Question

1. select all the equations represented by this tape diagram.

a. $4 + 3 =?$
b. $3 + 3 + 3 + 3 =?$
c. $? = 4 \cdot 3$
d. $? = 3 \cdot 3 \cdot 3 \cdot 3$
e. $4 \div 3 =?$
f. $4 =? \div 3$

Explanation:

The tape diagram has 4 sections, each labeled 3, and we need to find the total (?).

Step 1: Analyze Option A

The equation is \(4 + 3 =?\). But the tape diagram has 4 groups of 3, not 4 + 3. So A is incorrect.

Step 2: Analyze Option B

The equation is \(3 + 3 + 3 + 3 =?\). Since there are 4 sections of 3, adding them together is correct. So B is valid.

Step 3: Analyze Option C

The equation is \(? = 4 \cdot 3\). Multiplication is repeated addition, so 4 times 3 is the same as 3 + 3 + 3 + 3. So C is valid.

Step 4: Analyze Option D

The equation is \(? = 3 \cdot 3 \cdot 3 \cdot 3\). This is \(3^4\), which is not the same as 4 groups of 3. So D is incorrect.

Step 5: Analyze Option E

The equation is \(4 \div 3 =?\). Division is not what the tape diagram represents (it's about total from 4 groups of 3). So E is incorrect.

Step 6: Analyze Option F

The equation is \(4 =? \div 3\). Rearranging gives \(? = 4 \cdot 3\), which is the same as the total. So F is valid (since \(? = 4 \times 3\) implies \(4 =? \div 3\)).

Answer:

B. \(3 + 3 + 3 + 3 =?\), C. \(? = 4 \cdot 3\), F. \(4 =? \div 3\)