Let's try the idea of doubling with another fraction. Imagine you want to double a recipe that calls for 3/4 of a stick of butter. How many sticks of butter will you need?

The model on the left shows a rectangle broken into 4 sections, or fourths. 3 of these sections together is 3/4. Doubling that amount gives you a total of 6 sections of 1/4. Notice:

The second area model on the left shows how 1 2/4 is another name for 6/4.

When you double a fraction, you just double the numerator. The denominator does not change, because you are not changing the number of pieces that make up the whole. This method will work anytime you multiply a fraction by a whole number.

Now think about this. A friend is learning about fractions and tells you that 1/4 + 1/4 + 1/4 = 3/12. Explain why this is not correct. Write your answer in two to three sentences.