Question

divide the following by using short division. use multiplication to check the answer.
\\(7\enclose{longdiv}{4228}\\)

select the correct choice below and fill in the answer box(es) to complete your choice.
\\(\bigcirc\\) a. the quotient is \\(\square\\) r \\(\square\\).
\\(\bigcirc\\) b. the quotient is \\(\square\\) with no remainder.

Explanation:

Step1: Divide 4 by 7 (not possible, so consider 42)

42 ÷ 7 = 6. Write 6 above the tens place.

Step2: Bring down 2

Now we have 2. 2 ÷ 7 is not possible, so write 0 above the units place (wait, no, wait, the number is 4228. Wait, let's do short division properly.

Short division of 4228 by 7:

• 42 ÷ 7 = 6 (write 6 in the hundreds place? Wait, 4228 is a 4-digit number. Let's do digit by digit.

First digit: 4 (thousands place) ÷ 7: not possible, so take 42 (thousands and hundreds: 42). 42 ÷ 7 = 6. Write 6 in the hundreds place.

Next digit: 2 (tens place). 2 ÷ 7: not possible, so write 0 in the tens place? Wait, no, 22? Wait, no, after 42 (hundreds), we bring down the next digit, which is 2 (tens), making 22? Wait, no, 4228: digits are 4 (thousands), 2 (hundreds), 2 (tens), 8 (units).

Wait, short division steps:

Divide 4228 by 7:

• 7 into 4 (thousands): 0, so carry over 4 to the hundreds place, making 42 (hundreds). 7 into 42 is 6. Write 6 in the hundreds place.

• Bring down the next digit (2, tens place) to make 2 (wait, no, after 42 (hundreds) is divided by 7, we have 0 remainder? Wait, 42 - 42 = 0. Then bring down the next digit, which is 2 (tens). Now we have 2 (tens). 7 into 2: 0, so write 0 in the tens place, carry over 2 to the units place, making 28 (units).

• 7 into 28 is 4. Write 4 in the units place.

So the quotient is 604.

Now check by multiplication: 604 × 7 = 4228. Let's calculate 600×7=4200, 4×7=28, 4200+28=4228. So no remainder.

Step3: Check with multiplication

604 × 7 = (600 + 4) × 7 = 600×7 + 4×7 = 4200 + 28 = 4228, which matches the dividend. So no remainder.

Answer:

B. The quotient is 604 with no remainder.