FRACTIONS
COMMON MISTAKES
1
10/20/2009
Fractions – Changing Fractions to Decimals
How to Change Fractions
to Decimals
To change fractions to
decimals, you need to
divide the numerator (top
number) by the
denominator (bottom
number).

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2
Common Mistakes
 Dividing the denominator
by the numerator.
 Incorrect:
1.25
4
→ 4 5.00
5

4
≠ 1.25
5
Correct:
0.8
4
→ 5 4.0
5
Therefore,
4
= 0.8
5
Note: Be careful to divide
top number by bottom
number.
Fractions - Reducing
How to Reduce Fractions
To reduce fractions divide
the largest common number
into both the numerator
(the top) and the
denominator (the
bottom).

3
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Common Mistakes

Not reducing the fraction all
the way.

Incorrect

Correct
16 16 ÷ 2 8
=
=
24 24 ÷ 2 12
16 16 ÷ 8 2
=
=
24 24 ÷ 8 3
10/20/2009
Fractions, Mixed Numbers
How to create a mixed
number.
To make a mixed number, the
numerator must be larger than the
denominator.
Divide the denominator (the
bottom) into the numerator (the
top), the number of times it goes
is the whole number. The
remainder goes in the numerator.
10
Example: 7 Seven goes into 10 once, with 3 left over
So… 10 3



7
4
=1
Common Mistakes

Trying to make a mixed
number when the
numerator (the top) is
smaller than the
denominator (the bottom)

This cannot be made into a mixed number
7
10
7
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10/20/2009
Fractions – Lowest Common Denominator
How to find the LCD
Write the multiples of all the
denominators. Ex. 2 − 1


3
2
The denominators are 3 and 2.

Multiples of 2: 2,4, 6,8,10, 12

Multiples of 3: 3, 6, 9, 12
Common Mistakes

Not finding the smallest LCD

Finding a number that goes into both of
the denominators, NOT a number that
both denominators go into.

Ex.

Incorrect:
1 3
+
6 8
Select the smallest common number.


The LCD is 6
Write equivalent fractions


2 1 2 ⋅ 3 1⋅ 2 6 2
− =
−
= −
6
6
6 6
3 2

5
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In the example above, 2 will go into both 6
and 8; so students will use an LCD of 2 for
the problem.
Correct:

8
1 3 1⋅ 2 3 ⋅ 2 2 6
+ =
+
= + =
6 8 6 ⋅ 2 8 ⋅ 2 12 16 28
9 13
1 3 1⋅ 4 3 ⋅ 3 4
+
=
+
=
+ =
6 8 6 ⋅ 4 8 ⋅ 3 24 24 24
In the example above, the LCD is 24.
10/20/2009
Fractions – Adding and Subtracting
How to add and Subtract
Fractions
Make sure the fractions have a
common denominator. (see slide 2)
Add or Subtract the numerator.
Reduce the fraction



Common Mistakes


Not finding a common
denominator
Adding/subtracting both the
numerator and denominator.

Incorrect

Correct
2 4 6
+ =
3 8 11
2 1 2 ⋅ 8 1 ⋅ 3 16 3 19
+ =
+
=
+
=
3 8 24 24 24 24 24
Note: You can’t ever add or subtract
the denominators.
6
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10/20/2009
Fractions - Multiplying
How to Multiply Fractions
To multiply fractions,
multiply each of the
numerators (the top
numbers) together and each
of the denominators (the
bottom numbers) together.
Reducing can be done
before the multiplying or
after the products are found.


7
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Common Mistakes




Trying to find the Least
Common Denominator
before multiplying.
Not reducing the product all
the way.
21 32
Incorrect: 34 × 87 ≠ 28
×
28
Correct:
3 8 3 × 8 24 ÷ 4 6
× =
=
=
4 7 4 × 7 28 ÷ 4 7
Note: You do NOT need a
Common Denominator to
multiply fractions.
10/20/2009
Fractions - Dividing
How to Divide Fractions
Take the fraction following
the division sign and flip it
- take the reciprocal.
Multiply the fractions



Hint: You must cancel after you
have flipped the fraction.

Ex.

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Canceling before you flip.

Incorrect:




2 4 1 4 4 1
÷ = ⋅ =
=
3 8 3 4 12 3
By canceling the 2 from the first fraction into the 8 in the
second fraction the answer comes out wrong.
Correct:


2 4 2 8 16 4
÷ = ⋅ =
=
3 8 3 4 12 3
8
Common Mistakes
2 4 2 8 1 8 8 4
÷ = ⋅ = ⋅ = =
3 8 3 4 3 2 6 3
In this example, the canceling was done after the fraction
was flipped, thereby giving the correct solution.
Forgetting to flip the fraction following the
division sign.
Forgetting to reduce the final answer.
Flipping (taking the reciprocal) of both
fractions
10/20/2009