例子─分數去括號法則

分數的去括號法則【★小中大,內而外】

進行正、負分數的四則運算時,若算式中包含括號,需遵循以下規則:

先計算小括號 $(\quad )$ 內的算式,再計算中括號 $[\quad ]$ 內的算式,最後再計算大括號 $\{\quad \}$ 內的算式。

$\quad \dfrac12+\dfrac13\times \{\dfrac14-\dfrac15\div [\dfrac16-2^3\times \dfrac{1}{48}+(\dfrac13-\dfrac15)]\}$

$=\dfrac12+\dfrac13\times \{\dfrac14-\dfrac15\div [\dfrac16-8\times \dfrac{1}{48}+(\dfrac{5}{15}-\dfrac{3}{15})]\}$

$=\dfrac12+\dfrac13\times \{\dfrac14-\dfrac15\div [\dfrac16-\dfrac16+\dfrac{2}{15}]\}$

$=\dfrac12+\dfrac13\times \{\dfrac14-\dfrac15\div \dfrac{2}{15}\}$

$=\dfrac12+\dfrac13\times (\dfrac14-\dfrac15\times \dfrac{15}{2})$

$=\dfrac12+\dfrac13\times (\dfrac14-\dfrac32)$

$=\dfrac12+\dfrac13\times (\dfrac14-\dfrac64)$

$=\dfrac12+\dfrac13\times (-\dfrac54)$

$=\dfrac12+(-\dfrac{5}{12})$

$=\dfrac{6}{12}+(-\dfrac{5}{12})$

$=\dfrac{1}{12}$

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