練習問題
1章 正の数と負の数
4.四則の混じった計算
(問1)
(1) (−4)×(+3)−(−3)
(2) −12+(−2)×(−6)
(3) (−6)×3−(−2)×8
(4) 16÷(−4)−3
(5) −14−(−21)÷7
(6) (−15)÷3−(−24)÷2
(1) (−4)×(+3)−(−3)
(2) −12+(−2)×(−6)
(3) (−6)×3−(−2)×8
(4) 16÷(−4)−3
(5) −14−(−21)÷7
(6) (−15)÷3−(−24)÷2
(1) (−4)×(+3)−(−3)
=−12+3
=−9
(2) −12+(−2)×(−6)
=−12+12
=0
(3) (−6)×3−(−2)×8
=−18−(−16)
=−18+16
=−2
(4) 16÷(−4)−3
=−4−3
=−7
(5) −14−(−21)÷7
=−14−(−3)
=−14+3
=−11
(6) (−15)÷3−(−24)÷2
=−5−(−12)
=−5+12
=7
(問2)
(1) \(\left( -\dfrac {2} {3} \right) \times \left( -\dfrac {5} {9} \right) -\dfrac {7} {27}\)
(2) \(\left( -\dfrac {3} {4} \right) \times \dfrac {5} {6} -\dfrac {1} {4}\)
(3) \(\left( -\dfrac {1} {2} \right) \times \left( -\dfrac {6} {5} \right) -1.3\)
(4) \( -\dfrac {1} {6} - \left( -\dfrac {3} {10} \right) \times 5\)
(5) \( -3 \times \dfrac {7} {12} -\dfrac {2} {3} \times \left( -\dfrac {1} {4} \right) \)
(6) \( \dfrac {1} {2} \times \left( -\dfrac {1} {3} \right) -\dfrac {2} {3} \times \left( -\dfrac {1} {4} \right) \)
(1) \(\left( -\dfrac {2} {3} \right) \times \left( -\dfrac {5} {9} \right) -\dfrac {7} {27}\)
(2) \(\left( -\dfrac {3} {4} \right) \times \dfrac {5} {6} -\dfrac {1} {4}\)
(3) \(\left( -\dfrac {1} {2} \right) \times \left( -\dfrac {6} {5} \right) -1.3\)
(4) \( -\dfrac {1} {6} - \left( -\dfrac {3} {10} \right) \times 5\)
(5) \( -3 \times \dfrac {7} {12} -\dfrac {2} {3} \times \left( -\dfrac {1} {4} \right) \)
(6) \( \dfrac {1} {2} \times \left( -\dfrac {1} {3} \right) -\dfrac {2} {3} \times \left( -\dfrac {1} {4} \right) \)
(1) \(\left( -\dfrac {2} {3} \right) \times \left( -\dfrac {5} {9} \right) -\dfrac {7} {27}\)
\(=\dfrac {10} {27} -\dfrac {7} {27} \)
\(=\dfrac {3} {27} \)
\(=\dfrac {1} {9} \)
(2) \(\left( -\dfrac {3} {4} \right) \times \dfrac {5} {6} -\dfrac {1} {4}\)
\(=\left( -\dfrac {1} {4} \right) \times \dfrac {5} {2} -\dfrac {1} {4}\)
\(-\dfrac {5} {8} -\dfrac {2} {8}\)
\(-\dfrac {7} {8}\)
(3) \(\left( -\dfrac {1} {2} \right) \times \left( -\dfrac {6} {5} \right) -1.3\)
\(=\dfrac {6} {10} -\dfrac {13} {10}\)
\(=-\dfrac {7} {10}\)
(4) \( -\dfrac {1} {6} - \left( -\dfrac {3} {10} \right) \times 5\)
\(=-\dfrac {1} {6} +\dfrac {3} {2}\)
\(=-\dfrac {1} {6} +\dfrac {9} {6}\)
\(=\dfrac {8} {6}\)
\(=\dfrac {4} {3}\)
(5) \( -3 \times \dfrac {7} {12} -\dfrac {2} {3} \times \left( -\dfrac {1} {4} \right) \)
\(=-\dfrac {21} {12} +\dfrac {2} {12}\)
\(=-\dfrac {19} {12}\)
(6) \( \dfrac {1} {2} \times \left( -\dfrac {1} {3} \right) -\dfrac {2} {3} \times \left( -\dfrac {1} {4} \right) \)
