Name: _______________________________
Unit 1 Study Guide/Helpful Things to Remember
A fraction is part of a whole. We need fractions so we can talk about pieces or parts
of something. For example, you probably didn’t eat a whole pizza at the party; you
likely only ate a certain portion of it!
Numerator: the top part of the fraction. This tells us how many pieces we are
talking about.
Denominator: the bottom part of the fraction. This tells us how many total equal
pieces there are.
This picture shows that you ate ¼ of the pizza, or one out of the four pieces. ¾ of the pizza,
or 3 out of 4 pieces, are remaining.
Mixed Number: a number with both a whole number and a fraction. Ex: 1 ½
Improper Fraction: a number with a larger numerator than denominator. Ex: 7/4. NOTE:
Improper fractions are always greater than one! If 7/4 of a pizza is remaining, then I must
have had more than one whole pizza to begin with, since one pizza only has four slices.
Equivalent Fractions: fractions that are equal (have the same value). ½ and 4/8 are
equivalent.
Comparing Fractions
As a general rule, in order to compare fractions, you need to find a common
denominator first.

First, list the multiples of each denominator to find the lowest multiple that
each denominator has in common
o This number is the least common denominator (LCD)!

Next, change the denominators in the problem into the least common
denominator. This is accomplished by multiplying the numerator and
denominator of each fraction by a number that will yield that LCD on the
bottom.
(Continued on back)

Finally, rewrite the problem with your new (equivalent) fractions. You can
now add, subtract, or compare your fractions!
o Example: 1/4 vs. 2/3

Multiples of 4: 4, 8, 12, 16, 20...

Multiples of 3: 3, 6, 9, 12, 15, 18
12 is the LCD
For 1/4, the numerator and denominator need to be multiplied by 3 in order to yield
a 12 on the bottom. So 1/4 = 3/12. For 2/3 the numerator and denominator need to
be multiplied by 4 in order to produce a 12 on the bottom. So 2/3 = 8/12.
It is now easy to see that 3/12 is smaller than 8/12.
Comparing Fractions: Special Cases
*When both numerators are the same, no common denominator is needed.
Ex: 1/3 vs. 1/12
In the example above, you know that the fraction with the smaller denominator is
the bigger fraction. The fewer pieces the whole is divided into, the larger each piece
will be.
*When both denominators are the same, the fraction with the larger numerator is
the bigger fraction.
Ex: 1/5 vs. 4/5
Think: Would Ms. Alexander rather have one out of five pieces of the chocolate bar,
or four out of five pieces? 
Equivalent Fractions
*To find equivalent fractions, you must first find a common denominator (see
bottom of page 1/top of page 2). Then, you change your denominators into the
common denominator. REMBEMBER: You must multiply both your denominator
AND your numerator when finding equivalent fractions! Whatever is done to the
bottom must be done to the top!
Adding Fractions
*When adding fractions, remember to find a common denominator first! (See steps
on the bottom of page 1/top of page 2). YOU CANNOT ADD FRACTIONS WITH
UNLIKE DENOMINATORS!!!!
*When adding mixed numbers, the fraction part must be added before the whole
numbers!
*If your answer is an improper fraction (a fraction with a bigger numerator than
denominator), then you must get rid of it!
Ex. 5/4 = 1 ¼
*To convert an improper fraction, subtract one whole! For 5/4, a whole
would be 4/4. 5/4 minus 4/4 = 1/4. The whole that was taken away from
the improper fraction becomes a whole number.
Subtracting Fractions
*When subtracting fractions, remember to find a common denominator first! (See
steps on the bottom of page 1/top of page 2). YOU CANNOT SUBTRACT FRACTIONS
WITH UNLIKE DENOMINATORS!!!!
*When subtracting mixed numbers, remember that the fraction portion should be
done before the whole mumbers. If the fraction on the top is smaller than the
fraction on bottom, you need to borrow! (See example below).
We borrowed one whole from 15, so it became 14. The whole that we borrowed was
renamed “30/30” so it would fit in our fraction column. After adding our borrowed
30/30 to the 5/30 we already had, we ended up with 35/30. Now we can subtract!
Please see the Math Wiki for instructional videos!
Remember, practicing problems is the best way to learn
math! Good luck 