Question

find the difference.
21,807 - 10,739
round this number to
the nearest 1,000.
7,433,654
find the quotient.
9,276 + 8

Explanation:

First Sub - Question: Find the Difference \(21,807 - 10,739\)

Step 1: Align the numbers by place value

We write the numbers vertically, aligning the digits by their place values (units, tens, hundreds, thousands, etc.).
\[

$$\begin{align*} &21807\\ - &10739\\ \hline \end{align*}$$

\]

Step 2: Subtract digit by digit starting from the right - most digit

• Units place: \(7 - 9\). Since \(7<9\), we need to borrow from the tens place. The tens place has \(0\), so we need to borrow from the hundreds place. The hundreds place has \(8\), we borrow \(1\) from the hundreds place (making it \(7\)), and give it to the tens place. Now the tens place becomes \(10\), and we borrow \(1\) from the tens place (making it \(9\)) and give it to the units place. Now the units place is \(17\). So \(17 - 9=8\).
• Tens place: We had borrowed \(1\) earlier, so now we have \(9\) in the tens place. \(9 - 3 = 6\).
• Hundreds place: We had borrowed \(1\) earlier, so we have \(7\) in the hundreds place. \(7-7 = 0\).
• Thousands place: \(1 - 0=1\) (wait, no, the original number is \(21807\), the thousands digit is \(1\) (from \(21,807\), the \(1\) is in the thousands place? Wait, \(21,807\) is \(2\times10000 + 1\times1000+8\times100 + 0\times10+7\times1\), and \(10,739\) is \(1\times10000+0\times1000 + 7\times100+3\times10 + 9\times1\). Wait, let's re - do the subtraction:

\[

$$\begin{align*} 21807-10739&=(20000 + 1807)-(10000+739)\\ &=(20000 - 10000)+(1807 - 739)\\ &=10000+(1807 - 739) \end{align*}$$

\]
Now calculate \(1807-739\):

• Units: \(7 - 9\), borrow from tens. Tens is \(0\), borrow from hundreds. Hundreds is \(8\), becomes \(7\), tens becomes \(10\), borrow from tens, tens becomes \(9\), units becomes \(17\). \(17 - 9 = 8\).
• Tens: \(9-3 = 6\).
• Hundreds: \(7 - 7=0\).
• So \(1807 - 739 = 1068\). Then \(10000+1068=11068\).

Step 1: Identify the digit in the thousands place and the digit to its right (the hundreds place)

In the number \(7,433,654\), the digit in the thousands place is \(3\) (since \(7,433,654=7\times1000000+4\times100000 + 3\times10000+3\times1000+6\times100+5\times10 + 4\times1\)), and the digit in the hundreds place is \(6\).

Step 2: Apply the rounding rule

The rule for rounding to the nearest \(1000\) is: if the digit in the hundreds place (the digit to the right of the thousands place) is \(5\) or greater, we round up the thousands place digit; if it is less than \(5\), we leave the thousands place digit as it is and set the digits to the right of the thousands place to \(0\).
Since the digit in the hundreds place is \(6\) (which is greater than \(5\)), we add \(1\) to the thousands place digit. The thousands place digit is \(3\), so \(3 + 1=4\), and we set the digits to the right of the thousands place (hundreds, tens, units) to \(0\).
So \(7,433,654\) rounded to the nearest \(1000\) is \(7,434,000\).

Step 1: Divide the first digit of the dividend by the divisor

We start with the left - most digit of the dividend \(9\). \(9\div8 = 1\) with a remainder of \(1\). We write \(1\) above the thousands place (wait, \(9276\) is a four - digit number, \(9\) is in the thousands place? No, \(9276\) is \(9\times1000+2\times100 + 7\times10+6\times1\). So \(9\div8 = 1\) (quotient digit), and the remainder is \(9 - 8\times1=1\).

Step 2: Bring down the next digit

We bring down the next digit ( \(2\)) to the remainder. So we have \(12\). \(12\div8 = 1\) with a remainder of \(4\). We write \(1\) above the hundreds place.

Step 3: Bring down the next digit

We bring down the next digit ( \(7\)) to the remainder. So we have \(47\). \(47\div8 = 5\) with a remainder of \(7\) (since \(8\times5 = 40\), \(47-40 = 7\)). We write \(5\) above the tens place.

Step 4: Bring down the last digit

We bring down the last digit ( \(6\)) to the remainder. So we have \(76\). \(76\div8 = 9\) with a remainder of \(4\) (since \(8\times9=72\), \(76 - 72 = 4\)). We write \(9\) above the units place.

Step 5: Write the quotient and the remainder

The quotient is \(1159\) and the remainder is \(4\). If we want the decimal form, we can continue dividing by adding a decimal point and zeros to the dividend. \(40\div8 = 5\). So \(9276\div8=1159.5\)

Answer:

\(11068\)

Second Sub - Question: Round \(7,433,654\) to the nearest \(1,000\)