Question

Shawn said that you can use the properties of operations to solve the problems shown using mental math only. Identify the strategy that Shawn used for each problem. Then, evaluate the expression. Please help im stuck on this

Answer 1

For Expression A, a strategy could be to use the distributive property and then using the fact that the unit can be written in any fraction. To evaluate we have the following:

`(2)/(3)\cdot((3)/(2)-(1)/(3))=(2)/(3)\cdot(3)/(2)-(2)/(3)\cdot(1)/(3)=1-(2)/(9)=(9)/(9)-(2)/(9)=(7)/(9)`

For Expression B, we can see that 3/7 is the common factor of both summands, so we can use again the distributive property (but in the inverse way) and then add the two fractions that have the same denominator. We have:

`(3)/(5)\cdot(3)/(7)+(3)/(7)\cdot(2)/(5)=(3)/(7)\cdot((3)/(5)+(2)/(5))=(3)/(7)\cdot((5)/(5))=(3)/(7)\cdot1=(3)/(7)`