Final answer:
Option (b) 10×4 + 5×0.8 shows the correct use of partial products to solve 15×4.8 by breaking down 15 into 10 and 5, multiplying each by 4.8 (composed of 4 and 0.8), and then adding the results.
Step-by-step explanation:
To solve 15×4.8 using the method of partial products, you decompose one of the multipliers into its place value components and then multiply each component separately by the other multiplier. Afterward, you sum up all the partial products to get the total product.
Let's look at our expression options:
- (a) 15×(4+0.8) is just an expression of the distributive property and does not show the partial products themselves.
- (b) 10×4 + 5×0.8 shows the products of 10 and 4, and 5 and 0.8 as partial products, which is correct because 15 can be decomposed into 10 and 5.
- (c) 15×5−15×0.2 has subtraction, which doesn't apply here.
- (d) 10×5 + 5×0.8 involves the wrong decomposition of 15.
The correct answer is (b) 10×4 + 5×0.8 as it correctly shows the partial products method:
- 1st partial product: 10×4 = 40
- 2nd partial product: 5×0.8 = 4
Then you add the partial products together: 40 + 4 = 44, which is the product of 15×4.8.