Final answer:
An area model for multiplying 5.2 by 4 involves representing 5.2 as 5 + 0.2, then multiplying each part by 4, which gives 20 and 0.8, respectively, and combining these to get the product of 20.8.
Step-by-step explanation:
The student has asked how to use an area model to explain the product of 5.2 and 4. An area model is a visual representation of multiplication that breaks down each factor into more manageable parts. For the multiplication of 5.2 and 4, one can represent 5.2 as 5 + 0.2 and use a rectangle divided into two parts, one representing 5 and the other 0.2.
- First, draw a rectangle and divide it into two sections horizontally.
- Label one section with the number 5, representing the whole number part of 5.2, and the other section with the number 0.2, representing the decimal part.
- Multiply the number 4 with both parts of the rectangle separately. So, 4 × 5 = 20 for the first section and 4 × 0.2 = 0.8 for the second section.
- Add the results of both sections to get the total area (product). So, 20 + 0.8 = 20.8.
This area model shows that the product of 5.2 and 4 is 20.8.