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 \((18.3)(7.5)\), decompose \(18.3 = 18 + 0.3\) and \(7.5 = 7 + 0.5\).

Step2: Apply area model (distributive property)

The area model uses the distributive property: \((a + b)(c + d)=ac + ad + bc + bd\).
So, \((18 + 0.3)(7 + 0.5)=18\times7 + 18\times0.5 + 0.3\times7 + 0.3\times0.5\).
Calculate each term:

• \(18\times7 = 126\)
• \(18\times0.5 = 9\)
• \(0.3\times7 = 2.1\)
• \(0.3\times0.5 = 0.15\)

Step3: Sum the terms

Add the results: \(126 + 9 + 2.1 + 0.15 = 137.25\).

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

Step4: Apply area model (distributive property)

Using the distributive property: \((a + b)(c + d)=ac + ad + bc + bd\).
So, \((9 + 0.25)(12 + 0.7)=9\times12 + 9\times0.7 + 0.25\times12 + 0.25\times0.7\).
Calculate each term:

• \(9\times12 = 108\)
• \(9\times0.7 = 6.3\)
• \(0.25\times12 = 3\)
• \(0.25\times0.7 = 0.175\)

Step5: Sum the terms

Add the results: \(108 + 6.3 + 3 + 0.175 = 117.475\).

Answer:

1. \(\boldsymbol{137.25}\)
2. \(\boldsymbol{117.475}\)