**Adding and Subtracting
Fractions**

- Before we add and subtract fractions we must find the
**L**east**C**ommon**D**enominator (**LCD**). - If the
**L**east**C**ommon**D**enominator (also sometimes called**L**east**C**ommon**M**ultiple) is not obvious, we can always find the unit by finding the shortest rod that is a multiple of each denominator. - Once we find the
**L**east**C**ommon**D**enominator each fraction in the problem must be converted to an equivalent fraction expressed in terms of the common denominator (common terms) in order to be added together.. - First we must find a
**common denominator.**We'll look at the unit or denominator to decide which rods to use. In this case red for**2**and brown for**8**will be used. - Next we will make a train until we have rods of equal length.

**For Example:**

To add the fractions **1/2 + 1/3** we must first
choose rods which represent both of the denominators. Just as in our example
on finding the LCD, the denominator **2** would be represented by the
red rod and the denominator **3** would be represented by the light
green rod. Now create a **train **(rods lined up end-to-end) of red
rods and a train of light green rods until they are equal in length. (These
trains are also known as multiples).Once you have created trains equal
in length total the number of centimeters in each train. As shown below
3 red rods = 6 cm. and 2 light green rods = 6 cm. Therefore, the common
denominator is **6**.

Now we must change each fraction into the terms of the common denominator.
To do this, the numerator of each fraction must be mulitplied by the number
of rods it takes to find the **L**east **C**ommon **D**enominator.

**1/2**_{ }= Take the numerator 1 * 3 red rods = **3/6**

**1/3 **= Take the numerator 1 * 2 light green rods = **2/6**

Once you have the common terms just add your numerators.

**3/6 _{ }+ 2/6_{ }= **

**5/6 _{ }**is your answer.

Now let's try a subtraction problem: **1/2 _{ }-
1/8_{ }=**

- We find that the common denominator is
**8**in this case. We could keep stacking the red and browns together and find other common denominators, but remember we're looking for the__Least__Common Denominator. - Based on the order of operations rule, we will break this into two problems starting with 1/2 + 2/3.
- Remember, we must find a common denominator. In this case we will use red rods for 2 and light green rods for 3 will be used.
- Next we will make a train until we have rods of equal length.
- Just like the last example, once the rods are of equal length. We look
at the common denominator which will be 6 in this case. We could keep stacking
the red and light greens together and find other common denominators, but
remember we're looking for the
**L**east**C**ommon**D**enominator. - As a reminder, look at the unit or denominator to decide which rods to use. In this case dark green for 6 and purple for 4 will be used.
- Next, we will need to make a train until we have rods of equal length. Yours should look like the picture below.
- Again, once the rods are of equal length. We look at the common denominator which will be 12 in this case.

**1/2 _{ }= **Take the numerator 1 *
4 red rods

**1/8 _{ }= **Take the numerator 1 *
1 brown rod

Once you have the common terms just subtract your numerators.

**4/8 _{ }- 1/8_{ }= **

**3/8 _{ }**is your answer.

**For a real challenge try:**

**1/2 + 2/3 - 1/4**

**1/2 _{ }= **Take the numerator 1 * 3 red rods

**2/3 _{ }= **Take the numerator 2 * 2 light green rods

Once you have the common terms just add your numerators.

**3/6 _{ }+ 4/6_{ }= **

**Now we have a new problem 7/6 _{ }- 1/4 **

**7/6 _{ }= **Take the numerator 7 * 2 dark green rods

**1/4 _{ }= **Take the numerator 1 * 3 purple rods

Once you have the common terms just subtract your numerators.

**14/12 - 3/12 _{ }= **

**11/12 **is your answer.

_{Now it's your turn: }

_{Illustrate and solve each of the following using
Cuisenaire rods.}

_{1. }1/2 + 1/4_{ }= 2. 1/3_{ }+ 3/4_{ }=

3. 3/4 + 5/8_{ }= 4. 3/4_{ }-_{ }3/8_{ }=

5. 2/3_{ }-_{ }1/6_{ }+_{ }3/4_{ }=

Check your Answers.

**
Send comments to: silha@girltech.cs.rice.edu
This page was developed through GirlTECH
'97, a teacher training and student technology council program sponsored
by the Center for Research on
Parallel Computation (CRPC), a National
Science Foundation-funded Science
and Technology Center. **

**© June 1997 Molly Silha **