Sure, let's work through this division problem step-by-step.
1. First we need to identify the numbers:
- Dividend: \(34\)
- Divisor: \(7\)
2. Determine how many times the divisor (7) can fit into the dividend (34) without exceeding it.
- Calculate \(34 \div 7\):
- \(7 \times 1 = 7\)
- \(7 \times 2 = 14\)
- \(7 \times 3 = 21\)
- \(7 \times 4 = 28\)
- \(7 \times 5 = 35\) (which is greater than 34, so we use the previous result)
The quotient is \(4\) because \(7\) fits into \(34\) four times.
3. Next, we calculate the remainder:
- Multiply the divisor by the quotient: \(7 \times 4 = 28\)
- Subtract this result from the dividend: \(34 - 28 = 6\)
Therefore, the remainder is \(6\).
4. So, the division of 34 by 7 yields a quotient and remainder:
- Quotient: \(4\)
- Remainder: \(6\)
Thus, \(34 \div 7\) equals \(4\) with a remainder of \(6\).
So, the correct answer is [tex]\( D. 4 \, r \, 6 \)[/tex].
