問１
55 × 338 – 55 × 186 – 55 × 28 =
- 答え
- 6820
- 解き方
- 55 × 338 – 55 × 186 – 55 × 28
= 55 × ( 338 – 186 – 28 )
= 55 × 124
= 55 × ( 100 + 20 + 4 )
= 5500 + 1100 + 220 = 6820
問２
1023 × 20 – 10.23 × 1500 – 10230 × 0.5 =
- 答え
- 0
- 解き方
- 1023 × 20 – 10.23 × 1500 – 10230 × 0.5
= 1023 × 20 – 1023 × 15 – 1023 × 5
= 1023 × ( 20 – 15 – 5 )
= 1023 × 0 = 0
問３
3.033 × 1.8 + 0.606 × 18 + 9.07 × 0.18 =
- 答え
- 18
- 解き方
- 3.033 × 1.8 + 0.606 × 18 + 9.07 × 0.18
= 0.3033 × 18 + 0.606 × 18 + 0.0907 × 18
= ( 0.3033 + 0.606 + 0.0907 ) × 18
= 1 × 18 = 18
問４
9.42 × 40 – 6.28 × 30 + 3.14 × 40 =
- 答え
- 314
- 解き方
- 9.42 × 40 – 6.28 × 30 + 3.14 × 40
= 3.14 × 3 × 40 – 3.14 × 2 × 30 + 3.14 × 40
= 3.14 × ( 120 – 60 + 40 )
= 3.14 × 100 = 314
問５
22.5 × 3 – 2.5 × 9 =
- 答え
- 45
- 解き方
- 22.5 × 3 – 2.5 × 9
= 225 × 0.3 – 25 × 0.9
= 15 × 15 × 0.3 – 5 × 5 × 3 × 0.3
= 15 × 4.5 – 15 × 1.5
= 15 × ( 4.5 – 1.5 )
= 15 × 3 = 45
問６
3.9 × 451 + 1.5 × 3 × 451 + ( 5.4 – 3.8 ) × 451 =
- 答え
- 4510
- 解き方
- 3.9 × 451 + 1.5 × 3 × 451 + ( 5.4 – 3.8 ) × 451
= 3.9 × 451 + 4.5 × 451 + 1.6 × 451
= ( 3.9 + 4.5 + 1.6 ) × 451
= 10 × 451 = 4510
問７
\(\dfrac{1}{9}\) × 1.1 + \(\dfrac{1}{12}\) × 11 + \(\dfrac{1}{36}\) × 2.2 =
- 答え
- 1.1
- 解き方
- \(\dfrac{1}{9}\) × 1.1 + \(\dfrac{1}{12}\) × 11 + \(\dfrac{1}{36}\) × 2.2
\(\dfrac{1}{9}\) × 1.1 + \(\dfrac{1}{12}\) × 10 × 1.1 + \(\dfrac{1}{36}\) × 2 × 1.1
= ( \(\dfrac{1}{9}\) + \(\dfrac{5}{6}\) + \(\dfrac{1}{18}\) ) × 1.1
= \(\dfrac{2\ +\ 15\ +\ 1}{18}\) × 1.1
= 1 × 1.1 = 1.1
問８
6.25 + 3.14 × 7.7 – 1.57 × 2 × 1.7 =
- 答え
- 25.09
- 解き方
- 6.25 + 3.14 × 7.7 – 1.57 × 2 × 1.7
= 6.25 + 3.14 × ( 7.7 – 1.7 )
= 6.25 + 3.14 × 6
= 6.25 + 18.84 = 25.09
問９
1.58 × 1700 + 1580 × 2.3 + 79 × 120 =
- 答え
- 15800
- 解き方
- 1.58 × 1700 + 1580 × 2.3 + 79 × 120
= 158 × 17 + 158 × 23 + 79 × 2 × 60
= 158 × 17 + 158 × 23 + 158 × 60
= 158 × ( 17 + 23 + 60 )
= 158 × 100 = 15800
問１０
213 × 99 – 588 × 33 + 297 =
- 答え
- 1980
- 解き方
- 213 × 99 – 588 × 33 + 297
= 213 × 99 – 196 × 3 × 33 + 3 × 99
= 213 × 99 – 196 × 99 + 3 × 99
= ( 213 – 196 + 3 ) × 99
= 20 × 99 = 1980
問１１
11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 =
- 答え
