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Kuehn-Haven Middle School
Math Department
Parent’s Simple Guide
to Understanding Fractions
May, 2012
M.A.D. Method
Use: Change a mixed number to an improper
fraction.
What to do:
M = Multiply. Multiply (find the product of) the
denominator in the fraction by the whole number
A = Add. Add the numerator (top number of fraction) to
the product found in "M".
D = Denominator. Keep the Denominator (bottom
number of fraction) from the original fraction.
Quick Tips: 1. Follow the steps in order.
2. Follow the arrow clockwise.
+ +
3
6x
4
x
1. 6 x 4 = 24
2. 24 + 3 = 27
3.
27
Answer!
4
Improper Fractions
Improper Fraction: A fraction where the numerator is
larger than the denominator. (an elephant on a unicycle!)
What to do:
1). Divide the numerator by the denominator.
2). Find a remainder. The remainder is the part that is left
which becomes the new numerator.
3). Keep the denominator the same.
Quick Tips: Put the "numerator in the house" and the
"denominator at the door."
Example:
d
n
2
23
Example:
=
8
8
23
- 16
7
Answer: 2
7
8
Birthday Cake Method
Uses: Simplify a Fraction. Find Common
Denominators to make Equivalent Fractions. Find the
LCM or LCD. Prime Factors. Find the GCF (Greatest
Common Factor). Simplify Binomials and
Polynomials.
What is a "birthday cake?" The birthday cake
method is a simple division model. Start with the
bottom "layer" of the cake and build up using division.
Sometimes the "frosting" on the outside of the cake or
the top of the cake is important, or what is on the
inside is only what is needed. Cakes can range in size.
4). Divide.
3). The quotients
give a new layer.
2). Divide.
.
1). Always start at the bottom.
Let's give it a try
Simplifying Fractions
18
Start with the fraction:
24
3
3
2
/
4
9
12
18
24
The product of the outside “frosting” is the
Greatest Common Factor. So….
3 x 2 = 6 so the GCF is 6
18
divided by
6
24

6
=
3
4
We think simplest form is ¾ but check by
looking back at the birthday cake! Yes! ¾ is
the correct answer found on top of the cake.
Equivalent Fractions
2
Start with the fraction:
3
2
3
2
2
2
2
2
4
3
6
8
12
16
24
2/3 , 4/6, 8/12, and 16/24 are all equivalent fractions
The fraction
2
is placed at the top of the cake. Next, the
3
4
fraction is multiplied by 2 which results in
. You may
6
continue doing this by using the same number
each time like shown above or choose a different
number for the multiplier.
Prime Factors
A Prime Number: is a counting number that has
exactly two factors, 1 and the number itself. The
number 1 is neither prime more composite.
Prime Factorization: is factoring a number into its
prime factors only.
What to do?
What are the prime factors of 18? Start at the
bottom of the cake and divide "up" by prime numbers
only. These numbers can be in any order.
We say the cake is done when there is a "1" or candle
on the top of the cake. The number 1 is neither prime
nor composite.
The prime factors of 18 are the products of the
frosting (prime numbers) on the outside the cake:
3 x 2 x 3.
The prime factorization of 18: 2 x 32
1
3
2
3
3
6
18
Least Common Denominator
(LCD)
Use: Find common denominators to add or
subtract fractions with unlike denominators.
7
3
+
12 16
3
2
2
6
4
8
12
16
The Least Common Denominator is found by taking
the products of the outside “frosting” and the top
“frosting” of the birthday cake.
Tip: Think of an upside down “L”shape being the
“L”CD. Notice how the product of the shaded area
equals the LCD. 2 x 2 x 3 x 4 = 48.
7
3
+
=
12 16
28
9
37
+
=
48 48
48
Glossary
Composite Number-is a counting number that has
more than two factors
Denominator-bottom number within a fraction
GCF-the greatest number that is a common factor of
two or more numbers
Improper Fraction-numerator is equal to or larger
than the denominator
LCD-the least common denominator
LCM-the least number that is a common multiple of
two or more numbers
Mixed Number-consists of a whole number and a
fraction
Numerator-top number within a fraction
Prime Factorization- is factoring a number into its
prime factors only
Prime Number- is a counting number that has exactly
two factors, 1 and the number itself.
Product – The answer to a multiplication problem.
Reciprocal-the inverse of a fraction, meaning the
numerator becomes the denominator and the
denominator becomes the numerator