Question

4 - digit divide
solve. check by multiplying.

1. \\(2 \overline{)7,683}\\)

Explanation:

Step1: Divide thousands place

Divide 7 (thousands place) by 2. \( 7 \div 2 = 3 \) with remainder 1. Write 3 above thousands place. Multiply \( 2 \times 3 = 6 \), subtract \( 7 - 6 = 1 \).

Step2: Bring down hundreds digit

Bring down 6 (hundreds place) to make 16. \( 16 \div 2 = 8 \). Write 8 above hundreds place. Multiply \( 2 \times 8 = 16 \), subtract \( 16 - 16 = 0 \).

Step3: Bring down tens digit

Bring down 8 (tens place) to make 8. \( 8 \div 2 = 4 \). Write 4 above tens place. Multiply \( 2 \times 4 = 8 \), subtract \( 8 - 8 = 0 \).

Step4: Bring down ones digit

Bring down 3 (ones place) to make 3. \( 3 \div 2 = 1 \) with remainder 1. Write 1 above ones place. Multiply \( 2 \times 1 = 2 \), subtract \( 3 - 2 = 1 \).

Step5: Check by multiplying

The quotient is 3841, remainder 1. Check: \( 3841 \times 2 + 1 = 7682 + 1 = 7683 \), which matches the dividend.

Answer:

The quotient is \( 3841 \) with a remainder of \( 1 \), or as a mixed number \( 3841\frac{1}{2} \). The division result (quotient and remainder) is \( 3841 \) R \( 1 \).