Question

what is the quotient of 11,310 ÷ 26?
435 \\(\frac{20}{26}\\)
435
430
335 \\(\frac{20}{26}\\)

Explanation:

Step1: Perform the division

We divide 11310 by 26. First, we see how many times 26 goes into 11310.
We know that \(26\times435 = 26\times(400 + 35)=26\times400+26\times35 = 10400+910 = 11310\). Wait, no, let's calculate \(26\times435\): \(26\times400 = 10400\), \(26\times35=910\), \(10400 + 910=11310\)? Wait, \(26\times435=26\times(400 + 30+5)=26\times400+26\times30 + 26\times5=10400+780 + 130=10400 + 910=11310\). Wait, but \(26\times435 = 11310\)? Let's check \(435\times26\):
\[

$$\begin{align*} 435\times26&=(400 + 30+5)\times26\\ &=400\times26+30\times26 + 5\times26\\ &=10400+780+130\\ &=10400 + 910\\ &=11310 \end{align*}$$

\]
Wait, but the dividend is 11310, so \(11310\div26 = 435\)? Wait, no, wait \(26\times435 = 11310\), so the quotient is 435? Wait, but let's do the division step by step.
Divide 11310 by 26:
26 into 113 (the first three digits) is 4 times (264=104), subtract 104 from 113, we get 9. Bring down the next digit 1, making it 91. 26 into 91 is 3 times (263=78), subtract 78 from 91, we get 13. Bring down the last digit 0, making it 130. 26 into 130 is 5 times (265=130). So putting it together, 4 (hundreds place), 3 (tens place), 5 (ones place), so 435. Wait, but let's check \(26\times435\): as above, it's 11310. So the division \(11310\div26 = 435\). Wait, but the first option is \(435\frac{20}{26}\), but that would be if there was a remainder. Wait, maybe I made a mistake. Wait, 26435 = 11310? Let's calculate 26400=10400, 2635=910, 10400+910=11310. Yes, so 11310 divided by 26 is 435 with a remainder of 0? Wait, but the first option has a remainder. Wait, maybe the problem was written wrong? Wait, no, let's check the original problem: 11,310 ÷ 26. Let's do 11310 ÷26:

26*435 = 11310, so the quotient is 435, remainder 0. So the correct answer is 435.

Step2: Verify the options

Looking at the options, the second option is 435, which matches our calculation. The first option has a remainder, but since 26*435=11310, there is no remainder. So the correct quotient is 435.

Answer:

B. 435