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初中数学七年级上册(581题)


现场学习:我们知道\(|x| = \left\{ {\begin{array}{*{20}{l}}
{x(x > 0)} \\
{0(x = 0)} \\
{ - x(x < 0)}
\end{array}} \right.\)
,所以当\(x > 0\)时,\(\frac{x}{{|x|}} = \frac{x}{x} = 1\),当\(x < 0\)时,\(\frac{x}{{|x|}} = \frac{x}{{ - x}} = - 1\)

解决问题:已知\(a\)\(b\)是有理数,当\(ab \ne 0\)时,求\(\frac{a}{{|a|}} + \frac{b}{{|b|}}\)的值



知识点:第一章 有理数


参考答案:分四种情况:
①当\(a > 0\),\(b > 0\)时,\(\frac{a}{{|a|}} + \frac{b}{{|b|}} = 1 + 1 = 2\);
②当\(a < 0\),\(b < 0\)时,\(\frac{a}{{|a|}} + \frac{b}{{|b|}} = - 1 - 1 = - 2\);
③当\(a > 0\),\(b < 0\)时,\(\frac{a}{{|a|}} + \frac{b}{{|b|}} = 1 - 1 = 0\);
④当\(a < 0\),\(b > 0\)时,\(\frac{a}{{|a|}} + \frac{b}{{|b|}} = - 1 + 1 = 0\);
综上所述:\(\frac{a}{{|a|}} + \frac{b}{{|b|}}\)的值为2或\( - 2\)或0.

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