Question

Which of the following is equal to 3,124 ÷ 22?
A.
(2,200 + 22) + (880 + 22) + (44 + 22)
B.
(2,200 ÷ 22) + (880 ÷ 22) + (44 ÷ 22)
C.
(2,200 ÷ 22) - (880 ÷ 22) - (44 ÷ 22)
D.
(2,200 + 22) ÷ (880 + 22) ÷ (44 + 22)

Answer 1

To determine which option is equal to \( 3,124 \div 22 \), we will analyze each option one by one.

First, calculate \( 3,124 \div 22 \):
\[
3,124 \div 22 = 142
\]

Next, we will evaluate each provided option step by step.

**Option A:**
\[
(2,200 + 22) + (880 + 22) + (44 + 22)
\]
Calculating each component:
\[
2,200 + 22 = 2,222
\]
\[
880 + 22 = 902
\]
\[
44 + 22 = 66
\]
Now summing these results:
\[
2,222 + 902 + 66 = 3,190
\]
This does not equal 142.

**Option B:**
\[
(2,200 \div 22) + (880 \div 22) + (44 \div 22)
\]
Calculating each division:
\[
2,200 \div 22 = 100
\]
\[
880 \div 22 = 40
\]
\[
44 \div 22 = 2
\]
Now summing these results:
\[
100 + 40 + 2 = 142
\]
This equals 142, so Option B is likely correct.

**Option C:**
\[
(2,200 \div 22) - (880 \div 22) - (44 \div 22)
\]
Calculating each division (we already calculated these):
\[
(2,200 \div 22) = 100
\]
\[
(880 \div 22) = 40
\]
\[
(44 \div 22) = 2
\]
Now applying the operation:
\[
100 - 40 - 2 = 58
\]
This does not equal 142.

**Option D:**
\[
(2,200 + 22) \div (880 + 22) \div (44 + 22)
\]
Calculating the additions first:
\[
2,200 + 22 = 2,222
\]
\[
880 + 22 = 902
\]
\[
44 + 22 = 66
\]
So,
\[
(2,222 \div 902) \div 66
\]
Calculating \( 2,222 \div 902 \) first, which we can approximate but it won't lead us to 142.
Thus:
\[
\text{This does not equal } 142.
\]

After evaluating all options, we find that only **Option B** gives us the exact value of \( 3,124 \div 22 = 142 \).

Therefore, the correct answer is:
\[
\boxed{B}
\]