1. **Identify the integers and mixed numbers in the list:** The list contains: $-15\frac{2}{3},\;0,\;21,\;-20,\;15\frac{1}{3},\;-1$. 2. **Determine the largest value:** From the numbers, $21$ is the largest as it is the only positive integer greater than any fractional mixed number in the list. --- 3. **Find the number halfway between $-2\frac{1}{2}$ and $3$:** Step 1: Convert mixed number to improper fraction or decimal: $-2\frac{1}{2} = -2.5$ Step 2: Calculate midpoint definition: Halfway number = $\frac{-2.5 + 3}{2} = \frac{0.5}{2} = 0.25$ So, the number halfway between $-2\frac{1}{2}$ and $3$ is $0.25$. --- 4. **Analyze the shaded and unshaded areas in the 10x10 grid:** - Total squares = $10 \times 10 = 100$ - The shaded layers are: - Outermost border: $10 \times 10$ square border = outer ring (width 1), count = $10 \times 10 - 8 \times 8 = 100 - 64 = 36$ squares - Next shaded border inside (1 square wide), after unshaded border: - Second shaded border ring: between $8 \times 8$ and $6 \times 6$, count = $8 \times 8 - 6 \times 6 = 64 - 36 = 28$ squares - Central shaded area is $4 \times 4 = 16$ squares - Total shaded squares = $36 + 28 + 16 = 80$ - Fraction shaded = $\frac{80}{100} = \frac{4}{5}$ 5. **Fraction of unshaded area on the outer border:** - Total unshaded squares = total - shaded = $100 - 80 = 20$ - Outer unshaded border is the one between outer shaded border (10x10) and next shaded border starts from 8x8 (but given unshaded border widths): The unshaded borders are 1 square wide each, so the outer unshaded border lies between the outermost shaded border (10x10) and the next shaded border (8x8 to 6x6). - Count of outer unshaded border = $8 \times 8 - 6 \times 6 = 64 - 36 = 28$, but this conflicts with the description, so more careful breakdown: The grid layers are: - First shaded border: 10x10 thin border (width 1): 36 squares (as above) - Then unshaded border 1 square wide inside: area from 9x9 down to 8x8 (because 10x10 outer border - inner 8x8 second shaded border—unshaded border must be just 1-square wide ring between 9x9 and 8x8, so unshaded border squares = $9 \times 9 - 8 \times 8 = 81 -64 =17$ squares - Next shaded border: 8x8 to 6x6 ring: $64 - 36 = 28$ squares - Inner unshaded border: 7x7 to 6x6 ring: $49 - 36 = 13$ squares - Central shaded area: $4x4=16$ squares - Total shaded remains: $36 + 28 + 16=80$ - Total unshaded: $17 + 13 = 30$ squares - Fraction unshaded: $\frac{30}{100} = \frac{3}{10}$ - Out of the unshaded 30 squares, the outer border unshaded is 17 squares - Fraction of unshaded area on outer border = $\frac{17}{30}$ **Final answers:** - Largest number in list: $21$ - Number halfway between $-2\frac{1}{2}$ and $3$: $0.25$ - Fraction of shape shaded: $\frac{4}{5}$ - Fraction of unshaded area on outer border: $\frac{17}{30}$