- 396
- 解き方
- 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88
= 11 × ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 )
= 11 × ( 45 – 9 )
= 11 × 36 = 396
※ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 は覚えておこう！
問１２
( 0.34 × 1200 + 3.4 × 360 + 34 × 52 ) ÷ 100 =
- 答え
- 34
- 解き方
- ( 0.34 × 1200 + 3.4 × 360 + 34 × 52 ) ÷ 100
= ( 34 × 12 + 34 × 36 + 34 × 52 ) ÷ 100
= 34 × ( 12 + 36 + 52 ) ÷ 100
= 34 × 100 ÷ 100 = 34
問１３
1.35 × 6 + 13.5 × 4 – 0.135 × 456 =
- 答え
- 0.54
- 解き方
- 1.35 × 6 + 13.5 × 4 – 0.135 × 456
= 1.35 × 6 + 1.35 × 40 – 1.35 × 45.6
= 1.35 × ( 6 + 40 – 45.6 )
= 1.35 × 0.4
= 1.35 × \(\dfrac{2}{5}\)
= 0.27 × 2 = 0.54
問１４
11 × 11 + 22 × 22 + 33 × 33 + 44 × 44 =
- 答え
- 3630
- 解き方
- 11 × 11 + 22 × 22 + 33 × 33 + 44 × 44
= 11 × 11 + 2 × 11 × 2 × 11 + 3 × 11 × 3 × 11 + 4 × 11 × 4 × 11
= 121 + 121 × 4 + 121 × 9 + 121 × 16
= 121 × ( 1 + 4 + 9 + 16 )
= 121 × 30 = 3630
問１５
21 × 29 + 22 × 28 + 23 × 27 + 24 × 26 + 25 × 25 =
- 答え
- 3095
- 解き方
- 21 × 29 + 22 × 28 + 23 × 27 + 24 × 26 + 25 × 25
= 21 × ( 25 + 4 ) + 22 × ( 25 + 3 ) + 23 × ( 25 + 2 ) + 24 × ( 25 + 1 ) + 25 × 25
= 25 × ( 21 + 22 + 23 + 24 + 25 ) + 21 × 4 + 22 × 3 + 23 × 2 + 24 × 1
= 25 × { 20 × 5 + ( 1 + 2 + 3 + 4 + 5 ) } + 84 + 66 + 46 + 24
= 25 × ( 100 + 10 + 5 ) + 150 + 70
= 2500 + 250 + 125 + 220 = 3095
問１６
\(\dfrac{11}{19}\) × 181 – \(\dfrac{9}{19}\) × 181 + \(\dfrac{2}{19}\) × 9 =
- 答え
- 20
- 解き方
- \(\dfrac{11}{19}\) × 181 – \(\dfrac{9}{19}\) × 181 + \(\dfrac{2}{19}\) × 9
= \(\dfrac{1}{19}\) × ( 11 × 181 – 9 × 181 + 2 × 9 )
= \(\dfrac{1}{19}\) × { ( 11 – 9 ) × 181 + 18 }
= \(\dfrac{1}{19}\) × ( 2 × 181 + 18 )
= \(\dfrac{1}{19}\) × ( 362 + 18 )
= \(\dfrac{1}{19}\) × 380 = 20
問１７
12 × 3.3 – 13 × 3.03 – 15 × 3.03 + 16 × 3.3 =
- 答え
- 7.56
- 解き方
- 12 × 3.3 – 13 × 3.03 – 15 × 3.03 + 16 × 3.3
= 12 × 3.3 + 16 × 3.3 – ( 13 × 3.03 + 15 × 3.03 )
= ( 12 + 16 ) × 3.3 – { ( 13 + 15 ) × 3.03 }
= 28 × 3.3 – 28 × 3.03
= 28 × ( 3.3 – 3.03 )
= 28 × 0.27
= 28 × ( 0.2 + 0.07 )
= 5.6 + 1.96 = 7.56
問１８
\(\dfrac{5×6×7×8+6×7×8×9+7×8×9×10}{6×7×8}\) =
- 答え
- 29
- 解き方
\(\dfrac{5\ ×\ 6\ ×\ 7\ ×\ 8\ +\ 6\ ×\ 7\ ×\ 8\ ×\ 9\ +\ 7\ ×\ 8\ ×\ 9\ ×\ 10}{6\ ×\ 7\ ×\ 8}\)
