練習問題
1章 正の数と負の数
3.正の数・負の数の乗法と除法
(問1)
(1) (+4)×(+5)
(2) (−3)×(−6)
(3) (+2)×(−7)
(4) (−1)×(+8)
(1) (+4)×(+5)
(2) (−3)×(−6)
(3) (+2)×(−7)
(4) (−1)×(+8)
(1) (+4)×(+5)=+20
(2) (−3)×(−6)=+18
(3) (+2)×(−7)=−14
(4) (−1)×(+8)=−8
(問2)
(1) (+12)÷(+4)
(2) (−14)÷(−7)
(3) (−16)÷(+8)
(4) (+18)÷(−3)
(1) (+12)÷(+4)
(2) (−14)÷(−7)
(3) (−16)÷(+8)
(4) (+18)÷(−3)
(1) (+12)÷(+4)=+3
(2) (−14)÷(−7)=+2
(3) (−16)÷(+8)=−2
(4) (+18)÷(−3)=−6
(問3)
(1) (+3)×(−4)×(−5)
(2) 2×(−4)×(−6)×(−5)
(3) \(\left( -\dfrac {4} {5} \right) \times \left( -2\dfrac {1} {2} \right) \times \left( -\dfrac {1} {2} \right) \)
(4) 0.5×(−1.75)×(−8)
(1) (+3)×(−4)×(−5)
(2) 2×(−4)×(−6)×(−5)
(3) \(\left( -\dfrac {4} {5} \right) \times \left( -2\dfrac {1} {2} \right) \times \left( -\dfrac {1} {2} \right) \)
(4) 0.5×(−1.75)×(−8)
(1) (+3)×(−4)×(−5)=+(3×4×5)=60
(2) 2×(−4)×(−6)×(−5)=−(2×4×6×5)=−240
(3) \(-\left( \dfrac {4} {5} \right) \times \left( -2\dfrac {1} {2} \right) \times \left( -\dfrac {1} {2} \right) \)
=\( -\left( \dfrac {4} {5} \times \dfrac {5} {2} \times \dfrac {1} {2} \right) \)
=−1
(4) 0.5×(−1.75)×(−8)
=\( +\left( \dfrac {1} {2} \times 1\dfrac {3} {4} \times 8 \right) \)
=\( +\left( \dfrac {1} {2} \times \dfrac {7} {4} \times 8 \right) \)
=7
(問4) 次の値はいくつですか。
(1) \(5^{3}\)
(2) \(\left( -5\right) ^{3}\)
(3) \(-5^{3}\)
(4) \(-\left( -5\right) ^{3}\)
(5) \(-\left( -5 ^{3} \right)\)
(1) \(5^{3}\)
(2) \(\left( -5\right) ^{3}\)
(3) \(-5^{3}\)
(4) \(-\left( -5\right) ^{3}\)
(5) \(-\left( -5 ^{3} \right)\)
(1) \(5^{3} =5\times 5\times 5 =125\)
(2) \(\left( -5\right) ^{3} =\left( -5\right)\times \left( -5\right)\times \left( -5\right)=-125\)
(3) \(-5^{3} =-\left(5\times 5\times 5\right)=-125\)
(4) \(-\left( -5\right) ^{3} =-\left\{ \left( -5\right) \times \left( -5\right) \times \left( -5\right) \right\}=125 \)
(5) \(-\left( -5^{3} \right) =-\left\{ -\left( 5\times 5\times 5\right) \right\}=125 \)
(問5) 次の逆数はいくつですか。
(1) −5
(2) \(\dfrac {7} {3}\)
(3) \(-\dfrac {1} {4}\)
(4) −1
(1) −5
(2) \(\dfrac {7} {3}\)
(3) \(-\dfrac {1} {4}\)
(4) −1
(1) \(1\div \left( -5\right) =1\times \left( -\dfrac {1} {5} \right) =-\dfrac {1} {5}\)
(2) \(1\div \dfrac {7} {3} =1\times \dfrac {3} {7} =\dfrac {3} {7}\)
(3) \(1\div \left( -\dfrac {1} {4} \right) =1\times \left( -4\right) =-4\)
(4) 1÷(−1)=1×(−1)=−1
(問6)
(1)\(\dfrac {3} {4} \times \left( -1\dfrac {2} {3} \right) \)
(2)\(\left( -2\dfrac {2} {5} \right) \times \left( -1\dfrac {1} {3} \right) \)
(3)\(\left( 2\dfrac {1} {2} \right) \div \left( -\dfrac {5} {6} \right) \)
(4)\(\left( -1\dfrac {4} {5} \right) \div \left( -3\dfrac {3} {4} \right) \)
(1)\(\dfrac {3} {4} \times \left( -1\dfrac {2} {3} \right) \)
(2)\(\left( -2\dfrac {2} {5} \right) \times \left( -1\dfrac {1} {3} \right) \)
(3)\(\left( 2\dfrac {1} {2} \right) \div \left( -\dfrac {5} {6} \right) \)
(4)\(\left( -1\dfrac {4} {5} \right) \div \left( -3\dfrac {3} {4} \right) \)
(1)\(\dfrac {3} {4} \times \left( -1\dfrac {2} {3} \right) \)
\(= \dfrac {3} {4} \times \left( -\dfrac {5} {3} \right) \)
\(= -\left( \dfrac {3} {4} \times \times \dfrac {5} {3} \right) \)
\(= -\dfrac {5} {4}\)
(2)\(\left( -2\dfrac {2} {5} \right) \times \left( -1\dfrac {1} {3} \right) \)
\(= \left( -\dfrac {12} {5} \right) \times \left( -\dfrac {4} {3} \right) \)
\(= \dfrac {12} {5} \times \dfrac {4} {3}\)
\(= \dfrac {4} {5} \times 4\)
