正負の数　まとめ練習問題¶

\(+3,\quad +0.1\)

\(-2,\quad -0.5,\quad -\dfrac{3}{4}\)

どちらでもない。

(a) \(9\) 　　(b) \(4\) 　　(c) \(0\) 　　(d) \(\dfrac{7}{3}\) 　　(e) \(0.6\)

\(+5\) と \(-5\)

\(+\dfrac{3}{2}\) と \(-\dfrac{3}{2}\)

\(-3 < -1 < 0 < +2 < +5\)

\(-\dfrac{3}{2} = -1.5\) より、\(-0.5 = -\dfrac{1}{2}\) と比較すると \(-\dfrac{3}{2} < -0.5\)

(a) \(-3 > -5\)（数直線で右側）

(b) \(-\dfrac{1}{2} < -\dfrac{1}{3}\)（絶対値 \(\dfrac{1}{2} > \dfrac{1}{3}\) なので、負では逆転）

(c) \(-0.2 > -0.5\)

\(-3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3\)

\(+(4+7) = +11\)

\(-(5+8) = -13\)

\(-(9-6) = -3\)

\(-(7-3) = -4\)

\(0\)

\(-(1.2-0.5) = -0.7\)

\(-(0.3+0.8) = -1.1\)

通分して \(\dfrac{2}{4} - \dfrac{3}{4} = -\dfrac{1}{4}\)

通分して \(-\dfrac{4}{6} - \dfrac{1}{6} = -\dfrac{5}{6}\)

通分して \(\dfrac{6}{8} - \dfrac{5}{8} = +\dfrac{1}{8}\)

\((+8) + (-3) = +5\)

\((+5) + (+4) = +9\)

\((-6) + (-2) = -8\)

\((-3) + (+7) = +4\)

\(0 + (+5) = +5\)

\((+1.5) + (-2.8) = -1.3\)

\((-0.6) + (+1.4) = +0.8\)

\(\left(-\dfrac{3}{5}\right) + \left(-\dfrac{1}{5}\right) = -\dfrac{4}{5}\)

\(\left(+\dfrac{1}{3}\right) + \left(+\dfrac{1}{2}\right) = \dfrac{2}{6} + \dfrac{3}{6} = +\dfrac{5}{6}\)

\(\left(-\dfrac{5}{6}\right) + \left(+\dfrac{2}{3}\right) = -\dfrac{5}{6} + \dfrac{4}{6} = -\dfrac{1}{6}\)

正の数の和：\(3+7=10\)、負の数の和：\(5\)

\(10 - 5 = +5\)

\((-4) + (-2) + (+6) = -6 + 6 = 0\)

\(-8 + 3 + 5 - 2 = (3+5) - (8+2) = 8 - 10 = -2\)

\(6 - 4 - 7 + 3 = (6+3) - (4+7) = 9 - 11 = -2\)

\(-1.2 + 3.5 - 2.4 + 0.6 = (3.5+0.6) - (1.2+2.4) = 4.1 - 3.6 = 0.5\)

\(+24\)

\(-15\)

\(-42\)

\(+32\)

\((-3)\times(-2) = +6\)、\(6 \times (-5) = -30\)

（負が3個=奇数個 → 負）

負が3個（奇数個）→ 符号は負

\(2 \times 3 \times 4 \times 1 = 24\) → \(-24\)

\(-(0.4 \times 5) = -2\)

\(+(0.3 \times 0.2) = +0.06\)

符号は負、絶対値は \(\dfrac{3}{4} \times \dfrac{8}{9} = \dfrac{24}{36} = \dfrac{2}{3}\)

答え：\(-\dfrac{2}{3}\)

符号は正、絶対値は \(\dfrac{5}{6} \times \dfrac{3}{10} = \dfrac{15}{60} = \dfrac{1}{4}\)

答え：\(+\dfrac{1}{4}\)

\(+4\)

\(-6\)

\(-5\)

\(+5\)

\(-(4 \div 0.8) = -5\)

\(+(1.5 \div 0.3) = +5\)

逆数をかける：\(8 \times \left(-\dfrac{3}{4}\right) = -6\)

符号は正、\(\dfrac{3}{5} \times \dfrac{10}{9} = \dfrac{30}{45} = \dfrac{2}{3}\)

答え：\(+\dfrac{2}{3}\)

符号は負、\(\dfrac{7}{4} \times \dfrac{8}{7} = \dfrac{56}{28} = 2\)

答え：\(-2\)

符号は負、\(\dfrac{5}{6} \times \dfrac{12}{5} = \dfrac{60}{30} = 2\)

答え：\(-2\)

\((-6) \times (+2) = -12\)、\((-12) \div (-4) = +3\)

