Question

first, sort the cards that show ways the model can be represented.
equivalent
not equivalent
7 tenths
$7 \times 10$
1 tenth
$7 \times 0.1$

Explanation:

To solve this, we analyze each card:

Step 1: Interpret "7 tenths"

"7 tenths" means \( 7 \times \frac{1}{10} \) or \( 7 \times 0.1 \) (since \( \frac{1}{10} = 0.1 \)).

Step 2: Analyze \( 7 \times 10 \)

\( 7 \times 10 = 70 \), which is not equal to 7 tenths (0.7).

Step 3: Analyze "1 tenth"

"1 tenth" is \( 1 \times 0.1 = 0.1 \), not equal to 7 tenths (0.7).

Step 4: Analyze \( 7 \times 0.1 \)

\( 7 \times 0.1 = 0.7 \), which matches "7 tenths" (since 7 tenths = \( 0.7 \)).

Equivalent:

• 7 tenths
• \( 7 \times 0.1 \)

Not Equivalent:

• \( 7 \times 10 \)
• 1 tenth

(If the task is to sort them, the above groups show which belong to each category.)

Answer:

To solve this, we analyze each card:

Step 1: Interpret "7 tenths"

"7 tenths" means \( 7 \times \frac{1}{10} \) or \( 7 \times 0.1 \) (since \( \frac{1}{10} = 0.1 \)).

Step 2: Analyze \( 7 \times 10 \)

\( 7 \times 10 = 70 \), which is not equal to 7 tenths (0.7).

Step 3: Analyze "1 tenth"

"1 tenth" is \( 1 \times 0.1 = 0.1 \), not equal to 7 tenths (0.7).

Step 4: Analyze \( 7 \times 0.1 \)

\( 7 \times 0.1 = 0.7 \), which matches "7 tenths" (since 7 tenths = \( 0.7 \)).

Equivalent:

• 7 tenths
• \( 7 \times 0.1 \)

Not Equivalent:

• \( 7 \times 10 \)
• 1 tenth

(If the task is to sort them, the above groups show which belong to each category.)