Use the hundreds grid to answer the question?

Question

Give the decimal multiplication equation shown by the model. Explain how each part of the equation is shown on the model . Include the final product.

Answer 1

To help you with the question regarding a hundreds grid or a model that represents decimal multiplication, let's consider a common example where we multiply two decimals: for instance, $0.3$ (or $3/10$) and $0.4$ (or $4/10$).

Decimal Multiplication Equation:

The multiplication equation for the example would be: $$0.3\times 0.4$$

Explanation of Each Part with the Model:

1. Hundreds Grid Representation:

   • A hundreds grid is typically a square grid with 10 rows and 10 columns, totaling 100 small squares, where each square represents $0.01$ (or 1 hundredth).

2. Representing $0.3$:

   • To represent $0.3$ on the hundreds grid, we shade in 3 rows (30 squares out of 100). This shows that $0.3$ represents 30 hundredths. In the grid, you could visualize this as covering 30 out of the 100 total squares.

3. Representing $0.4$:

   • For $0.4$, you would shade in 4 columns on the grid (40 squares out of 100). This indicates that $0.4$ represents 40 hundredths. You can visualize this as covering 40 squares out of the total 100.

4. Finding the Overlap for the Product:

   • To find the product $0.3\times 0.4$, you would look for the area where the rows representing $0.3$ overlap with the columns representing $0.4$.
   • Typically, for a grid divided into tenths, you would find that $0.3$ (30 hundredths) and $0.4$ (40 hundredths) produce a shaded area that represents $0.12$ (or $12$ hundredths) because $30$ multiplied by $40$ gives $1200$ when considering it as $1200$ hundredths of $10000$.

Final Product:

The final product of $0.3\times 0.4$ is: $$0.12$$

In conclusion, using a hundreds grid, the described model allows us to visually illustrate the multiplication of $0.3$ and $0.4$ leading to a final product of $0.12$.