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## Arithmetic (all content)

### Course: Arithmetic (all content)>Unit 5

Lesson 21: Multiplying fractions

# Multiplying 2 fractions: fraction model

Visuals can be used to multiply fractions in a variety of ways, such as by using fraction models. By drawing rectangles and dividing them into equal parts, we can use an area model to multiply fractions. help to illustrate how the numerators and denominators of the two fractions interact to produce a product. Created by Sal Khan.

## Want to join the conversation?

• Ok. When you are simplifying or dividing, keep these in mind:
Any even number is divisible by 2, so if both the numerator and the denominator are even, then you can continue to simplify it by 2.
If the digits of a number add up to a multiple of 3, then it is divisible by 3. So when both the numerator and denominator are multiples of 3, then you can simplify it by 3.
Numbers ending in 5 or 0 are divisible by 5.
You can just continue to simplify fractions with the 2, 3, and/or 5; these usually should be sufficient. And when two or more fractions are getting multiplied, you can take the numerator of one fraction and use it to simplify another fractions denominator (which will make the final multiplication easier). For example, if you have (5/8)x(2/3), then first simplify it to (5/4)x(1/3)heres a tip • I have no idea what he is talking about and I've watched this video 3 times • vote this for a cookie. • I did not understand any of this I need more details. • I keep getting stuck on the practice problems even though I have watched it at least 5 times. • When solving this type of simple math do we really need to understand it visually or conceptually? • I think it helps to understand it both ways. For example if you can teach the math to someone else, then you really understand all of it, which is I guess the goal. Of course, while you don't technically "need" to understand both, especially with the simpler parts of math it is often very helpful seeing as the harder math usually includes many of the same concepts and if you don't understand all the aspects then that makes it harder to learn higher maths.
• Is it possible to have a fraction as a numerator or denominator? Just curious. • pupusas con queso y salsa • Let's think a little bit about what it means to multiply fractions. Say I want to multiply 1/2 times 1/4. Well, one way to think about this is we could view this as 1/2 of a 1/4. And what do I mean there? Well let me take a whole, let me take a whole here, and let me divide it into fourths. So let me divide it into fourths, so I'll divided into 4 equal sections. And so 1/4 would be 1 of these 4 equal sections. But we want to take 1/2 of that. So how do we take half of that? Well, we could divide this into 2 equal sections, and then just take 1 of them. So divide it into 2 equal sections, and then take 1 of them. So we're taking this pink area, this whole pink area is 1/4, and now we're going to take 1/2 of it. We're now going to take 1/2 of it. So that's this yellow square right over here. But what fraction of the whole does this yellow represent? Well, it now represents 1 out of 1, 2, 3, 4, 5, 6, 7, 8 equal sections. So this right over here, this represents 1/8 of the whole. And so we see conceptually that 1/2 times 1/4, it completely makes sense, that 1/2 of 1/4 should be 1/8. And it hopefully makes sense that you get this 8 by multiplying the 2 times the 4. You started with 4 equal sections, but then you divided each of those 4 equal sections into 2 equal sections. So then you have 8 total equal sections that you split your whole into. Let's do another example, but now let's multiply two fractions that don't have 1's in the numerator. So let's multiply, let's multiply 2/3 times 4/5. And I encourage you now to pause the video and do something very similar to what I just did. Try to represent 4/5 of a whole and then try to represent 2/3 of that 4/5 and see what fraction of the whole you actually have. So pause now. So let's think about this. Let's represent 4/5. So if I have a whole like this, let me try to divide it into 5 equal sections. 5 equal sections, so let's say that is 1 equal section, that is 2 equal sections, that is 3, 4, and 5-- I can do a better job than this. This is always the hard part. I'm trying my best to make them look, at least, like equal sections-- 2, 3, 4, and 5. I think you get the point here. I'm trying to make them equal sections. And we want 4/5. So we want 4 of these 5 equal sections. So this would be 1 of the 5 equal sections, 2 of them, 3 of them, and then 4 of them. So that right over there is 4/5. Now we can view this as 2/3 of the 4/5. So how can we think about that? Well, we could take this section and divide it into thirds. So let's do that. Divide it into thirds. So we're going divide it into 3 equal sections. So that's 1/3, and then 2/3. So we took each of the 5 equal sections, and we divided them into 3 equal sections. Now what's going to be 2/3 of the 4/5? Well, that's going to be this part right over here. So let me make this clear. This is 1/3 of the 4/5. And then this would be 2/3 of the 4/5. So this right over here, would be 2/3 of the 4/5, or 2/3 times 4/5. But what fraction of the whole does that represent? Well, how many total, how many total equal sections do we now have? Well, we have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. So we have 15 equal sections. I'm using a new color. We have 15 equal sections, and that make sense. We started with 5 equal sections, but then we divided each of those into 3 equal sections. So now we have 5 times 3 total equal sections. And then how many of those are now colored in? Well, we see it's 2 times 4. 1, 2, 3, 4, 5, 6, 7, 8. How many of them are in the 2/3 of the 4/5, I should say. And there's 8 of them, 8 of the 15 equals sections. And so there you have it. It should hopefully now make visual sense, or it makes conceptual sense, that 2/3 times 4/5-- you can obviously compute it by just multiplying the numerators, 2 times 4 is 8. And then multiplying the denominators, 3 times 5 is 15-- but hopefully this now makes conceptual sense as 2/3 of 4/5. • Mathematicians worldwide hold the Riemann Hypothesis of 1859 (posed by German mathematician Bernhard Riemann (1826-1866)) as the most important outstanding maths problem. The hypothesis states that all nontrivial roots of the Zeta function are of the form (1/2 + b I).
Hardest Math Problems and Equations - Unsolved Math Problems
Goldbach's Conjecture﻿

One of the greatest unsolved mysteries in math is also very easy to write. Goldbach's Conjecture is, “Every even number (greater than two) is the sum of two primes.” You check this in your head for small numbers: 18 is 13+5, and 42 is 23+19.

In 1995, Franco and Pom-erance proved that the Crandall conjecture about the aX + 1 problem is correct for almost all positive odd numbers a > 3, under the definition of asymptotic density. However, both of the 3X + 1 problem and Crandall conjecture have not been solved yet Now do't that make scence 