Learn to Multiply Fractions & Understand Improper Fractions & Mixed Numbers - [29]

More Lessons: www.MathAndScience.com
Twitter: / jasongibsonmath
In this lesson, you will learn how to multiply a fraction by a whole number. We will write every whole number as a fraction, then multiply the fractions together. The resulting answer in many cases will be an improper fraction, which can be converted into a mixed number. When multiplying fractions, we first multiply the numerators together and then multiply the denominators together. This will form the answer which can be simplified as usual to lowest terms. If we get an improper fraction as a result, it represents that we have more than one whole item. We divide the numerator by the denominator as usual and obtain the remainder. This forms the basis of the mixed number representation of the answer. We also use models and pictures to visualize what an improper fraction actually means and how it relates to the corresponding mixed number.

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[@russelltimmins1870]

Brackets would be better than a ‘dot’ as in the Anglo Saxon world this is used for decimal notation.

[@MathAndScience]

I hear what you are saying but using a dot for multiplication is standard in all of math.

[@russelltimmins1870]

@@MathAndScience I agree and use dots myself but I think that the use of brackets which students learning multiplication of fractions at this early stage will be familiar with in their parallel algebra classes, is more useful and indeed supports the ideas of brackets taught in algebra. Everything outside the bracket is multiplying the number in the fraction that is itself a multiplying agent, namely the numerator.

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[@hemarajue2736]

Fraction is meaningless if no denominator. Suppose if you're given a piece of pizza, how can you judge you got the right amount of pizza? Multiplication of fractions is easier compared to addition,here we simply multiply their respective numerators and denominators. But addition is somewhat complicated,if the denominators are same we simply add the numerators and keep the denominators; if the denominators are different,we essentially convert each fraction to its equivalent fraction so that denominators become the same. While an art makes you happy knowledge keeps you humble. Happiness is somewhat related to our emotional quotient and knowledge to our intelligence. Art is like an image that reflects your feelings. Knowledge is like a light that reflects your image.

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[@pamelafrancis4476]

My problem was confusing 3 and 2/3 (three plus two-thirds) with 3 times 2/3 because 2 times X is written 2X (not 2 x X). But putting the whole number over 1 when multiplying, the penny has dropped. Thank you!

[@MathAndScience]

Yes I agree that is super confusing and I wish we didn’t write mixed numbers that way!

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[@russelltimmins1870]

I love your work here but I must say I have some serious issues with this tutorial.

[@MathAndScience]

What are the problems you have with it?

[@russelltimmins1870]

@@MathAndScience I do not want to be over critical as I believe your tutorials are extraordinarily good for the most part, in particular your in depth teaching of early trigonometry from the standpoint of vectors in my opinion was outstanding. My only criticism on this more fundamental level of mathematics is that more is needed to explain the reason why numerators multiply themselves and the same for denominators. Physical models I always found when training teachers helped the solidification of the true understanding to be brought out. When it is understood and not merely memorised then we can say that learning has truly taken place. Please do not take this out of context but we teachers are also learners. Looking forward to your next upload.

[@MathAndScience]

I definitely hear what you’re saying, but I think this is just a matter of philosophy. I firmly believe with my teaching thousands of students that the best way to learn is first to build solid skills. The student needs to understand in the beginning that it’s not hard to do and then after that they build their confidence. As they go more and more through Math they will understand more of these subtle details that you’re talking about. If you start out with a very deep discussion that goes over the head of the students the most students will just completely turn off and not understand anything. That’s been my experience. A similar analogy will be in physics we teach kids that an atom has protons and little bitty electrons which are little balls that are flying around the nucleus. We know 100% at this model of an atom is completely false. It is simply not true. But we can’t teach a third grader what the wave function of an electron is and what A probability density is. We can’t teach quantum mechanics to young kids so we start with a model that’s easy to understand, and as they go higher and higher through math then we can teach more and more about what we believe is actually going on. And truthfully the wave function of the electron is probably not the correct description either. It’s the same with this basic math concepts - how far down the rabbit hole do you want to go with a third grader or fourth grader. I pick my point the point that is the simplest I feel we should go while still building skills. And other people can disagree and that’s totally fine but in my experience this is what builds the most skills early on builds confidence and then the student feels empowered to conquer further topics. Thank you for your comment and have a great day!

[@russelltimmins1870]

@@MathAndScience I think you are right when you mention philosophy. As I said I admire your work and would love to have a philosophical discussion with you in some utopian parallel world but I respect your standpoint. Good luck with your future work.

[@MathAndScience]

Thank you so much! I respect all viewpoints and appreciate your ideas and discussion. Take care!

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