Question

Evaluate each expression for the given value. Use the properties of operations.

Answer 1

Given the expression

`1(4)/(9)\text{ + }t\text{ +}2(2)/(9),\text{ when t = }3(1)/(3)`

Substitute for the value of t, we have

`1(4)/(9)\text{ + 3}(1)/(3)\text{ +}2(2)/(9)`

Solving the above expression using the properties of operation

Step 1:

Convert all mixed fractions into improper fractions.

`\begin{gathered} 1(4)/(9)\text{ + 3}(1)/(3)\text{ +}2(2)/(9) \\ \Rightarrow((9*1)+4)/(9)\text{ + }((3*3)+1)/(3)+((9*2)+2)/(9) \\ =(13)/(9)+(10)/(3)+(29)/(9) \end{gathered}`

Step 2:

Take LCM (Least Common Multiple) of the denominators, and solve using the LCM as the common denominator.

`\begin{gathered} \text{LCM = 9} \\ \text{Thus,} \\ (13)/(9)+(10)/(3)+(29)/(9) \\ =\frac{13\text{ + 30 + 20}}{9} \\ =(63)/(9) \\ =7 \end{gathered}`

Hence, the solution to the above expression is 7.