\(=-\dfrac {1} {6} +\dfrac {1} {6}\)
\(=0\)
(問3)
(1) \(\left( -\dfrac {1} {5} \right) \div \dfrac {4} {25} +\dfrac {3} {4}\)
(2) \( -\dfrac {2} {3} -\left( -\dfrac {1} {2} \right) \div \left( -\dfrac {1} {3} \right) \)
(3) \( \dfrac {2} {3} \div \left( -\dfrac {1} {2} \right) -\dfrac {1} {4} \div \left( -\dfrac {3} {8} \right) \)
(4) \( \left( -3 \right) \div \dfrac {3} {5} + \left( -\dfrac {3} {4} \right) \div \left( -\dfrac {5} {12} \right) \)
(5) \( -\dfrac {2} {3} \div 2 + \dfrac {8} {9} \times \left( -\dfrac {1} {2} \right) \)
(6) \( \dfrac {3} {5} \times \dfrac {3} {4} - \left( -\dfrac {2} {7} \right)\div \left( -\dfrac {8} {21} \right) \)
(1) \(\left( -\dfrac {1} {5} \right) \div \dfrac {4} {25} +\dfrac {3} {4}\)
(2) \( -\dfrac {2} {3} -\left( -\dfrac {1} {2} \right) \div \left( -\dfrac {1} {3} \right) \)
(3) \( \dfrac {2} {3} \div \left( -\dfrac {1} {2} \right) -\dfrac {1} {4} \div \left( -\dfrac {3} {8} \right) \)
(4) \( \left( -3 \right) \div \dfrac {3} {5} + \left( -\dfrac {3} {4} \right) \div \left( -\dfrac {5} {12} \right) \)
(5) \( -\dfrac {2} {3} \div 2 + \dfrac {8} {9} \times \left( -\dfrac {1} {2} \right) \)
(6) \( \dfrac {3} {5} \times \dfrac {3} {4} - \left( -\dfrac {2} {7} \right)\div \left( -\dfrac {8} {21} \right) \)
(1) \(\left( -\dfrac {1} {5} \right) \div \dfrac {4} {25} +\dfrac {3} {4}\)
\(=\left( -\dfrac {1} {5} \right) \times \dfrac {25} {4} +\dfrac {3} {4}\)
\(=-\dfrac {5} {4} +\dfrac {3} {4}\)
\(=-\dfrac {2} {4}\)
\(=-\dfrac {1} {2}\)
(2) \( -\dfrac {2} {3} -\left( -\dfrac {1} {2} \right) \div \left( -\dfrac {1} {3} \right) \)
\( =-\dfrac {2} {3} -\left( -\dfrac {1} {2} \right) \times \left( -3\right) \)
\( =-\dfrac {2} {3} -\dfrac {3} {2} \)
\( =-\dfrac {4} {6} -\dfrac {9} {6} \)
\( =-\dfrac {13} {6} \)
(3) \( \dfrac {2} {3} \div \left( -\dfrac {1} {2} \right) -\dfrac {1} {4} \div \left( -\dfrac {3} {8} \right) \)
\( =\dfrac {2} {3} \times \left( -2 \right) -\dfrac {1} {4} \times \left( -\dfrac {8} {3} \right) \)
\( =-\dfrac {4} {3} +\dfrac {2} {3} \)
\( =-\dfrac {2} {3} \)
(4) \( \left( -3 \right) \div \dfrac {3} {5} + \left( -\dfrac {3} {4} \right) \div \left( -\dfrac {5} {12} \right) \)
\( =\left( -3 \right) \times \dfrac {5} {3} + \left( -\dfrac {3} {4} \right) \times \left( -\dfrac {12} {5} \right) \)
\(=-5+\dfrac {9} {5}\)
\(=-\dfrac {25} {5}+\dfrac {9} {5}\)
\(=-\dfrac {16} {5}\)
(5) \( -\dfrac {2} {3} \div 2 + \dfrac {8} {9} \times \left( -\dfrac {1} {2} \right) \)
\( =-\dfrac {2} {3} \times \dfrac {1} {2} -\dfrac {4} {9} \)
