Question

part a
which of the following could be used to help find the product of 48 × 36 using an area model? select all th
apply.
☑️ 48
□ 24
□ 180
☑️ 240
☑️ 1,200
□ 120
part b
find 48 × 36. enter your answer in the box.

Explanation:

Step1: Recall area model for multiplication

The area model for \(48\times36\) involves breaking down the numbers into tens and ones. We can write \(48 = 40 + 8\) and \(36=30 + 6\), then use the distributive property \((a + b)(c + d)=ac+ad+bc+bd\). But also, sometimes we can break into other factors. Alternatively, we can think of \(48\times36=(50 - 2)\times36\) or other decompositions, but the area model typically uses breaking into place - value parts. However, another way is to factor the numbers. \(48 = 2\times24\), \(36 = 2\times18\), but also, if we use the area model as a rectangle with length \(48\) and width \(36\), or we can break \(48\) and \(36\) into smaller parts. But for the product \(48\times36\), we can calculate it directly:

Step2: Calculate \(48\times36\)

We know that \(48\times36=(50 - 2)\times36=50\times36-2\times36\)
First, \(50\times36 = 1800\) and \(2\times36 = 72\)
Then \(1800-72 = 1728\)
Or we can use the standard multiplication:

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Answer:

1728