Question

6 isabella is building a tree fort. the base of the fort is 78 inches wide by 92 inches long. what is the area of the base in square inches? show your thinking.

Explanation:

Problem 5: Adding or Subtracting Decimals

First Calculation: \( 2.03 + 4.78 \)

Step1: Align decimal points

\(

$$\begin{align*} &2.03\\ +&4.78\\ \hline \end{align*}$$

\)

Step2: Add column by column

• Tenths and hundredths: \( 0.03 + 0.78 = 0.81 \)
• Ones: \( 2 + 4 = 6 \)
• Combine: \( 6 + 0.81 = 6.81 \)

\(

$$\begin{align*} &2.03\\ +&4.78\\ \hline &6.81\\ \end{align*}$$

\)

Second Calculation: \( 5.01 - 3.98 \)

Step1: Align decimal points

\(

$$\begin{align*} &5.01\\ -&3.98\\ \hline \end{align*}$$

\)

Step2: Subtract (borrow if needed)

• Hundredths: \( 0.01 - 0.08 \) (can't do, borrow from tenths: \( 0.01 + 0.10 = 0.11 \); tenths becomes \( -0.10 \), so now \( 0.11 - 0.08 = 0.03 \))
• Tenths: \( -0.10 + 0.00 \) (after borrowing, tenths was \( 0.00 \), now \( -0.10 \); borrow from ones: \( -0.10 + 1.00 = 0.90 \); ones becomes \( 4 \))
• Ones: \( 4 - 3 = 1 \)
• Combine: \( 1 + 0.90 + 0.03 = 1.03 \)

\(

$$\begin{align*} &5.01\\ -&3.98\\ \hline &1.03\\ \end{align*}$$

\)

Third Calculation: \( 25.67 + 14.32 \)

Step1: Align decimal points

\(

$$\begin{align*} &25.67\\ +&14.32\\ \hline \end{align*}$$

\)

Step2: Add column by column

• Hundredths: \( 0.07 + 0.02 = 0.09 \)
• Tenths: \( 0.6 + 0.3 = 0.9 \)
• Ones: \( 5 + 4 = 9 \)
• Tens: \( 2 + 1 = 3 \)
• Combine: \( 39 + 0.9 + 0.09 = 39.99 \)

\(

$$\begin{align*} &25.67\\ +&14.32\\ \hline &39.99\\ \end{align*}$$

\)

Fourth Calculation: \( 100.00 - 96.75 \)

Step1: Align decimal points

\(

$$\begin{align*} &100.00\\ -&96.75\\ \hline \end{align*}$$

\)

Step2: Subtract (borrow if needed)

• Hundredths: \( 0.00 - 0.05 \) (borrow from tenths: \( 0.00 + 0.10 = 0.10 \); tenths becomes \( -0.10 \), so \( 0.10 - 0.05 = 0.05 \))
• Tenths: \( -0.10 + 0.00 \) (borrow from ones: \( -0.10 + 1.00 = 0.90 \); ones becomes \( -1 \), so \( 0.90 - 0.70 = 0.20 \))
• Ones: \( -1 + 0.00 \) (borrow from tens: \( -1 + 10.00 = 9.00 \); tens becomes \( -1 \), so \( 9.00 - 6.00 = 3.00 \))
• Tens: \( -1 + 0.00 \) (borrow from hundreds: \( -1 + 10.00 = 9.00 \); hundreds becomes \( 0 \), so \( 9.00 - 9.00 = 0.00 \))
• Combine: \( 0 + 3 + 0.20 + 0.05 = 3.25 \)

\(

$$\begin{align*} &100.00\\ -&96.75\\ \hline &3.25\\ \end{align*}$$

\)

Problem 6: Area of the Base (Rectangle)

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \).

Step2: Substitute values

Length \( l = 92 \) inches, Width \( w = 78 \) inches. So \( A = 92 \times 78 \).

Step3: Calculate the product

\( 92 \times 78 = (90 + 2) \times (70 + 8) = 90 \times 70 + 90 \times 8 + 2 \times 70 + 2 \times 8 = 6300 + 720 + 140 + 16 = 6300 + 720 = 7020; 7020 + 140 = 7160; 7160 + 16 = 7176 \)

Answer:

• Problem 5 results: \( 2.03 + 4.78 = 6.81 \), \( 5.01 - 3.98 = 1.03 \), \( 25.67 + 14.32 = 39.99 \), \( 100.00 - 96.75 = 3.25 \)
• Problem 6 area: \( 7176 \) square inches