\( =-\dfrac {1} {3} -\dfrac {4} {9} \)
\( =-\dfrac {3} {9} -\dfrac {4} {9} \)
\( =-\dfrac {7} {9} \)
(6) \( \dfrac {3} {5} \times \dfrac {3} {4} - \left( -\dfrac {2} {7} \right)\div \left( -\dfrac {8} {21} \right) \)
\( =\dfrac {9} {20} - \left( -\dfrac {2} {7} \right)\times \left( -\dfrac {21} {8} \right) \)
\( =\dfrac {9} {20} -\dfrac {3} {4} \)
\( =\dfrac {9} {20} -\dfrac {15} {20} \)
\( =-\dfrac {6} {20} \)
\( =-\dfrac {3} {10} \)
(問4)
(1) \(5\times \{ -4-\left( 3-11\right) \} \)
(2) \(16\div \{ -3+\left( 4-9\right) \} \)
(3) \(-14\div \left(-7-5\right)+ \left(-12\right)\div \left(-4-2\right) \)
(4) \(-3 \times \left( \dfrac {2} {7} -\dfrac {2} {3} \right) \)
(5) \(1.1 \div \left( \dfrac {2} {7} -\dfrac {3} {5} \right) \)
(6) \( \left( -\dfrac {1} {8} +\dfrac {3} {4} \right) \div \left( -\dfrac {5} {12} \right) \)
(1) \(5\times \{ -4-\left( 3-11\right) \} \)
(2) \(16\div \{ -3+\left( 4-9\right) \} \)
(3) \(-14\div \left(-7-5\right)+ \left(-12\right)\div \left(-4-2\right) \)
(4) \(-3 \times \left( \dfrac {2} {7} -\dfrac {2} {3} \right) \)
(5) \(1.1 \div \left( \dfrac {2} {7} -\dfrac {3} {5} \right) \)
(6) \( \left( -\dfrac {1} {8} +\dfrac {3} {4} \right) \div \left( -\dfrac {5} {12} \right) \)
(1) \(5\times \{ -4-\left( 3-11\right) \} \)
\(=5\times \{ -4-\left( -8\right) \} \)
\(=5\times \left( -4+8\right) \)
\( =5\times 4\)
\( =20\)
(2) \(16\div \{ -3+\left( 4-9\right) \} \)
\( =16\div \{ -3+\left( -5\right) \} \)
\( =16\div \left( -8\right) \)
\( =-2\)
(3) \(-14\div \left(-7-5\right)+ \left(-12\right)\div \left(-4-2\right) \)
\(=-14 \div \left(-12\right)+ \left(-12\right)\div \left(-6\right) \)
\( =\dfrac {7} {6} + 2\)
\( =\dfrac {7} {6} + \dfrac {12} {6}\)
\( =\dfrac {19} {6}\)
(4) \(-3 \times \left( \dfrac {2} {7} -\dfrac {2} {3} \right) \)
\(=-3 \times \left( \dfrac {6} {21} -\dfrac {14} {21} \right) \)
\(=-3 \times \left( -\dfrac {8} {21} \right) \)
\( =\dfrac {24} {21}\)
\( =\dfrac {8} {7}\)
(5) \(1.1 \div \left( \dfrac {2} {7} -\dfrac {3} {5} \right) \)
\( =\dfrac {11} {10} \div \left( \dfrac {10} {35} -\dfrac {21} {35} \right) \)
\( =\dfrac {11} {10} \div \left( -\dfrac {11} {35} \right) \)
\( =\dfrac {11} {10} \times \left( -\dfrac {35} {11} \right) \)
\( =-\dfrac {7} {2}\)
(6) \( \left( -\dfrac {1} {8} +\dfrac {3} {4} \right) \div \left( -\dfrac {5} {12} \right) \)
\( =\left( -\dfrac {1} {8} +\dfrac {6} {8} \right) \times \left( -\dfrac {12} {5} \right) \)
\( =\dfrac {5} {8} \times \left( -\dfrac {12} {5} \right) \)