\((-3) \div 6 = -\dfrac{1}{2}\)、\(\left(-\dfrac{1}{2}\right) \times (-8) = +4\)

負が3個（奇数）→ 符号は負

\(2 \times 5 \div 4 \times 3 = \dfrac{30}{4} = \dfrac{15}{2}\)

答え：\(-\dfrac{15}{2}\)

\(\dfrac{2}{3} \times 9 = 6\)、負が1個（奇数）→ 符号は負で \(-6\)、\((-6) \div (-6) = +1\)

負が3個 → 符号は負

\(\dfrac{1}{2} \times \dfrac{4}{3} \times \dfrac{6}{5} = \dfrac{24}{30} = \dfrac{4}{5}\)

答え：\(-\dfrac{4}{5}\)

\(25\)

\(64\)

\(+9\)

\(-27\)

\(+16\)

奇数乗 → \(-1\)

偶数乗 → \(+1\)

\(-(5^2) = -25\)

\(-(2^4) = -16\)

\(\left(-\dfrac{1}{2}\right)^3 = -\dfrac{1}{8}\)（奇数乗 → 負）

\(\left(-\dfrac{2}{3}\right)^2 = +\dfrac{4}{9}\)（偶数乗 → 正）

\(+0.01\)

\(-(0.2)^3 = -(0.008) = -0.008\)

かけ算を先に：\(3 + (-8) = -5\)

\(9 - 5 = 4\)

\(2 - 9 \times 2 = 2 - 18 = -16\)

\(-8 + 12 = 4\)

\(16 \div (-2) + 7 = -8 + 7 = -1\)

\(-9 + (-8) = -17\)

\((-3) \times 4 - 5 \times (-1) = -12 + 5 = -7\)

\(-2 + 4 \times (-1) = -2 + (-4) = -6\)

\(\dfrac{1}{4} \times 8 - 3 = 2 - 3 = -1\)

\(\dfrac{4}{9} \div \dfrac{2}{3} = \dfrac{4}{9} \times \dfrac{3}{2} = \dfrac{2}{3}\)

\(\dfrac{2}{3} + 1 = \dfrac{5}{3}\)

\(0.25 \times (-4) + 3 = -1 + 3 = 2\)

\(2 \times (-4) = -8\)

カッコ内：\(5-8=-3\)、\((-3)^2=9\)

\((-3) \times 9 = -27\)

\((-3)^2 - 2 \times (-5) = 9 + 10 = 19\)

\(\{4-6\} \times (-3) = (-2) \times (-3) = 6\)

\((-1) \times (5 - 4) = (-1) \times 1 = -1\)

\(\{-9 + (-1)\} \div (-5) = (-10) \div (-5) = 2\)

\(-3 + (-5) = -8\) ℃

\(-20 + 35 = +15\) m

\((-3) + 2 = -1\)

\((-4) - (-3) = -4 + 3 = -1\)

\((-2)^2 - 5 = 4 - 5 = -1\)

\(-(-3)^2 + 2 \times (-3) = -9 + (-6) = -15\)

前半：\(\left(-\dfrac{3}{4}\right)^2 = \dfrac{9}{16}\)

\(\dfrac{9}{16} \times \left(-\dfrac{8}{3}\right) = -\dfrac{72}{48} = -\dfrac{3}{2}\)

後半：\(\left(-\dfrac{1}{2}\right)^3 = -\dfrac{1}{8}\)

\(\left(-\dfrac{1}{8}\right) \div \dfrac{1}{4} = -\dfrac{1}{8} \times 4 = -\dfrac{1}{2}\)

合計：\(-\dfrac{3}{2} + \left(-\dfrac{1}{2}\right) = -\dfrac{4}{2} = -2\)

\(0.25 \div \left(-\dfrac{1}{4}\right) = 0.25 \times (-4) = -1\)

\((-2)^3 \times 0.25 = (-8) \times 0.25 = -2\)

\((-1) - (-2) = -1 + 2 = 1\)

\((-2)^3 = -8\)、\(3 \times (-2)^2 = 3 \times 4 = 12\)、\(2 \times (-2) = -4\)

第1分数の分子：\((-3)^2 - (-1)^3 = 9 - (-1) = 10\)

第1分数の分母：\((-2)^2 + (-1)^4 = 4 + 1 = 5\)

第1分数：\(\dfrac{10}{5} = 2\)

第2分数の分子：\((-2)^3 = -8\)

第2分数の分母：\((-3) \times (-1)^5 = (-3) \times (-1) = 3\)

第2分数：\(\dfrac{-8}{3} = -\dfrac{8}{3}\)

答え：\(2 - \left(-\dfrac{8}{3}\right) = 2 + \dfrac{8}{3} = \dfrac{6}{3} + \dfrac{8}{3} = \dfrac{14}{3}\)