Drag the tiles to the correct boxes to complete the pairs. Match each expression to its simplified form.
[tex]$\begin{array}{ll}
(6 r+7)+(13+7 r) & \left(13-\frac{3}{2} r\right)-(1-r) \\
\left(7 r-\frac{3}{2}\right)-\left(\frac{2}{3}+6 r\right) & (-8-r)+(2 r-4)
\end{array}$[/tex]
Answer (1)
Combine like terms in ( 6 r + 7 ) + ( 13 + 7 r ) to get 13 r + 20 .
Simplify ( 13 − 2 3 r ) − ( 1 − r ) to obtain 12 − 2 1 r .
Simplify ( 7 r − 2 3 ) − ( 3 2 + 6 r ) to get r − 6 13 .
Combine like terms in ( − 8 − r ) + ( 2 r − 4 ) to get − 12 + r .
The simplified expressions are: 13 r + 20 , 12 − 2 1 r , r − 6 13 , − 12 + r .
Explanation
Understanding the Problem We are given four expressions involving the variable r, and we need to match each expression to its simplified form.
Simplifying the First Expression First, let's simplify the expression ( 6 r + 7 ) + ( 13 + 7 r ) . Combining like terms, we have 6 r + 7 r + 7 + 13 = 13 r + 20 .
Simplifying the Second Expression Next, let's simplify the expression ( 13 − 2 3 r ) − ( 1 − r ) . Distributing the negative sign, we have 13 − 2 3 r − 1 + r = 12 − 2 3 r + r = 12 − 2 3 r + 2 2 r = 12 − 2 1 r .
Simplifying the Third Expression Now, let's simplify the expression ( 7 r − 2 3 ) − ( 3 2 + 6 r ) . Distributing the negative sign, we have 7 r − 2 3 − 3 2 − 6 r = 7 r − 6 r − 2 3 − 3 2 = r − 6 9 − 6 4 = r − 6 13 .
Simplifying the Fourth Expression Finally, let's simplify the expression ( − 8 − r ) + ( 2 r − 4 ) . Combining like terms, we have − 8 − 4 − r + 2 r = − 12 + r .
Matching the Expressions Now, we match each simplified expression to its corresponding simplified form in the table:
( 6 r + 7 ) + ( 13 + 7 r ) simplifies to 13 r + 20 .
( 13 − 2 3 r ) − ( 1 − r ) simplifies to 12 − 2 1 r .
( 7 r − 2 3 ) − ( 3 2 + 6 r ) simplifies to r − 6 13 .
( − 8 − r ) + ( 2 r − 4 ) simplifies to − 12 + r .
Examples
Understanding how to simplify algebraic expressions is crucial in many real-world applications. For instance, when calculating the total cost of items with discounts or taxes, you often need to combine like terms to find the final price. Similarly, in physics, simplifying expressions helps in solving equations related to motion or forces. By mastering these simplification techniques, you can efficiently solve problems in various fields, making complex calculations more manageable and accurate.
