Multiplying Fractions with whole numbers

There are two ways to look at multiplying a fraction by a whole number.

First the "whole" can be a set of objects, and a question might ask to find how many objects are in a fractional part of a set.

For example, if there are 8 cookies in a pack, one-half of the pack would contain 4 cookies.

An important thing to remember is that the word "of" in these examples means the number is multiplied by the fraction.

Here is a video that uses models to show how to multiply fractions by whole numbers.

If the factors are reversed (as they can be according to the Commutative Property of Multiplication), the problem takes on a slightly different meaning.

In this case, the "whole" is one rectangle. Rectangles are divided into fractional parts and a number of them are taken together (added over and over again, which is the same as multiplying).

If all 6 halves are put back together again, they would form 3 wholes.