Long division is a way to show the steps for dividing numbers in decimal form. It finds the quotient one digit at a time, from left to right.
Here is the long division for \(512 \div 4\).
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Two numbers that multiply to equal 1 are reciprocals.
8 and \(\frac{1}{8}\) are reciprocals because \(8 \boldcdot \frac{1}{8} = 1\).
\(\frac{2}{5}\) is a reciprocal of \(\frac{5}{2}\) because \(\frac{2}{5} \boldcdot \frac{5}{2} = 1\).
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A unit rate is a rate per 1.
For example, 12 people share 2 pies equally. One unit rate is 6 people per pie, because \(12 \div 2 = 6\). The other unit rate is \(\frac16\) of a pie per person, because \(2 \div 12 = \frac16\).