### Learn Fractions with Cuisenaire Rods

• Before we add and subtract fractions we must find the Least Common Denominator (LCD).
• If the Least Common Denominator (also sometimes called Least Common Multiple) 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 Least Common Denominator 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..

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 Least Common Denominator.

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

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

3/6 + 2/6 =

Now let's try a subtraction problem: 1/2 - 1/8 =

• 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.

• 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.
• 1/2 = Take the numerator 1 * 4 red rods = 4/8

1/8 = Take the numerator 1 * 1 brown rod = 1/8

Once you have the common terms just subtract your numerators.

4/8 - 1/8 =

For a real challenge try:

1/2 + 2/3 - 1/4

• 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 Least Common Denominator.
• 1/2 = Take the numerator 1 * 3 red rods = 3/6

2/3 = Take the numerator 2 * 2 light green rods = 4/6

3/6 + 4/6 =

Now we have a new problem 7/6 - 1/4

• 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.
• 7/6 = Take the numerator 7 * 2 dark green rods = 14/12

1/4 = Take the numerator 1 * 3 purple rods = 3/12

Once you have the common terms just subtract your numerators.

14/12 - 3/12 =

`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.`