Question

learning goal 2.5: students will multiply multi-digit decimals to the thousandths. find each product using the area model. 1. (18.3)(7.9) 2. (9.25)(12.7)

Explanation:

Step1: Decompose the numbers

For \( (18.3)(7.9) \), decompose \( 18.3 = 18 + 0.3 \) and \( 7.9 = 7 + 0.9 \).

Step2: Apply area model (rectangle with 4 parts)

• Top - left: \( 18\times7 = 126 \)
• Top - right: \( 18\times0.9 = 16.2 \)
• Bottom - left: \( 0.3\times7 = 2.1 \)
• Bottom - right: \( 0.3\times0.9 = 0.27 \)

Step3: Sum the products

Add all four parts: \( 126 + 16.2 + 2.1 + 0.27 = 144.57 \)

For \( (9.25)(12.7) \), decompose \( 9.25 = 9 + 0.25 \) and \( 12.7 = 12 + 0.7 \).

Step4: Apply area model (rectangle with 4 parts)

• Top - left: \( 9\times12 = 108 \)
• Top - right: \( 9\times0.7 = 6.3 \)
• Bottom - left: \( 0.25\times12 = 3 \)
• Bottom - right: \( 0.25\times0.7 = 0.175 \)

Step5: Sum the products

Add all four parts: \( 108 + 6.3 + 3 + 0.175 = 117.475 \)

Answer:

1. \( (18.3)(7.9) = \boldsymbol{144.57} \)
2. \( (9.25)(12.7) = \boldsymbol{117.475} \)