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

On the other hand, notice that:

`-(2)/(3)\text{ x -}(4)/(5)\text{ x 9 = }(24)/(5)\text{ = 4.8}`

thus:

`-(2)/(3)\text{ x -}(4)/(5)\text{ x 9 = }(24)/(5)\text{ = 4 }(4)/(5)`

Now, notice that:

`9\text{ x }(2)/(3)\text{ x }(4)/(5)=\text{ }\frac{9\text{ x 2 x 4}}{3\text{ x 5}}\text{ = }(72)/(15)\text{ = }(24)/(5)\text{ = 4.8}`

thus:

`9\text{ x }(2)/(3)\text{ x }(4)/(5)=4\text{ }(4)/(5)`

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