Question

Multiplying and Adding Fractions 1 2 3 6 + Situation: Find the value of this fraction computation: 2 3 4 Calculation with Distribution Calculation without Distribution (Show all steps.) (Show all steps.) I think is easier: to distribute. . to not distribute. Why I Think It Is Easier

Answer 1

`6((1)/(2)+(2)/(3)+(3)/(4))`

With distribution:

`\begin{gathered} 6((1)/(2)+(2)/(3)+(3)/(4)) \\ =(6)(1)/(2)+(6)(2)/(3)+(6)(3)/(4) \\ =(6)/(2)+(12)/(3)+(18)/(4) \\ =((6\cdot6)+(4\cdot12)+(3\cdot18))/(12) \\ =(36+48+54)/(12) \\ =(138)/(12) \\ =(23)/(2) \end{gathered}`

Without distribution:

`\begin{gathered} 6((1)/(2)+(2)/(3)+(3)/(4)) \\ =6\lbrack((6\cdot1)+(4\cdot2)+(3\cdot3))/(12)\rbrack \\ =6((6+8+9)/(12)) \\ =6((23)/(12)) \\ =(6\cdot23)/(12) \\ =(23)/(2) \end{gathered}`

It's easier to solve it without distribution because we're dealing with smaller numbers if we're not distributing 6 accross the terms. This makes carrying out the math more simple since we're looking at smaller numbers.