Question

divide the following by using short division. use multiplication to check the answer.
20,035 ÷ 5

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

Explanation:

Step1: Perform Short Division

Divide \(20035\) by \(5\).

• \(2 \div 5\) is not possible, so we take \(20\). \(20 \div 5 = 4\), write \(4\) above the \(0\) in the ten - thousands place.
• Next digit is \(0\). \(0\div5 = 0\), write \(0\) above the \(0\) in the thousands place.
• Next digit is \(0\). \(0\div5 = 0\), write \(0\) above the \(0\) in the hundreds place.
• Next digit is \(3\). \(3\div5\) is not possible, so we take \(35\). \(35\div5 = 7\), write \(7\) above the \(5\) in the ones place.

So, \(20035\div5 = 4007\).

Step2: Check by Multiplication

To check, we multiply the quotient by the divisor. If \(4007\times5\) equals \(20035\), then our division is correct.
\(4007\times5=(4000 + 7)\times5=4000\times5+7\times5 = 20000+35 = 20035\), which matches the dividend. So there is no remainder.

Answer:

B. The quotient is \(4007\) with no remainder.