<例題>次の計算をしなさい。
1) 1/2+1/6+1/9
2) 1/2−1/3+1/4−1/5
3) 8×2−4×3+8÷2
4) 12÷2+(5/6)×9
5) 12÷3+(7/3)×9+6×5÷3
6) (7/5−3/4)−(2/5−1/4)
7) 3×(5/6−1/5)
8) 5/6+5/9
9) 7/12+7/18
10) (1/2)×(5/6−1/3)
<解答>1) 1/2+1/6+1/9=3/6+1/6+1/9
=4/6+1/9
=2/3+1/9
=6/9+1/9=7/9
2) 1/2−1/3+1/4−1/5=3/6−2/6+1/4−1/5
=1/6+1/4−1/5
=2/12+3/12−1/5
=5/12−1/5
=25/60−12/60
=13/60
3) 8×2−4×3+8÷2=16−4×3+8÷2
=16−12+8÷2
=16−12+4
=4+4
=8
4) 12÷2+(5/6)×9=12+(5/6)×9
=7/2+(5/2)×3
=12+15/2
=24/2+15/2
=39/2
5) 12÷3+(7/3)×9+6×5÷3=4+(7/3)×9+6×5÷3
=4+(7/1)×3+6×5÷3
=4+21/1+6×5÷3
=4+21+6×5÷3
=4+21+30÷3
=4+21+10
=25+10
=35+10
6) (7/5−3/4)−(2/5−1/4)=(28/20−15/20)−(2/5−1/4)
=13/20−(2/5−1/4)
=13/20−(8/20−5/20)
=13/20−3/20
=10/20
=1/2
7) 3×(5/6−1/5)=3×(25/30−6/30)
=3×(19/30)
=1×(19/10)
=19/10
8) 5/6+5/9=5/3×1/2+5/3×1/3
=5/3×(1/2+1/3)
=5/3×(3/6+2/6)
=5/3×(5/6)
=25/18
9) 7/12+7/18=7/6×1/2+7/6×1/3
=7/6×(1/2+1/3)
=7/6×(3/6+2/6)
=7/6×(5/6)
=35/36
10) (1/2)×(5/6−1/3)=(1/2)×(1/3×5/2−1/3×1/1)
=(1/2)×(1/3)×(5/2−1/1)
=(1/2)×(1/3)×(5/2−2/2)
=(1/2)×(1/3)×(3/2)
=(1/2)×(1/1)×(1/2)
=1/4
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