Download Fractions Notes A Fraction – is a number that represents a piece of

Fractions Notes
A Fraction – is a number that represents a piece of or part of a whole number.
¾ represents 3 pieces out of 4.
Numerator - The top # of a fraction which shows how many used/unused parts you have.
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Green = ¾ while White = ¼ in the drawing above.
Denominator – The bottom # of a fraction which shows how many parts the whole is divided into.
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The pieces of the denominator must all be the same size!
To say fractions give the numerator followed by the denominator in nds, rds, or ths, etc.
 3/5 – say “three fifths”
2/3 – say “two thirds” 11/42 – say “eleven forty seconds”
Forms of Fractions
Proper Fractions – The numerator is less than the denominator.
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4/7
2/5
15/16
Improper Fractions – The denominator is equal to, or less than the numerator.
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3/2
13/10
4/4
Mixed Numbers – There is a whole number combined (mixed) with a fraction.
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2½
10 ¾
6 2/3
Fractions Notes
Changing Forms of Fractions
Improper to Mixed –
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To change improper fractions to mixed fractions (or whole #s), you divide the numerator
by the denominator.
The product “answer” becomes the whole #, the remainder becomes the numerator and
the divisor “# you’re dividing by” becomes (stays) the denominator.
Ex: 3/2
3 2=1½
Ex: 11/4
11 ÷ 4 = 2 ¾
3/2 = 1 ½
11/4 = 2 ¾
Mixed to Improper –
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To change mixed numbers to improper fractions, you multiply the whole number by the
denominator then add the numerator. You keep the same denominator (unless you can
reduce the fraction…).
Ex: 3 ½
3x2=6
6+ 1 = 7
Ex: 11 ¾
11 x 4 = 44
44 + 3 = 47
3 ½ = 7/4
11 ¾ = 47/4
* Note: you can check you work changing forms of fractions by doing the opposite procedure to
switch the number back. For example, if you changed a mixed number to an improper fraction, you
can check your work by changing the improper fraction back to a mixed number.
Fractions Notes
Simplifying (Reducing) Fractions
A fraction can be reduced if the numerator and the denominator have common factors they can be
divided by.
To reduce a fraction, divide the numerator and the denominator by a common factor (preferably the
Greatest Common Factor).
Ex: 12/20
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Both 12 and 20 can be reduced by 2 because they’re even numbers.
12 ÷ 2 = 6 and 20 ÷ 2 = 10 now you have 6/10.
6/10 can also be reduced by 2 because they’re both even numbers.
6 ÷ 2 = 3 and 10 ÷ 2 = 5 now you have 3/5.
3/5 is the simplest/lowest form of this fraction because there are no other common factors
(except 1 – which doesn’t change anything).
 12/20 = 3/5
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This question could have been completed in one step if we divided by the GCF of 4.
12 ÷ 4 = 3 and 20 ÷ 4 = 5
 12/20 = 3/5
Ex: 7/21
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7 is the GCF of 7 and 21, so we’ll divide by that.
7 ÷ 7 = 1 and 21 ÷ 7 = 3
 7/21 = 1/3
Fractions Notes
Adding and Subtracting Fractions
In order to add or subtract fractions, they must have a COMMON DENOMINATOR.
Ex: 1/5 + 2/5
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These numbers have a common denominator of 5 so we can begin adding.
Add the numerators – 1 + 2 = 3
Keep the denominator the same – 5
 1/5 + 2/5 = 3/5
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Check to see if you can reduce your answer…3/5 cannot be reduced because it has no
common factors (other than 1).
Ex: 1/3 + 2/5
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These numbers do not have a common denominator so we must make one.
Choose a multiple of the denominators (3 and 5).
3 x 5 = 15 and 5 x 3 = 15
Now multiply the numerators by the same # as you did to its denominator.
1 x 5 = 5 and 2 x 3 = 6
Now we have 5/15 + 6/15 (common denominators), so we can add.
Add the numerators – 5 + 6 = 11
Keep the denominator the same – 15
 5/15 + 6/15 = 11/15
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Check to see if you can reduce your answer…11/15 cannot be reduced because it has no
common factors (other than 1).
Fractions Notes
Comparing Fractions (using common denominators)
In order to compare fractions you must have a common denominator.
Ex: Compare 4/5 and 7/8.
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Make the denominator 40 here by multiplying 5 x 8.
Multiply the numerators by the same numbers you used for the denominators.
4 x 8 = 32 and 7 x 5 = 35.
32/40 and 35/40 can now be compared.
The fraction with the largest (value) numerator is the larger fraction.
 32/40 < 35/40
 therefore 4/5 < 7/8
Comparing Fractions (using cross multiplication)
To compare fractions using cross multiplication, you multiply the denominator of the left fraction up
to the numerator of the right fraction. Then multiply the denominator on the right up to the
numerator on the left. The highest value product (answer when multiplying) is the larger fraction.
Ex: Compare 4/5 and 7/8.
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5 x 7 = 35 and 8 x 4 = 32
 Therefore 7/8 > 4/5
Ex: Compare 2/5 and 4/7.
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5 x 4 = 20 and 7 x 2 = 14
 Therefore 4/7 > 2/5