Numbers With Unlike Numbers With Unlike

DenominatorsDenominators Find the multiples of Find the multiples of

each denominator.each denominator.

1= 4, 8, 12, 16, 20, 30

1= 10, 20, 30, 40, 50+

4

10

3

1

To Add Mixed Fractions To Add Mixed Fractions With Unlike DenominatorsWith Unlike Denominators

Compare the lists of multiples. Compare the lists of multiples. Circle the common multiples Circle the common multiples between the two lists.between the two lists.

1= 4, 8, 12, 16, 20, 24

1= 10, 20, 30, 40, 50+ 10

3

14


1= 4, 8, 12, 16, 20, 24

1= 10, 20, 30, 40, 50+ 10

3

14

Use the least commonUse the least common

multiple as the multiple as the denominator.denominator.


1= 4, 8, 12, 16, 20, 24

1= 10, 20, 30, 40, 50+ 10

3

14

This number is also calledThis number is also called

the least common the least common denominator.denominator.


1

1+ 10

3

14 20

20

Find the equivalent fractions for Find the equivalent fractions for 1/4 & 1/10 with 20 as the 1/4 & 1/10 with 20 as the denominator.denominator.

Ask yourself whatyou multiply 4 by

to get 20.x 5 =


1

1+ 10

3

14 20

20


x 5 =

That’s right 5. Sinceyou are looking for

the equivalent fractionyou know the top

number must also bemultiplied by 5.

x 5 =


1

1+ 10

3

14 20

20


x 5 =x 5 = To find the top number

just multiply 1 x 5 toget your equivalent

fraction.

5


1

1+ 10

3

14 20

20


x 5 =x 5 = Now ask what you

multiply the 10 byto get 20.

5

x 2 =


1

1+ 10

3

14 20

20


x 5 =x 5 = 5

x 2 =

That’s right 2. Since you are looking for the equivalent fraction you know the top number must also be multiplied by 2.

x 2 = 2


1

1+ 10

3

1

4 20

20

Now just add the Now just add the numerators.numerators.

x 5 =x 5 = 5

x 2 =Remember! We never add the denominators.

x 2 = 2

720


1

1+ 10

3

1

4 20

20

Now add the whole Now add the whole numbers.numbers.

x 5 =x 5 = 5

x 2 =x 2 = 2

7204

Add These Mixed NumbersAdd These Mixed Numbers

1316+

Use the shortcut to find the

Least CommonDenominator

(LCD).

6

6

10

3


1316+

Now find theequivalent

fractions for1/3 & 1/6.

6

6x 1 =

x 2 =

Ask what do you multiply 3 by to get 6and what do you multiply 6 by to get 6.

10

3


1316+

Since you arewriting equivalent

fractions, nowmultiply the topnumbers by the

same number you did in the bottom.

6

6x 1 =

x 2 =x 1 =

x 2 =10

3


1316+

Now multiplyacross.

6

6x 1 =

x 2 =x 1 =

x 2 =

1

210

3


1316+

Add yournew

numerators.

6

6x 1 =

x 2 =x 1 =

x 2 =

1

2

36

3

10


1316+

Add yourwhole

numbers.

6

6x 1 =

x 2 =x 1 =

x 2 =

1

2

36

3

10

13

Simplify Your AnswerSimplify Your Answer

36

13 33 = 13 1

2÷÷


4513+

Find the common

multiples for5 and 3. Write

this numberas your newdenominator.

15

15

11

2


4513+

Ask yourselfwhat you

multiply thebottom number

by to get 15.

15

15x 5 =

x 3 =11

2


4513+

Multiply thetop numberby the samenumber you

did in thebottom.

15

15x 5 =

x 3 =x 5 =

x 3 =

2

11


4513+

Multiplyacross.

15

15x 5 =

x 3 =x 5 =

x 3 =

5

1211

2


4513+

Now addyour new

numerators.15

15x 5 =

x 3 =x 5 =

x 3 =

5

12

1715

11

2

Change Your Improper Change Your Improper FractionFraction

to a Mixed Numberto a Mixed Number

4513+

15

15x 5 =

x 3 =x 5 =

x 3 =

5

12

1715

11

215)17

1

152

215

Add Your 1 to Your Whole Add Your 1 to Your Whole NumbersNumbers

4513+

15

15x 5 =

x 3 =x 5 =

x 3 =

5

12

1715

11

215)17

1

152

215

1

14

Put Your Remainder FractionPut Your Remainder FractionNext to Your AnswerNext to Your Answer

4513+

15

15x 5 =

x 3 =x 5 =

x 3 =

5

12

1715

11

215)17

1

152

215

1

14 215

Your Final Answer Is 14 2/15Your Final Answer Is 14 2/15

4513+

15

15x 5 =

x 3 =x 5 =

x 3 =

5

12

1715

11

215)17

1

152

215

1

14 215


5658+

24

24x 3 =

x 4 =x 3 =

x 4 =

15

20

3524

24

324)35

1

11

1124

24

1

28 1124

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Fraction XI Adding Mixed Numbers With Unlike Denominators By Monica Yuskaitis