Final answer:
In evaluating the representation of 0.7×0.4 using a 10-by-10 grid, the true statements are that the total number of squares is 100, each square represents 0.01, and the shaded area equals the product of 0.4 and 0.7.
Step-by-step explanation:
We've been tasked with identifying three true statements about the representation of the decimal multiplication problem 0.7×0.4=0.28, which uses a 10-by-10 grid model with 4 x 7 squares shaded. Let's evaluate each statement:
- A. The total number of squares in the grid is 100. This is true because a 10-by-10 grid contains 10 rows of 10 squares each.
- B. Each square in the grid represents 0.01. This is true because the total grid represents a whole (1), and since there are 100 squares, each represents 1/100, which is 0.01.
- C. The product of 4 and 7 is equal to the area of the shaded region. This is false as the actual shaded area represents 0.4 and 0.7, not whole numbers 4 and 7.
- D. The product of 0.4 and 0.7 is equal to the area of the shaded region. This is true because the model is designed to visually represent the multiplication of two decimals. The 28 shaded squares out of 100 represent 28/100 or 0.28, which is the product of 0.4 and 0.7.
- E. The representation demonstrates the distributive property of multiplication. This is false as the model does not show this property but rather a visual representation of the multiplication of two decimals.
- F. The area of the shaded region represents the sum of 0.4 and 0.7. This is false because it represents the product, not the sum. The sum of 0.4 and 0.7 would be 1.1, which cannot be represented in a 100-square model as it would exceed the total number of squares.
Therefore, the true statements are A, B, and D.