Question

Marco says that -2/3 * -45 * 9 + 9 * 2/3 * 4/5 both have a product of 4 and 4/5 explain whether or not Marco is correct

Answer 1

Question:

Solution:

Since 4 4/5 is a mixed number, we have that

$4\text{ }\frac{4}{5}\text{ = }\frac{(4\text{ x 5 ) + 4}}{5}\text{ = }\frac{24}{5}=\text{ 4.8}$

On the other hand, notice that:

$-\frac{2}{3}\text{ x -}\frac{4}{5}\text{ x 9 = }\frac{24}{5}\text{ = 4.8}$

thus:

$-\frac{2}{3}\text{ x -}\frac{4}{5}\text{ x 9 = }\frac{24}{5}\text{ = 4 }\frac{4}{5}$

Now, notice that:

$9\text{ x }\frac{2}{3}\text{ x }\frac{4}{5}=\text{ }\frac{9\text{ x 2 x 4}}{3\text{ x 5}}\text{ = }\frac{72}{15}\text{ = }\frac{24}{5}\text{ = 4.8}$

thus:

$9\text{ x }\frac{2}{3}\text{ x }\frac{4}{5}=4\text{ }\frac{4}{5}$

Then, we can conclude that both expressions have a product of 4 4/5.