\( =-\dfrac {3} {2}\)
(問5)
(1) \( -4^{2} \div 8 - \left(-3\right) \)
(2) \( 3^{2} +8\times \left(-2^{2} \right)\)
(3) \(\left(-2\right)^{4} +\left(-12\right)\div \dfrac {6} {5}\)
(4) \(\left(-2^{2} \right)-\left(-3\right)^{2} \times \left(-2\right)\)
(5) \(7^{2} +2\times \left(-5^{2} \right)\)
(6) \(3^{3} +\left(-3\right)^2 \times \left(-2\right)^3\)
(1) \( -4^{2} \div 8 - \left(-3\right) \)
(2) \( 3^{2} +8\times \left(-2^{2} \right)\)
(3) \(\left(-2\right)^{4} +\left(-12\right)\div \dfrac {6} {5}\)
(4) \(\left(-2^{2} \right)-\left(-3\right)^{2} \times \left(-2\right)\)
(5) \(7^{2} +2\times \left(-5^{2} \right)\)
(6) \(3^{3} +\left(-3\right)^2 \times \left(-2\right)^3\)
(1) \( -4^{2} \div 8 - \left(-3\right) \)
\(=-16\div 8+3\)
\(=-2+3\)
\(=1\)
(2) \( 3^{2} +8\times \left(-2^{2} \right)\)
\(=9+8\times \left(-4\right)\)
\(=9+\left(-32\right)\)
\(=-23\)
(3) \(\left(-2\right)^{4} +\left(-12\right)\div \dfrac {6} {5}\)
\(=16+\left(-12\right)\times \dfrac {5} {6}\)
\(=16+\left(-10\right)\)
\(=6\)
(4) \(\left(-2^{2} \right)-\left(-3\right)^{2} \times \left(-2\right)\)
\(=-4-9\times \left(-2\right)\)
\(=-4+18\)
\(=14\)
(5) \(7^{2} +2\times \left(-5^{2} \right)\)
\(=49+2\times \left(-25\right)\)
\(=49-50\)
\(=-1\)
(6) \(3^{3} +\left(-3\right)^2 \times \left(-2\right)^3\)
\(=27+9\times \left(-8\right)\)
\(=27-72\)
\(=-45\)
(問6)
(1) \(\left(\dfrac {1} {2} \right)^3 -\left(-\dfrac {1} {4} \right)^2 \)
(2) \(2-\left(-\dfrac {4} {3} \right)^2 \div \dfrac {2} {3} \)
(3) \(\left(-4\right)^3 \div \dfrac {4} {3} -3 \times \left(-2^4 \right) \)
(4) \(\left(-\dfrac {8} {9} \right)\times \left(-0.75\right)^2 -0.25^2 \)
(5) \(\left(-0.125\right)\div \left(-0.5\right)^3 -1.25^2 \)
(6) \(\left(-0.375\right)^2 \div 0.25^2 -0.75^2 \)
(1) \(\left(\dfrac {1} {2} \right)^3 -\left(-\dfrac {1} {4} \right)^2 \)
(2) \(2-\left(-\dfrac {4} {3} \right)^2 \div \dfrac {2} {3} \)
(3) \(\left(-4\right)^3 \div \dfrac {4} {3} -3 \times \left(-2^4 \right) \)
(4) \(\left(-\dfrac {8} {9} \right)\times \left(-0.75\right)^2 -0.25^2 \)
(5) \(\left(-0.125\right)\div \left(-0.5\right)^3 -1.25^2 \)
(6) \(\left(-0.375\right)^2 \div 0.25^2 -0.75^2 \)
(1) \(\left(\dfrac {1} {2} \right)^3 -\left(-\dfrac {1} {4} \right)^2 \)
\(=\dfrac {1} {8} -\dfrac {1} {16} \)
\(=\dfrac {2} {16} -\dfrac {1} {16} \)
\(=\dfrac {1} {16} \)
(2) \(2-\left(-\dfrac {4} {3} \right)^2 \div \dfrac {2} {3} \)
\(=2-\dfrac {16} {9} \times \dfrac {3} {2} \)
\(=2-\dfrac {8} {3}\)
\(=\dfrac {6} {3} -\dfrac {8} {3}\)
