Question

the work shows the long division of \\(647 \div 3\\).
find the values of \\(a\\) and \\(b\\) in the long division problem.
\\(a = \\)
\\(b = \\)
so, \\(647 \div 3 = 215 + \\)

Explanation:

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<reasoning>

Analyze the final step of long division

To find the value of \(a\), we look at the last division step. We are dividing \(17\) by the divisor \(3\). The quotient digit above this step is \(5\). We multiply the divisor by this quotient digit:
\[
3 \times 5 = 15
\]
Thus, the value subtracted from \(17\) is \(a = 15\).

Calculate the remainder

To find the value of \(b\), which represents the remainder of the division, we subtract \(a\) from \(17\):
\[
b = 17 - a = 17 - 15 = 2
\]
Thus, the remainder is \(b = 2\).

Express the division with a fractional remainder

The division of \(647\) by \(3\) yields a quotient of \(215\) and a remainder of \(2\). We write this as:
\[
647 \div 3 = 215 + \frac{2}{3}
\]
Thus, the missing term in the equation is \(\frac{2}{3}\).
</reasoning>

<answer>
Find the values of \(a\) and \(b\) in the long division problem.

\(a =\) <blank>15</blank>

\(b =\) <blank>2</blank>

So, \(647 \div 3 = 215+\) <blank>\(\frac{2}{3}\)</blank>
</answer>

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Answer:

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<reasoning>

Analyze the final step of long division

To find the value of \(a\), we look at the last division step. We are dividing \(17\) by the divisor \(3\). The quotient digit above this step is \(5\). We multiply the divisor by this quotient digit:
\[
3 \times 5 = 15
\]
Thus, the value subtracted from \(17\) is \(a = 15\).

Calculate the remainder

To find the value of \(b\), which represents the remainder of the division, we subtract \(a\) from \(17\):
\[
b = 17 - a = 17 - 15 = 2
\]
Thus, the remainder is \(b = 2\).

Express the division with a fractional remainder

The division of \(647\) by \(3\) yields a quotient of \(215\) and a remainder of \(2\). We write this as:
\[
647 \div 3 = 215 + \frac{2}{3}
\]
Thus, the missing term in the equation is \(\frac{2}{3}\).
</reasoning>

<answer>
Find the values of \(a\) and \(b\) in the long division problem.

\(a =\) <blank>15</blank>

\(b =\) <blank>2</blank>

So, \(647 \div 3 = 215+\) <blank>\(\frac{2}{3}\)</blank>
</answer>

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"Mathematics",
"Arithmetic",
"Long Division"
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