Question

this series of problems will build your fluency with considering overlapping elements when analyzing part-whole relationships.

• use the answer key to determine that you accurately solved the problem.
• if necessary, revise your work.

in each problem below, determine what fraction of the 4×4 grid is covered with colored tiles.
1.
(grid with colored tiles and numbers, total shaded blocks is 48, 64 total blocks, 24×2=48, 32×2=64, fractions 48/64, 24/32, 12/17)

Explanation:

Step1: Identify total and shaded blocks

Total blocks: \( 8 \times 8 = 64 \) (since it's an 8x8 grid, not 4x4 as mislabeled? Wait, the grid shown has 8 rows/columns. Shaded blocks: 48.

Step2: Calculate the fraction

Fraction = \( \frac{\text{Shaded}}{\text{Total}} = \frac{48}{64} \)

Step3: Simplify the fraction

Divide numerator and denominator by 16: \( \frac{48 \div 16}{64 \div 16} = \frac{3}{4} \)? Wait, no, 48÷16=3, 64÷16=4? Wait 48 and 64 have GCD 16? 48=16×3, 64=16×4. Wait but maybe the initial grid is 8x8 (64 blocks), shaded 48. So \( \frac{48}{64} = \frac{3}{4} \) when simplified. But let's check the given 48/64. Simplify: divide numerator and denominator by 16: 3/4, or by 8: 6/8, 3/4. Wait maybe the problem's 4x4 is a typo, it's 8x8. So the fraction is \( \frac{48}{64} \), which simplifies to \( \frac{3}{4} \), but the given work has 48/64. Let's confirm: total blocks 64, shaded 48. So fraction is \( \frac{48}{64} = \frac{3}{4} \) (simplified) or \( \frac{48}{64} \) as is.

Answer:

The fraction of the grid (assuming 8×8, 64 total blocks) covered with colored tiles is \(\frac{48}{64}\) (or simplified \(\frac{3}{4}\)). If we use the given numbers: shaded = 48, total = 64, so \(\frac{48}{64} = \frac{3}{4}\) (simplified) or \(\frac{48}{64}\).