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:
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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).
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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.
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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.
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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 \(0.12\).
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