算数【入試】ばらす・まとめる計算

問１

3.16 × 26 + 13 × 3.68 – 5 × 13 =

答え

65

解き方

3.16 × 26 + 13 × 3.68 – 5 × 13
= 3.16 × 13 × 2 + 13 × 3.68 – 5 × 13
= ( 3.16 × 2 + 3.68 – 5 ) × 13
= ( 6.32 + 3.68 – 5 ) × 13
= 5 × 13 = 65

問２

15.7 × 3 + 0.785 × 28 – 3.14 × 17 =

答え

15.7

解き方

15.7 × 3 + 0.785 × 28 – 3.14 × 17
= 3.14 × 5 × 3 + 0.785 × 4 × 7 – 3.14 × 17
= 3.14 × 15 + 3.14 × 7 – 3.14 × 17
= 3.14 × ( 15 + 7 – 17 )
= 3.14 × 5 = 15.7

問３

480 × 3.7 + 74 × 9.6 – 48 × 31.8 =

答え

960

解き方

480 × 3.7 + 74 × 9.6 – 48 × 31.8
= 48 × 10 × 3.7 + 74 × 48 × 0.2 – 48 × 31.8
= 48 × ( 37 + 14.8 – 31.8 )
= 48 × 20 = 960

問４

1.25 × 56 – 32 × 0.25 – 0.625 × 64 =

答え

22

解き方

1.25 × 56 – 32 × 0.25 – 0.625 × 64
= 0.25 × 5 × 56 – 32 × 0.25 – 0.25 × 2.5 × 64
= 0.25 × ( 280 – 32 – \(\dfrac{5}{2}\) × 64 )
= \(\dfrac{1}{4}\) × ( 280 – 32 – 160 )
= 70 – 8 – 40 = 22

問５

3 × 4 × 3.14 – 0.785 × 12 × 6 + 4 × 1.57 × 8 =

答え

31.4

解き方

3 × 4 × 3.14 – 0.785 × 12 × 6 + 4 × 1.57 × 8
= 12 × 3.14 – 0.785 × 4 × 3 × 6 + 2 × 2 × 1.57 × 8
= 12 × 3.14 – 3.14 × 3 × 6 + 2 × 3.14 × 8
= 3.14 × ( 12 – 18 + 16 )
= 3.14 × 10 = 31.4