Question

name: date: cut-paste visual mapping of units background: sometimes, there is a need to change from one unit of measure to another. there are many ways to do this. today, we will use a method called visual mapping. procedure: find the conversion factor(s) on the cut - out page needed to change from the starting unit to the desired unit. cut the conversion factor(s) out, and paste them here. then do the math. data & calculations: 1) 8 θ × (5 □ / θ) = □ 2) 5 □ × (0.15 ¢ / □) = □ 3) 1.5 □ = □ 4) 0.5 ↑ = □ θ 5) 1.5 □ = □ θ 6) 6.0 θ = □ 7) 8 □ = □ 8) 10 □ = □ ↑ 9) 25 cm = □ mm

Explanation:

To solve these unit conversion problems, we'll use the given conversion factors (from the cut - out page, as per the procedure) and perform the necessary arithmetic operations. Let's assume some common unit conversion relationships (since the exact conversion factors from the cut - out are not fully clear, but we can use standard ones for illustration, and we'll also analyze the given partial solutions):

Problem 9: Convert 25 cm to mm

Step 1: Recall the conversion factor

We know that 1 cm = 10 mm. So the conversion factor from cm to mm is 10 (mm/cm).

Step 2: Multiply the value in cm by the conversion factor

To convert 25 cm to mm, we use the formula: \( \text{Value in mm}=\text{Value in cm}\times\text{Conversion factor} \)

Substitute the values: \( 25\space\text{cm}\times10\space\frac{\text{mm}}{\text{cm}} = 250\space\text{mm} \)

Let's analyze the first few given problems (1 - 3) to understand the pattern:

Problem 1: \( 8\oplus\times\frac{5\square}{\oplus}=40\square \)

Step 1: Identify the operation

We have a multiplication of the quantity in \( \oplus \) units by a conversion factor (with units \( \frac{\square}{\oplus} \)).

Step 2: Perform the multiplication

\( 8\times5 = 40 \), so \( 8\oplus\times\frac{5\square}{\oplus}=40\square \)

Problem 2: \( \frac{5\square}{2}\times\frac{\oplus}{0.15\square}=\frac{5}{0.3}\oplus\approx16.67\oplus \) (But the given answer is \( 0.75\otimes \)? Wait, maybe the units and conversion factors are specific to the cut - out. Let's assume the given \( \frac{5\square}{2} \) and conversion factor \( \frac{\oplus}{0.15\square} \), but maybe there is a miscalculation or different unit definition. However, following the first problem's pattern of multiplication/division with conversion factors.

Problem 3: \( 1.5\square\times\text{conversion factor}=\text{result in}\otimes \)

If we assume a conversion factor (from the cut - out) that when multiplied by 1.5 gives 0.15 (as per the given answer), the conversion factor would be \( \frac{0.15}{1.5}=0.1 \) (i.e., \( 1\square = 0.1\otimes \))

For the remaining problems (4 - 8), we need the specific conversion factors from the cut - out page. But since we don't have the full set of conversion factors, we can't solve them completely without that information. However, for problem 9 (converting 25 cm to mm), we can solve it with the standard unit conversion:

Answer:

(for problem 9):
\( 25\space\text{cm}=\boxed{250}\space\text{mm} \)

For the other problems, we need the conversion factors from the cut - out page provided in the activity to complete the calculations.