LBASS
Little Boys Always Stain Shirts
L – Determine the LCD
B – Build up the fractions so they have the LCD
A – Add fractions with like denominators if this is the operation.
S – Subtract fractions with like denominators if this is the operation.
S – Simplify the fraction, if it can be reduced.
Least Common Denominator
The Least Common Denominator (LCD) and Least Common Multiple are obtained
in the same way. However, the LCD uses two or more denominators (bottom
number of a fraction) where as the LCM uses any two or more numbers. The
following breakdown of the terms used in Least Common Multiple will help
understand its meaning.
Least: the smallest common multiple
Common: the same multiple
Multiple: Multiples are obtained by multiplying a number by the counting
numbers (1, 2, 3, etc.). Therefore the multiples of 3 are 3, 6, 9, etc.
Example
To find the Least common multiple of 3 and 5, we first list some of their multiples
until we find the first common multiple.
Multiples of 3
Multiples of 5
3x1=3
5x1=5
3x2=6
5x2=10
3x3=9
5x3=15
3x4=12
3x5=15
Since 15 is the first common multiple, it is the least common multiple for 3 and 5.
Guided Practice
List the multiples of 8 and 20.
Multiples of 8
Multiples of 20
8x1 =
20x1 =
8x2 =
20x2 =
8x3 =
20x3 =
8x4 =
20x4 =
8x5 =
20x5 =
The first common multiple is the Least Common Multiple. Therefore, the LCM for
8 and 20 is _________.
Building Equivalent Fractions
Building equivalent fractions is the reverse of reducing fractions. When we reduce
fractions, we make the numerator and denominator the smallest numbers possible
such that we still have an equivalent fraction in lowest terms. When we build
equivalent fractions, we normally start with a reduced fraction and build it up so
that it has a common denominator. In order to add or subtract fractions we need a
common denominator.
Example
Suppose we want to add 2/3 + 1/5. We first look at the two denominators 3 & 5
and determine the common denominator.
Multiples of 3
Multiples of 5
1x3=3
1x5=5
2x3=6
2x5=10
3x3=9
3x5=15
3x4=12
3x5=15
The least common multiple (denominator) is 15.
Therefore, we want to build up 2/3 & 1/5 so that they have the common
denominator of 15. To build up fractions, we always multiply by 1 since this is an
identity (it doesn’t change the value of the fraction) when multiplying. Since we
want the fraction 2/3 to have a denominator of 15, we need to multiply by 5/5 to
give us 10/15:
2
3
5
× =
5
10
15
. Remember that when we multiply fractions we
multiply straight across, numerator times numerator and denominator times
denominator. For the fraction 1/5, we also want it to have a denominator of 15.
Therefore we multiply it by 3/3:
1
5
3
× =
3
3
15
.
Guided Practice
Determine the LCD for the following fractions: 3/8 and 5/12. Then build up each
fraction so that they have the LCD.
Adding and Subtracting Fractions with like Denominators
Adding Fractions with like Denominators
When adding fractions with like denominators, we add the numerators and keep
the common denominator.
2
3
Example: + =
7
7
Guided Practice:
2+3
=
7
5
7
Add the following fractions:
___ + ___
3 2
+ =
=
6 6
Subtracting Fractions with like Denominators
When subtracting fractions with like denominators, we subtract the numerators and
keep the common denominator.
4
3
Example: − =
5
5
Guided Practice:
4−3
5
=
1
5
Subtract the following fractions:
___ − ___
5 2
− =
=
8 8
Simplifying Fractions
There is more than one way to simplify a fraction. This handout will show you
only one way.
1. Use a factor tree to break down the numerator and the denominator into their
prime factors.
2. Write the prime factorization of both the numerator and the denominator.
3. Look at each factor in both the numerator and the denominator and choose
the factor with the smallest or same exponent. Multiply these factors to
obtain the Greatest Common Factor (GCF).
4. Divide both the numerator and the denominator by the GCF to simplify the
fraction into its simplest terms.
Example
Simplify the following fraction: 24/60.
1. Use a factor tree to break down the numerator and the denominator into their
prime factors.
24 = 2*2*2*3
60 = 2*2*3*5
2. Write the prime factorization of both the numerator and the denominator.
24 = 23*3
60 = 22*3*5
3. Look at each factor in both the numerator and the denominator and choose
the factor with the smallest or same exponent. Multiply these factors to
obtain the Greatest Common Factor (GCF).
GCF = 22*3 = 12
4. Divide both the numerator and the denominator by the GCF to simplify the
fraction into its simplest terms.
2
24 24 ÷ 12
=
=
5
60 60 ÷ 12
Guided Practice
Simplify the following fraction: 40/72
1. Use a factor tree to break down the numerator and the denominator into their
prime factors.
40 =
72 =
2. Write the prime factorization of both the numerator and the denominator.
40 =
72 =
3. Look at each factor in both the numerator and the denominator and choose
the factor with the smallest or same exponent. Multiply these factors to
obtain the Greatest Common Factor (GCF).
GCF =
=
4. Divide both the numerator and the denominator by the GCF to simplify the
fraction into its simplest terms.
____ ÷ ____
40
=
=
____ ÷ ____
72
Adding and Subtracting Fractions with unlike Denominators
To add and subtract fractions you first need a common denominator. Therefore, if
the fractions don’t have a common denominator, then follow the steps above to
build up the fractions so that they have the least common denominator. Once the
fractions have a common denominator, we add or subtract the numerators and keep
the common denominator.
Example
To add 2/3 + ¼ , we first determine the common denominator.
Multiples of 3
Multiples of 4
1x3=3
1x4=4
2x3=6
2x4=83x4=12
3x3=9
3x4=12
The lowest common multiple (denominator) is 12.
Now we want to build up the fractions so that they have the low common
denominator. In order to get a common denominator of 12, multiple 2/3 times 4/4
to get 8/12.
3/12.
1
4
3
2
3
× =
3
4
× =
3
4
12
8
12
. For the fraction ¼ , we need to multiply it by 3/3 to get
. Now that our fractions have common denominators, we can add
them by adding the numerators and keeping the common denominator. Therefore
8
12
+
3
12
=
11
12
Guided Practice
1. Determine the LCD for the following fractions: 2/3 and ¾.
2. Build up each fraction so that they have the LCD.
3. Add the two fractions.