How to do the butterfly method for multiplying fractions

I first got to know about the “Butterfly Method” in fractions from one of friend’s son. My friend, knowing that I have been teaching Math for many years in Singapore, commented to me, “My son’s school just adopted Singapore Math, and I don’t understand the math!”. Curious, I asked the Mom to elaborate and she started talking about the “Butterfly Method”. The son went on to explain this to me.

To add two fractions,

• First, you multiply the numerators and denominators diagonally and add –  that becomes your new numerator
• Then, you multiply the denominators – that becomes your new denominator

I became very curious. I understand how the math works, but how about the student? I went on to ask him, “Do you know why you are doing this?”. He replied matter-of-factly, “Well, you just do it!” Determined to show him the conceptual way, I told him that we need to first make sure the pieces are the same size and we do so by changing the fractions to equivalent fractions with the same denominator.

At this point in time, the student was getting a little impatient with me! “Why are we doing this? This is too much work. I like my trick and it works!”, he says. I knew this is coming, and I asked him to add three fractions using the butterfly method. He was dumbfounded.

In our opinion, tricks like the butterfly method should be avoided when students are first introduced to fractions. There are several reasons, e.g.

• There is no conceptual understanding in the instruction.
• It reinforces the belief that fractions is just a bunch of tricks.
• What happens if you add three or more fractions?

The session with the young boy left a deep impression on me. Other than learning a new method that I have not heard of, it made me realized the difficulties of starting a new curriculum. Singapore Math, with its focus on conceptual understanding and visualization, has become very popular in the United States over the years, and many private and public schools have replaced their curriculum with Singapore Math. However, it is not easy.

Many teachers teach the way that they were taught, and in this case, the teacher might be teaching the way that she was taught when she was a student; never mind that she is using the Singapore Math curriculum, and never mind that the Singapore Math curriculum has no mention of the “Butterfly Method” at all.

This was the turning point for me. That was when I started professional development for teachers using the Singapore Math curriculum, and through my interactions with teachers, started realizing the support that teachers need, not just in a two-day workshop, but on a on-going basis, throughout the school year. This is also the reason why we started our online Singapore Math membership site, so that we can serve the community of teachers on a regular basis.

In the opening example, although the final answer is correct, students failed to see directly that 2/5 + 1/5 is simply 3/5 and resorted to using algorithms or tricks without thinking. Have you seen similar behavior in your students?

More Fraction Resources

For more fraction resources, refer to our main fractions page.