How does the product of a fraction and a whole number compare to the whole number?

Question

6th grade math question

Answer 1

If the fraction is greater than 1, in other words the numerator is greater than the denominator, the product will be greater than the whole number.

If the fraction is less than one, in other words the numerator is less than the denominator, the product will be less than the whole number.

If the fraction is equal to 1, in other words the numerator is equal to the denominator, the product will equal the whole number.

Answer 2

Hi Susan--

 

Hilary's answer is right on. And you can think of it this way, too:

 

Consider the phrase "half of a pizza."

 

The half is 1/2

"of" means "times" -- "OF" something is the same as "TIMES" something

And "a pizza" is 1, as in one whole pizza.

 

So the half OF a pizza is 1/2 x 1

 

And half a pizza is certainly smaller than a whole pizza, which is very sad :-)

 

If your fraction is bigger than 1, say 3/2 x 1, then you'd have 3 halves of a pizza, which is MORE than 1 whole pizza.

 

Any time you are multiplying fractions (or anything, really)--draw a picture. Pizzas, rectangles, numbers of smiley faces--VISUAL helpers.

 

Hope this helps, along with Hilary's answer.

 

Good luck,

 

Matt up in New York