例 題 


<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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