Adding Fractions and Mixed Numbers

1
Adding Fractions and Mixed Numbers
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Steps in Adding Fractions

• 1. Make sure all fractions have the same
  denominator
• If not find the Least Common Denominator (by
  finding the least common multiple of
  denominators)
• Then find fractions equivalent to original
  fractions, but with all having the same
  denominator. (by multiplying the top and bottom
  by the same number

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Steps in Adding Fractions

• 2. Once you have common denominators, also called
  like denominators, add the numerators together
• Only the numerators of fractions are to be added
  
• Denominators are never added together

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Steps in Adding Fractions

• 3. In answer, write the sum of the numerators as
  your new numerator. Keep the denominator the same

5
Steps in Adding Fractions

• 4. Reduce or convert the final answer if
  necessary
• Reduce all fractions not in simplest terms
• Convert any improper fractions to mixed or whole
  numbers

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Common Multiple
A number that is a multiple of two or more
numbers.
Some multiples of 3 6 6, 12, 18, 24, 30, 36,
42
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Least Common Multiple
The smallest common multiple of a set of two or
more numbers.
5 5, 10, 15, 20, 25, 30
6 6, 12, 18, 24, 30, 36
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Shortcut for Finding the Least Common Denominator
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
5 will divide evenly into 10, so 10 is your LCD
or LCM.
5
1

10
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To Add or Subtract Fractions With Unlike
Denominators
Find the multiples of each denominator.
1
4, 8, 12, 16, 20, 24
4
1

6, 12, 18, 24, 30
6
10
To Add or Subtract Fractions With Unlike
Denominators
Find the common multiples of each denominator.
1
4, 8, 12, 16, 20, 24
4
1

6, 12, 18, 24, 30
6
11
To Add or Subtract Fractions With Unlike
Denominators
Find the least of the common multiple.
1
4, 8, 12, 16, 20, 24
4
1

6, 12, 18, 24, 30
6
12
To Add or Subtract Fractions With Unlike
Denominators
This number is also called the least common
denominator.
1
4, 8, 12, 16, 20, 24
4
1

6, 12, 18, 24, 30
6
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To Add or Subtract Fractions With Unlike
Denominators
Rewrite the fractions using the least common
denominator or least common multiple.
1
4
12
1

12
12
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To Add or Subtract Fractions With Unlike
Denominators
Find the equivalent fractions for 1/4 1/12 with
12 as the denominator.
You know that 1/12 is equal to 1/12 so Put a 1
over the Bottom 12.
1
4
12
1
1

12
12
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To Add or Subtract Fractions With Unlike
Denominators
Find the equivalent fractions for 1/4 1/12 with
12 as the denominator.
1
3 is the correct choice. Since you are looking
for the equivalent fraction you know the
top number must also be multiplied by 3.
x 3
4
12
x 3
1
1

12
12
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To Add or Subtract Fractions With Unlike
Denominators
Find the equivalent fractions for 1/4 1/12 with
12 as the denominator.
1
3
To find the top number just multiply 1 x 3 to get
your equivalent fraction.
x 3
4
12
x 3
1
1

12
12
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To Add or Subtract Fractions With Unlike
Denominators
Now just add the numerators.
1
3
x 3
4
12
Remember when adding fractions you never add the
denominators.
x 3
1
1

12
12
4
12
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To Add or Subtract Fractions With Unlike
Denominators
Reduce if needed.
1
3
x 3
4
12
x 3
Check to see if there is a number that goes into
both numerator and denominator.
1
1

12
12
4
12
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To Add or Subtract Fractions With Unlike
Denominators
Reduce if needed.
1
3
x 3
4
12
x 3
4 goes into both 4 and 12, so divide both numbers
by 4.
1
1

12
12
4
12
20
To Add or Subtract Fractions With Unlike
Denominators
Reduce if needed.
1
3
x 3
4
12
x 3
1
1

12
12
Final Answer
4
4
1

12
4
3

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Adding Mixed Numbers

• For adding mixed numbers, steps remain the same,
  but dont forget to add the whole numbers as the
  end step
• Also, special circumstances arise when sums end
  up with whole numbers and improper fractions
• For these, you must convert the improper fraction
  and add it to the whole number

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Steps in Adding Mixed Numbers

• 1. Make sure all fractions have the same
  denominator
• If not find the Least Common Denominator
• Then find fractions equivalent to original
  fractions, but with all having the same
  denominator.

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Steps in Adding Mixed Numbers

• 2. Once you have common denominators,, add the
  numerators together

3. In answer, write the sum of the numerators as
your new numerator. Keep the denominator the
same.
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Steps in Adding Mixed Numbers

• 4. Add the whole numbers.
• 5. Reduce or convert the final answer if
  necessary
• Reduce all fractions not in simplest terms
• Convert any improper fractions to mixed or whole
  numbers and add this to the sum of the whole
  numbers.