\(= \dfrac {16} {5} \)
(3)\(\left( 2\dfrac {1} {2} \right) \div \left( -\dfrac {5} {6} \right) \)
\(= \left( \dfrac {5} {2} \right) \div \left( -\dfrac {5} {6} \right) \)
\(= \dfrac {5} {2} \times \left( -\dfrac {6} {5} \right) \)
\(= -\left( \dfrac {5} {2} \times \dfrac {6} {5} \right) \)
\(= -\left( \dfrac {1} {2} \times 6 \right) \)
\(= -3\)
(4)\(\left( -1\dfrac {4} {5} \right) \div \left( -3\dfrac {3} {4} \right) \)
\( =\left( -\dfrac {9} {5} \right) \div \left( -\dfrac {15} {4} \right) \)
\( =\left( -\dfrac {9} {5} \right) \times \left( -\dfrac {4} {15} \right) \)
\( =\dfrac {9} {5} \times \dfrac {4} {15}\)
\( =\dfrac {3} {5} \times \dfrac {4} {5}\)
\( =\dfrac {12} {25} \)
(問7)
(1) 6×(−6)÷(−12)
(2) (−45)÷(−9)×6÷(−10)
(3) \( \left( -\dfrac {3} {4} \right) \div \dfrac {1} {2} \times \left( -\dfrac {2} {3} \right) \div 1\dfrac {1} {5}\)
(1) 6×(−6)÷(−12)
(2) (−45)÷(−9)×6÷(−10)
(3) \( \left( -\dfrac {3} {4} \right) \div \dfrac {1} {2} \times \left( -\dfrac {2} {3} \right) \div 1\dfrac {1} {5}\)
(1) 6×(−6)÷(−12)
\(=6 \times \left( -6\right)\times \left( -\dfrac {1} {12} \right) \)
\(=+ \left( 6 \times 6 \times \dfrac {1} {12} \right) \)
\(=3\)
(2) (−45)÷(−9)×6÷(−10)
\(=\left( -45\right) \times \left( -\dfrac {1} {9} \right) \times 6 \times \left( -\dfrac {1} {10} \right) \)
\(=-\left( 45 \times \dfrac {1} {9} \times 6 \times \dfrac {1} {10} \right) \)
\(=-3\)
(3) \( \left( -\dfrac {3} {4} \right) \div \dfrac {1} {2} \times \left( -\dfrac {2} {3} \right) \div 1\dfrac {1} {5}\)
\(= \left( -\dfrac {3} {4} \right) \div \dfrac {1} {2} \times \left( -\dfrac {2} {3} \right) \div \dfrac {6} {5}\)
\(= \left( -\dfrac {3} {4} \right) \times 2 \times \left( -\dfrac {2} {3} \right) \times \dfrac {5} {6}\)
\(= +\left( \dfrac {3} {4} \times 2 \times \dfrac {2} {3} \times \dfrac {5} {6} \right)\)
\(=\dfrac {5} {6}\)
(問8)
(1) \(2^{3} \div \left( -6\right) ^{2} \times \left( -3^{2} \right) \)
(2) \(5^{2} \div \left( -2\right) ^{2} \div \left( -1\right) ^{5}\div 3^{2}\)
(3) \(\left( -\dfrac {1} {2} \right) ^{3} \times \left( -\dfrac {2} {3} \right) ^{2} \div \left( -\dfrac {1} {6} \right) \)
(1) \(2^{3} \div \left( -6\right) ^{2} \times \left( -3^{2} \right) \)
(2) \(5^{2} \div \left( -2\right) ^{2} \div \left( -1\right) ^{5}\div 3^{2}\)
(3) \(\left( -\dfrac {1} {2} \right) ^{3} \times \left( -\dfrac {2} {3} \right) ^{2} \div \left( -\dfrac {1} {6} \right) \)
(1) \(2^{3} \div \left( -6\right) ^{2} \times \left( -3^{2} \right) \)
\(=8\div 36\times \left( -9\right)\)
\(=8\times \dfrac {1} {36}\times \left( -9\right)\)
\(= -\left( 8\times \dfrac {1} {36} \times 9\right)\)
\(-2\)
(2) \(5^{2} \div \left( -2\right) ^{2} \div \left( -1\right) ^{5}\div 3^{2}\)
\(=25\div 4\div \left( -1\right) \div 9\)
\(=25\times \dfrac {1} {4} \div \left( -1\right) \times \dfrac {1} {9}\)
\(=-\left( 25\times \dfrac {1} {4}\div -1 \times \dfrac {1} {9} \right)\)
\(=- \dfrac {25} {36}\)
(3) \(\left( -\dfrac {1} {2} \right) ^{3} \times \left( -\dfrac {2} {3} \right) ^{2} \div \left( -\dfrac {1} {6} \right) \)
\(=\left(-\dfrac {1} {8} \right)\times \dfrac {4} {9} \div \left(-\dfrac {1} {6} \right) \)
\(=\left(-\dfrac {1} {8} \right)\times \dfrac {4} {9} \times \left(-6\right) \)
\(=+\left(\dfrac {1} {8} \times \dfrac {4} {9} \times 6\right)\)
\(=\dfrac {1} {3}\)