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


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(問1)
(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)=+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)=+(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) \(5^{3} =5\times 5\times 5 =125\)
(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) \(1\div \left( -5\right) =1\times \left( -\dfrac {1} {5} \right) =-\dfrac {1} {5}\)
(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)\(\dfrac {3} {4} \times \left( -1\dfrac {2} {3} \right) \)
 \(= \dfrac {3} {4} \times \left( -\dfrac {5} {3} \right) \)
 \(= -\left( \dfrac {3} {4} \times \times \dfrac {5} {3} \right) \)
 \(= -\dfrac {5} {4}\)

(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)
 \(=6 \times \left( -6\right)\times \left( -\dfrac {1} {12} \right) \)
 \(=+ \left( 6 \times 6 \times \dfrac {1} {12} \right) \)
 \(=3\)

(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) \(2^{3} \div \left( -6\right) ^{2} \times \left( -3^{2} \right) \)
 \(=8\div 36\times \left( -9\right)\)
 \(=8\times \dfrac {1} {36}\times \left( -9\right)\)
 \(= -\left( 8\times \dfrac {1} {36} \times 9\right)\)
 \(-2\)

(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) \(\left( -\dfrac {1} {2} \right) ^{3} \times \left( -\dfrac {2} {3} \right) ^{2} \div \left( -\dfrac {1} {6} \right) \)
 \(=\left(-\dfrac {1} {8} \right)\times \dfrac {4} {9} \div \left(-\dfrac {1} {6} \right) \)
 \(=\left(-\dfrac {1} {8} \right)\times \dfrac {4} {9} \times \left(-6\right) \)
 \(=+\left(\dfrac {1} {8} \times \dfrac {4} {9} \times 6\right)\)
 \(=\dfrac {1} {3}\)


   





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