(1) $1 \frac{2}{3} \div 5.5 + 1 \frac{7}{12} \div (2.25 - \square) = 1 \frac{1}{6}$ の $\square$ に当てはまる数を求めます。 (2) $(1999 \times \frac{1}{24} + \square) \times 1 \frac{3}{5} - 3 \frac{5}{11} \times 3 \frac{2}{3} = 127$ の $\square$ に当てはまる数を求めます。

1. 問題の内容

(1) $1 \frac{2}{3} \div 5.5 + 1 \frac{7}{12} \div (2.25 - \square) = 1 \frac{1}{6}$ の $\square$ に当てはまる数を求めます。

(2) $(1999 \times \frac{1}{24} + \square) \times 1 \frac{3}{5} - 3 \frac{5}{11} \times 3 \frac{2}{3} = 127$ の $\square$ に当てはまる数を求めます。

2. 解き方の手順

(1)

まず、与えられた式を整理します。

$1 \frac{2}{3} = \frac{5}{3}$

$5.5 = \frac{11}{2}$

$1 \frac{7}{12} = \frac{19}{12}$

$2.25 = \frac{9}{4}$

$1 \frac{1}{6} = \frac{7}{6}$

したがって、式は次のようになります。

$\frac{5}{3} \div \frac{11}{2} + \frac{19}{12} \div (\frac{9}{4} - \square) = \frac{7}{6}$

$\frac{5}{3} \times \frac{2}{11} + \frac{19}{12} \div (\frac{9}{4} - \square) = \frac{7}{6}$

$\frac{10}{33} + \frac{19}{12} \div (\frac{9}{4} - \square) = \frac{7}{6}$

$\frac{19}{12} \div (\frac{9}{4} - \square) = \frac{7}{6} - \frac{10}{33}$

$\frac{7}{6} - \frac{10}{33} = \frac{77}{66} - \frac{20}{66} = \frac{57}{66} = \frac{19}{22}$

$\frac{19}{12} \div (\frac{9}{4} - \square) = \frac{19}{22}$

$\frac{9}{4} - \square = \frac{19}{12} \div \frac{19}{22}$

$\frac{9}{4} - \square = \frac{19}{12} \times \frac{22}{19}$

$\frac{9}{4} - \square = \frac{22}{12} = \frac{11}{6}$

$\square = \frac{9}{4} - \frac{11}{6}$

$\square = \frac{27}{12} - \frac{22}{12} = \frac{5}{12}$

(2)

$(1999 \times \frac{1}{24} + \square) \times 1 \frac{3}{5} - 3 \frac{5}{11} \times 3 \frac{2}{3} = 127$

$(1999 \times \frac{1}{24} + \square) \times \frac{8}{5} - \frac{38}{11} \times \frac{11}{3} = 127$

$(1999 \times \frac{1}{24} + \square) \times \frac{8}{5} - \frac{38}{3} = 127$

$(1999 \times \frac{1}{24} + \square) \times \frac{8}{5} = 127 + \frac{38}{3}$

$(1999 \times \frac{1}{24} + \square) \times \frac{8}{5} = \frac{381}{3} + \frac{38}{3} = \frac{419}{3}$

$1999 \times \frac{1}{24} + \square = \frac{419}{3} \times \frac{5}{8} = \frac{2095}{24}$

$1999 \times \frac{1}{24} = \frac{1999}{24}$

$\frac{1999}{24} + \square = \frac{2095}{24}$

$\square = \frac{2095}{24} - \frac{1999}{24} = \frac{96}{24} = 4$

3. 最終的な答え

(1) $\frac{5}{12}$

(2) 4