fraction help: Will the product of 15 and 4/5 be greater than 15?

[beccav]

This is the problem, I think I have some of it.

15 * 4/5

will the product be greater than 15? I think the answer in no
How do you know? because you re taking 3/5 away from 15 so you will have less

Will the product be great than 4/5? yes

How do you know? I'm not sure

can someone help me understand this

thank you

 

[ksdhart]

This is a problem of reasoning, where thinking about what the question is asking and what you know is very helpful. When working with fractions, I like to use the analogy of slices of pizza. For the problem 15 * 4/5, you have a pizza divided into 15 slices. These slices are further split up into five equal groups, and you take four of those five groups. Is it possible for your part of the pizza to be more than 15 slices? Why or why not? Similarly, suppose the pizza had initially been divided into 10 slices, then further split up into five equal groups, of which you take four. Is your portion more than 4/5 of a slice of pizza? What if the pizza had been initially divided into 5 slices? What if the pizza weren't divided at all and you took four-fifths?

 

[stapel]

This is the problem, I think I have some of it.

15 * 4/5

will the product be greater than 15? I think the answer in no

You know that anything divided by itself is 1; for instance, 5/5 = 1. Is 4/5 more or less than 1?

You know that anything multiplied by 1 is itself; it doesn't change; for instance, 6*1 = 6.

If you multiply something by "more than 1", do you get more or less than what you'd started with? For instance, is 6 * (2) (being two "times" or "of" six) more or less than six?

If you multiply something by "less than 1", do you get more or less than what you'd started with? For instance, is 6 * (1/2) (being one-half "times" or "of" six), more or less than six?

Using this reasoning, is 15 * (4/5) more or less than fifteen?

How do you know? because you re taking 3/5 away from 15 so you will have less

You're not subtracting, are you? Aren't you multiplying? But are you multiplying by something bigger than 1, which will give you something bigger than what you'd started with; or are you multiplying by something smaller than 1, which will give you something smaller than what you'd started with?

Will the product be great than 4/5? yes

Use the same reasoning, but with the roles reversed. Is 15 more or less than 1? If you multiply 4/5 by 15, will you get something more or less than 4/5?

How do you know? I'm not sure

Use the reasoning explained above.