Which multiplication problem is represented by the model?
$\frac{1}{2} \times \frac{4}{5}$
$\frac{1}{6} \times \frac{2}{5}$
$\frac{5}{6} \times \frac{1}{2}$
$\frac{5}{12} \times \frac{1}{12}$
Answer (2)
The multiplication problem represented by the model is frac{5}{6} \times frac{1}{2}. Using the fractions from the shaded rows and columns, we can see that the calculation is frac{1}{2} \times frac{5}{6} or rearranged as frac{5}{6} \times frac{1}{2}. This results in frac{5}{12}.
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The model represents a 2x6 grid.
Identify the fraction of shaded rows as 2 1 and shaded columns as 6 5 .
The multiplication problem is 2 1 × 6 5 .
The correct answer is 6 5 × 2 1 .
Explanation
Understanding the Model The model is a 2x6 grid. We need to determine which multiplication problem is represented by the shaded region of the grid.
Calculating Total Cells The grid has 2 rows and 6 columns, for a total of 2 × 6 = 12 cells.
Identifying Shaded Rows and Columns The shaded region consists of 1 row and 5 columns. So, there is one row that is shaded and five columns that are shaded.
Determining Fractions of Shaded Rows and Columns The fraction of rows that are shaded is 2 1 . The fraction of columns that are shaded is 6 5 .
Formulating Multiplication Problem The multiplication problem represented by the model is 2 1 × 6 5 .
Calculating the Result Multiplying the fractions, we get 2 1 × 6 5 = 2 × 6 1 × 5 = 12 5 .
Matching with Options Comparing this result with the given options, we see that the correct answer is 6 5 × 2 1 .
Examples
Understanding fractions and their multiplication is crucial in many real-life scenarios. For instance, when baking, you might need to halve a recipe that calls for 3 2 cup of flour. This means you need to calculate 2 1 × 3 2 , which equals 3 1 cup. Visual models like the one in the problem help to understand these fractional parts and their multiplication, making everyday tasks easier and more intuitive.
