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

Both Laura and Sean arrive at the same answer of 8/3 by using different methods.

Laura starts by multiplying 2/3 by 4 to find the total amount of 2/3 in 4 units.

Sean starts by finding the total amount of 2/3 in one group and then multiplying that amount by the number of groups, 4.

Both methods lead to the same answer, so it doesn't matter which method is used. The important thing is that the answer is correct.

Answer 2

Answer: So our equation is
`(2)/(3) *4`

Laura does:

`(2)/(3)*4 = 2*(1)/(3)  *4 = 2*(4)/(3)  = (4)/(3) + (4)/(3)  = (8)/(3)`

while Sean does:

`(2)/(3)*4 = (2)/(3) + (2)/(3) +(2)/(3)  + (2)/(3)  = (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.