Question

Laura and Sean find the product of 2/3 x 4 using different methods.

Laura: It’s 2 thirds of 4.
2/3 x 4 = 4/3 + 4/3 = 2 x 4/3 = 8/3

Sean: It’s 4 groups of 2 thirds.
2/3 + 2/3 + 2/3 + 2/3 = 4 x 2/3 = 8/3

Use words, pictures, or numbers to compare their methods.

Answer 1

Answer: So our equation is $\frac{2}{3} *4$

Laura does:

$\frac{2}{3}*4 = 2*\frac{1}{3}  *4 = 2*\frac{4}{3}  = \frac{4}{3} + \frac{4}{3}  = \frac{8}{3}$

while Sean does:

$\frac{2}{3}*4 = \frac{2}{3} + \frac{2}{3} +\frac{2}{3}  + \frac{2}{3}  = \frac{8}{3}$

So sean sums four times the number 2/3, while Laura sums two times the number 4/3, this is because we are working with a multiplication, and the order of the factors does not alter the product.

The two are splitting the equations in different ways.