Teachers and textbooks usually explain multiplying and dividing with fractions in just a few words. In effect, their explanation is: “Do it like this and it will work.” There is no attempt to give the student any understanding of:
- Why is that the way to do it? Why does it work?
- Is it consistent with how we multiply and divide other numbers?
- Is it consistent with our understanding of fractions?
- When adding fractions with the same denominator, the denominator of the answer is the same. But when multiplying them, the denominator of the answer has to be different. Why?
- Why can we multiply unlike fractions but we cannot add them directly
- When dividing by a fraction, the fraction does a somersault. Why?
Sadly, because these issues are not explained, students never really understand what they are doing with fractions. It is just a mechanical process. They might know HOW to do the calculations, but they do not know WHY they are doing it that way, or why the result they get is really correct. I strongly suspect that many teachers don’t know why either.
In the next few sections I’ll explain step-by-step what to do and also why to do it. I’ll show that the steps are consistent with multiplying and dividing with whole numbers and that they are also consistent with the understanding of fractions that we have built up thus far in these notes.
This website presents extracts of each chapter in the related book called Fractions For Parents. The chapters are listed on the side of this page.
If you would like to buy the book to see all of the content, please click here.
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I must agree that the “why” behind mathematical operations and proceeses are not understood. Few learners understand the reasoning behind what they are doing. Math is taught in recipes😁 with no understanding of the logic or rreasonong, and so many people can only do the type of sum shown in the example they are given. This includes many teachers in the classroom – no fault of their own. We teach like we were taught, yes?. I can see your book assisting to provide that reasoning. Much needed!