\(=-\dfrac {2} {3}\)
(3) \(\left(-4\right)^3 \div \dfrac {4} {3} -3\times \left(-2^4 \right) \)
\(\left(-4\right)^3 \times \dfrac {3} {4} -3\times \left(-16\right)\)
\(=-48+48\)
\(=0\)
(4) \(\left(-\dfrac {8} {9} \right)\times \left(-0.75\right)^2 -0.25^2 \)
\(=\left(-\dfrac {8} {9} \right)\times \left(-\dfrac {3} {4} \right)^2-\left(\dfrac {1} {4} \right)^2\)
\(=\left(-\dfrac {8} {9} \right)\times \dfrac {9} {16} -\dfrac {1} {16} \)
\(=-\dfrac {1} {2} -\dfrac {1} {16} \)
\(=-\dfrac {8} {16} -\dfrac {1} {16} \)
\(=-\dfrac {9} {16} \)
(5) \(\left(-0.125\right)\div \left(-0.5\right)^3 -1.25^2 \)
\(=\left(-\dfrac {1} {8} \right) \div \left(-\dfrac {1} {2} \right)^3 -\left(\dfrac {5} {4} \right)^2\)
\(=\left(-\dfrac {1} {8} \right) \times \left(-2\right)^3 -\dfrac {25} {16} \)
\(=\left(-\dfrac {1} {8} \right) \times \left(-8\right) -\dfrac {25} {16} \)
\(=1-\dfrac {25} {16} \)
\(=-\dfrac {9} {16} \)
(6) \(\left(-0.375\right)^2 \div 0.25^2 -0.75^2 \)
\(=\left(-\dfrac {3} {8} \right)^2 \div \left(\dfrac {1} {4} \right)^2-\left(\dfrac {3} {4} \right)^2\)
\(=\left(-\dfrac {3} {8} \right)^2 \times 4^2 -\left(\dfrac {3} {4} \right)^2\)
\(=\dfrac {9} {64} \times 16-\dfrac {9} {16}\)
\(=\dfrac {9} {4} -\dfrac {9} {16}\)
\(=\dfrac {36} {16} -\dfrac {9} {16}\)
\(=\dfrac {27} {16}\)
(問7)
(1) \(\left(-12\right)\times \left(\dfrac {7} {6} -\dfrac {7} {4} \right)\)
(2) \(24\times \left(\dfrac {1} {6} +\dfrac {3} {2} -\dfrac {9} {8} \right)\)
(3) \(\left(-7\right)\times 26+\left(-7\right)\times \left(-6\right)\)
(4) \(19\times 3.1415-3.1415\times 9\)
(1) \(\left(-12\right)\times \left(\dfrac {7} {6} -\dfrac {7} {4} \right)\)
(2) \(24\times \left(\dfrac {1} {6} +\dfrac {3} {2} -\dfrac {9} {8} \right)\)
(3) \(\left(-7\right)\times 26+\left(-7\right)\times \left(-6\right)\)
(4) \(19\times 3.1415-3.1415\times 9\)
(1) \(\left(-12\right)\times \left(\dfrac {7} {6} -\dfrac {7} {4} \right)\)
\(=\left(-12\right)\times \dfrac {7} {6} -\left(-12\right)\times \dfrac {7} {4}\)
\(=-14-\left(-21\right)\)
\(=-14+21\)
\(=7\)
(2) \(24\times \left(\dfrac {1} {6} +\dfrac {3} {2} -\dfrac {9} {8} \right)\)
\(=24\times \dfrac {1} {6} +24\times \dfrac {3} {2} -24\times \dfrac {9} {8} \)
\(=4+36-27\)
\(=13\)
(3) \(\left(-7\right)\times 26+\left(-7\right)\times \left(-6\right)\)
\(=\left(-7\right)\times \{26+ \left(-6\right)\} \)
\(=\left(-7\right)\times 20\)
\(=-140\)
(4) \(19\times 3.1415-3.1415\times 9\)
\(=3.1415\times \left(19-9\right)\)
\(=3.1415\times 10\)
\(=31.415\)