Fraction xii subtracting unlike denominators
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Fraction XII Subtracting Unlike Denominators. By Monica Yuskaitis. Common Multiple. A number that is a multiple of two or more numbers. Some multiples of 4 & 6 12, 24, 36. Least Common Multiple. The smallest common multiple of a set of two or more numbers. 8 = 8, 16, 24, 32, 40, 48.

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Fraction xii subtracting unlike denominators

Fraction XIISubtracting Unlike Denominators

By Monica Yuskaitis


Common multiple
Common Multiple

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

Some multiples of 4 & 6

12, 24, 36


Least common multiple
Least Common Multiple

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

8 = 8, 16, 24, 32, 40, 48

6 = 6, 12, 18, 24, 30, 36


Shortcut for finding the least common denominator or least common multiple
Shortcut for Finding the Least Common Denominator or Least Common Multiple

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.

1

3 will divide evenly into 9,

so 9 is your LCD or LCM.

3

1

-

9


To subtract fractions with unlike denominators
To Subtract Fractions With Unlike Denominators Common Multiple

  • Find the multiples of each denominator.

1

5

= 5, 10, 15, 20, 25, 30

1

-

10

= 10, 20, 30, 40, 50


To subtract fractions with unlike denominators1
To Subtract Fractions With Unlike Denominators Common Multiple

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

1

5 = 5, 10, 15, 20, 25, 30

1

-

10 = 10, 20, 30, 40, 50


To subtract fractions with unlike denominators2
To Subtract Fractions With Unlike Denominators Common Multiple

  • Use the lowest common multiple as the denominator.

1

5 = 5, 10, 15 ,20 ,25 ,30

1

-

10 = 10, 20, 30, 40, 50


To subtract fractions with unlike denominators3
To Subtract Fractions With Unlike Denominators Common Multiple

  • This number is also called the least common denominator.

1

5 = 5, 10, 15 ,20 ,25 ,30

1

-

10 = 10, 20, 30, 40, 50


To subtract fractions with unlike denominators4
To Subtract Fractions With Unlike Denominators Common Multiple

  • Rewrite the fractions using the least common denominator or least common multiple.

1

5

10

1

-

10

10


To subtract fractions with unlike denominators5
To Subtract Fractions With Unlike Denominators Common Multiple

  • Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator.

You know that 1/10

is equal to 1/10 so

Put a 1 over the

Bottom 10.

1

5

10

1

1

-

10

10


To subtract fractions with unlike denominators6
To Subtract Fractions With Unlike Denominators Common Multiple

  • Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator.

To find the top

number, ask yourself

what do you multiply

the 5 by to get 10.

1

5

10

1

1

-

10

10


To subtract fractions with unlike denominators7
To Subtract Fractions With Unlike Denominators Common Multiple

  • Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator.

That’s right 2. Since

you are looking for

the equivalent fraction

you know the top

number must also be

multiplied by 2.

1

x 2 =

5

10

x 2 =

1

1

-

10

10


To subtract fractions with unlike denominators8
To Subtract Fractions With Unlike Denominators Common Multiple

  • Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator.

1

2

x 2 =

To find the top number

just multiply 2 x 1 to

get your equivalent

fraction.

5

10

x 2 =

1

1

-

10

10


To subtract fractions with unlike denominators9
To Subtract Fractions With Unlike Denominators Common Multiple

  • Now just add the numerators.

1

2

x 2 =

5

10

Remember when

subtracting fractions you never subtract the denominators.

x 2 =

1

1

-

10

10

1

10


Subtract these fractions
Subtract these Fractions Common Multiple

Use the short

cut to find the

Least Common

Denominator

(LCD).

1

2

8

1

-

8

8


Subtract these fractions1
Subtract these Fractions Common Multiple

Now find the

equivalent

fractions for

1/2 & 1/8.

1

2

8

x 4 =

1

-

8

x 1 =

8

Ask what do you multiply 2 by to get 8

and what do you multiply 8 by to get 8.


Subtract these fractions2
Subtract these Fractions Common Multiple

Since you are

writing equivalent

fractions, now

multiply the top

numbers by the

same number you

did in the

bottom.

1

x 4 =

2

8

x 4 =

1

x 1 =

-

8

x 1 =

8


Subtract these fractions3
Subtract these Fractions Common Multiple

1

4

Now multiply

across.

x 4 =

2

8

x 4 =

1

1

x 1 =

-

8

x 1 =

8


Subtract these fractions4
Subtract these Fractions Common Multiple

1

4

Subtract

your new

numerators.

x 4 =

2

8

x 4 =

1

1

x 1 =

-

8

x 1 =

8

3

8


Subtract these fractions5
Subtract these Fractions Common Multiple

Find the

common

Multiples for

5 and 3. Write

This number

As your new

denominator.

2

5

15

1

-

3

15


Subtract these fractions6
Subtract these Fractions Common Multiple

Ask yourself

what you

multiply the

bottom number

by to get 15.

2

5

15

x 3 =

1

-

3

x 5 =

15


Subtract these fractions7
Subtract these Fractions Common Multiple

Multiply the

top number

by the same

number you

did in the

bottom.

2

x 3 =

5

15

x 3 =

1

x 5 =

-

3

x 5 =

15


Subtract these fractions8
Subtract these Fractions Common Multiple

Multiply

across.

2

6

x 3 =

5

15

x 3 =

1

5

x 5 =

-

3

x 5 =

15


Subtract these fractions9
Subtract these Fractions Common Multiple

Now subtract

your new

numerators.

2

6

x 3 =

5

15

x 3 =

1

5

x 5 =

-

3

x 5 =

15

1

15


Subtract these fractions10
Subtract these Fractions Common Multiple

5

20

x 4 =

6

24

x 4 =

1

3

x 3 =

-

8

x 3 =

24

17

24


Subtract these fractions11
Subtract these Fractions Common Multiple

2

6

x 3 =

3

9

x 3 =

1

1

x 1 =

-

9

x 1 =

9

5

9


Subtract these fractions12
Subtract these Fractions Common Multiple

4

12

x 3 =

5

15

x 3 =

2

10

x 5 =

-

3

x 5 =

15

2

15