If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: MAP Recommended Practice>Unit 34

Lesson 22: Multiplication as scaling

# Multiplication as scaling with fractions

Learn about the concept of multiplication as scaling. Watch and understand how multiplying fractions can be seen as scaling, or resizing, the value of a number. Visualize this concept with various examples, reinforcing their understanding of multiplication as a scaling process. Created by Sal Khan.

## Want to join the conversation?

• hi is this easy for anyone because sadly i DO NOT GET IT!
• Hi! I don't know if your question has been answered yet, but if not, maybe this will help. What Sal is trying to explain in the video is that anytime you multiply a number, let's say x, by another number, let's say m, that is less than 1, then the product will be less than the original number x. That is, given a positive integer x, and another positive integer m, and m<1, then mx < x.

Now if you multiply a number, x, by a number, m, that is greater than 1, then their product will be greater than x. That is, if x is a positive integer, and m is a positive integer and m>1, then mx > x.

Finally, if you multiply a number x by a number m that is equivalent to 1, then the product of the numbers will be equivalent to x. That is, if x is a positive integer, and m=1, then mx = x.

SO..... to relate it to the video, in each scenario Sal gives, x = 2/3. So that is the positive integer that you will multiply by other positive integers to compare their products. But the point he is trying to make is that you don't actually have to multiply in order to know if the product will be less than, greater than, or equal to 2/3.

In the first example, 2/3 (remember, x) is being multiplied by 7/8. So the m I was talking about before is 7/8. Now 7/8 is less than 1, so 2/3*7/8 < 2/3 (if you want to prove it to yourself, 2/3*7/8 = 14/24 = 7/12, and so you can compare 7/12 with 2/3, 2/3=8/12, so we can now see that 7/12 is in fact less than 8/12).

In the second example, 2/3 is being multiplied by 8/7. So m=8/7 now. Since 8/7 > 1, then 2/3*8/7 > 2/3. Again, you can prove that to yourself by actually doing the math like I did in the paragraph above.

Finally, in the last example, even though it doesn't initially look like it, 2/3 is being multiplied by 5/5. Now 5/5 = 1, so 2/3*5/5 = 2/3.

Sorry for the lengthy explanation, but hopefully that's helpful to someone out there!
• I don't want to watch this but i have to i have no choice.
• Yup, The videos are kind of confusing, wish they changed that.
• I am stuck in this section and really worried, what is the exact way for knowing that which number is greater than 1 or less than
1/3 x 575, 4/3 x 575, 5/6 x 575. how can we know that which one of them greater or lesser (1/3, 4/3, 5/6)I am stuck in this section and really worried, what is the exact way for knowing that which number is greater than 1 or less than
1/3 x 575, 4/3 x 575, 5/6 x 575. how can we know that which one of them greater or lesser (1/3, 4/3, 5/6)I am stuck in this section and really worried, what is the exact way for knowing that which number is greater than 1 or less than
1/3 x 575, 4/3 x 575, 5/6 x 575. how can we know that which one of them greater or lesser (1/3, 4/3, 5/6)
• Here's how to find if a fraction is greater than 1 or less than one. Let's look at your fractions. You have 1/3, 4/3, and 5/6. There are 2 numbers in each fraction. Let's look at the first one. 1/3 has 1 as the numerator, and 3 as the denominator. If the numerator is smaller than the denominator, it's less than 1. If the numerator is larger than the denominator, it's larger than 1. So 1/3 and 5/6 are both less than 1, and 4/3 is greater than 1. Now time for the comparison. 5/6 is the odd one out when we're looking at denominators. Let's look at the LCM (Least Common Multiple). 6 is the LCM, so let's convert the denominators with 3 to 6, by multiplying both the numerator and denominator by 2, so the new fractions are 2/6, 8/6, and 5/6. Now we just order all of the fractions by their numerator, so the least to greatest is 2/6, 5/6, and 8/6.
Sorry for the lengthy explanation, but it's the easiest way to give the answer, and to the point where something is learned!
• I don't understand this, What is scaling.
• A scale factor is a number which scales, or multiplies, some quantity. In the equation y = Cx, C is the scale factor for x. C is also the coefficient of x, and may be called the constant of proportionality of y to x.
• Wait is this basically just multiplying fractions?
• Yes you are right.
• but 3x5=15 so it is equal for 15/15 that's a whole
• It is a whole number because 7/7 well you divide 7 and 7 so you get 1 but if somewone asked what 1 x 1/1 that one will be 1/1 x 1/2 so it equals 1/2
• I dont get it
• If you break it down and start by crossing out 2/3 from each expression, you can see the first expression had the lowest value because its factor 7/8 was less than 1. The second expression had the highest value because its factor 8/7 was greater than 1, and the third expression was in the middle because it was equal to 1, being greater than 7/8 and less than 8/7. So from least to greatest, it would be 7/8, 1, 8/7. Then don't forget to multiply 2/3 back to each number to get the full expression back.
• Whats 9 plus 10?
• its 21