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Each big square below represents one whole. An array with $10$ columns and $10$ rows that represents $1$ whole. $10$ rows of $10$ are shaded. An array with $10$ columns and $10$ rows that represents $1$ whole. $10$ rows of $10$ are shaded. An array with $10$ columns and $10$ rows that represents $1$ whole. $1$ column of $10$ $4$ is shaded. An array with $10$ columns and $10$ rows that represents $1$ whole. $1$ column of $10$ $4$ is shaded. What percent is represented by the shaded area?

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Math Problems

Algebra 2

Solve system of equations: Complex word problems

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Q. Each big square below represents one whole. An array with

10

columns and

10

rows that represents

1

whole.

10

rows of

10

are shaded. An array with

10

columns and

10

rows that represents

1

whole.

10

rows of

10

are shaded. An array with

10

columns and

10

rows that represents

1

whole.

1

column of

10

4

is shaded. An array with

10

columns and

10

rows that represents

1

whole.

1

column of

10

4

is shaded. What percent is represented by the shaded area?

Arrays Description: We have four arrays, each with $10$ columns and $10$ rows, representing four wholes. The first two arrays are completely shaded, which means each of them represents $100\%$ shaded area.
Calculate Total Squares: Calculate the total number of squares in one whole array. Since there are $10$ columns and $10$ rows, the total number of squares in one array is $10 \times 10 = 100$ squares.
Determine Shaded Squares: Determine the number of shaded squares in the third and fourth arrays. Each of these arrays has $1$ column of $3$ shaded squares, so for each array, there are $3$ shaded squares.
Calculate Total Shaded Squares: Calculate the total number of shaded squares in all four arrays. The first two arrays have $100$ shaded squares each, and the third and fourth arrays have $3$ shaded squares each. So the total shaded squares are $100 + 100 + 3 + 3 = 206$ shaded squares.
Calculate Total Squares in Arrays: Calculate the total number of squares in all four arrays. Since each array has $100$ squares and there are four arrays, the total number of squares is $4 \times 100 = 400$ squares.
Determine Shaded Area Percentage: Determine the percentage of the shaded area. The percentage is given by the formula $(\frac{\text{Number of Shaded Squares}}{\text{Total Number of Squares}}) \times 100\%$ . So the percentage of the shaded area is $(\frac{206}{400}) \times 100\%$ .
Calculate Shaded Area Percentage: Perform the calculation to find the percentage. $(206 / 400) \times 100\% = 0.515 \times 100\% = 51.5\%$ .