Egg Carton Fractions and Basic Operations
We can use the idea of multiplying by combining equal groups or parts of groups. Egg carton models can show how these multiplication concepts apply to fraction computation.
Consider 4 x 1/3. Using the grouping idea, that would mean 4 groups of 1/3. Let's see how that looks...
Here's another example, 2/5 x 3 (or 3 x 2/5 - remember the commutative property, lesson 3?)...
What if both numbers are fractions? We can still use the grouping idea. 2/3 x 9/12 could be thought of as "2/3 of a group of 9/12" or more concisely, "2/3 of 9/12".
Here's one more example, 1/7 x 2/3. This could be "1/7 of 2/3" or "2/3 of 1/7". Either way, we need an egg carton that can be divided into both sevenths and thirds. This egg carton will need at least 21 spaces. We'll look at both interpretations...
Because of the commutative property, we get the same product for both multiplication problems. 1/7 x 2/3 and 2/3 x 1/7 both are equal to 2/21:
These models can be used with common fractions, improper fractions, mixed numbers and complex fractions. All we have to do is to be sure to use an egg carton size that can show the fraction denominators, and keep true to the meaning of multiplication.