= 5 + 9 + \(\dfrac{7\ ×\ 8\ ×\ 3\ ×\ 3\ ×\ 2\ ×\ 5}{6\ ×\ 7\ ×\ 8}\)
= 5 + 9 + \(\dfrac{6\ ×\ 7\ ×\ 8\ ×\ 3\ ×\ 5}{6\ ×\ 7\ ×\ 8}\)
= 14 + 15 = 29
問１９
( 888 – 88 × 9 ) ÷ 6 + 48 × 15 ÷ 9 =
- 答え
- 96
- 解き方
- ( 888 – 88 × 9 ) ÷ 6 + 48 × 15 ÷ 9
= ( 148 × 6 – 44 × 2 × 3 × 3 ) ÷ 6 + 16 × 3 × 3 × 5 ÷ 9
= ( 148 – 132 ) + 16 × 5
= 16 + 80 = 96
問２０
2.15 + 4.6 × 5.7 – 1.9 × 2.3 =
- 答え
- 24
- 解き方
- 2.15 + 4.6 × 5.7 – 1.9 × 2.3
= 1.15 + 1 + 4.6 × 5.7 – 1.9 × 2.3
= 2.3 × 0.5 + 1 + 2.3 × 2 × 5.7 – 1.9 × 2.3
= 2.3 × ( 0.5 + 11.4 – 1.9 ) + 1
= 2.3 × 10 + 1 = 24
問２１
83 × 567 + 86 × 567 – 34 × 567 + 135 × 433 =
- 答え
- 135000
- 解き方
- 83 × 567 + 86 × 567 – 34 × 567 + 135 × 433
= ( 83 + 86 – 34 ) × 567 + 135 × 433
= 135 × 567 + 135 × 433
= 135 × ( 567 + 433 )
= 135 × 1000 = 135000
問２２
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
= ( 10 – 5 ) × 13
= 5 × 13 = 65
問２３
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２４
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 + 48 × 14.8 – 48 × 31.8
= 48 × ( 37 + 14.8 – 31.8 )
= 48 × 20 = 960
問２５
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２６
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
問２７
2.5 × 34.2 + 17.1 × 1.1 – 6.1 × 7.1 =
- 答え
- 61
- 解き方
- 2.5 × 34.2 + 17.1 × 1.1 – 6.1 × 7.1
= 2.5 × 17.1 × 2 + 17.1 × 1.1 – 6.1 × 7.1
= 17.1 × ( 2.5 × 2 + 1.1 ) – 6.1 × 7.1
= 17.1 × 6.1 – 6.1 × 7.1
= 6.1 × ( 17.1 – 7.1 )
= 6.1 × 10 = 61
問２８
2 × 7 × 9 + 21 × 45 – 2 × 7 × 18 – 7 × 27 =
- 答え
- 630
- 解き方
- 2 × 7 × 9 + 21 × 45 – 2 × 7 × 18 – 7 × 27
= 2 × 7 × 9 + 3 × 7 × 9 × 5 – 2 × 7 × 9 × 2 – 7 × 9 × 3
= 2 × 63 + 63 × 15 – 63 × 4 – 63 × 3
= 63 × ( 2 + 15 – 4 – 3 )
= 63 × 10 = 630
問２９
99 × 35 – 48 × 9 – 99 × 9 + 48 × 36 =
- 答え
- 3576
- 解き方
- 99 × 35 – 48 × 9 – 99 × 9 + 48 × 36
= 99 × ( 35 – 9 ) + 48 × ( 36 – 9 )
= 99 × 24 + 48 × 25
= 99 × 24 + 24 × 2 × 25
= 24 × ( 99 + 50 )
= 24 × ( 100 – 1 + 50 )
= 2400 – 24 + 1200
= 3600 – 24 = 3576
問３０
3.9 × 1.8 + 2.6 × 2.8 – 0.65 × 4.6 ÷ ( 3 – 0.7 ) =
- 答え
- 13
- 解き方
- 3.9 × 1.8 + 2.6 × 2.8 – 0.65 × 4.6 ÷ ( 3 – 0.7 )
= 1.3 × 3 × 1.8 + 1.3 × 2 × 2.8 – 1.3 × 0.5 × 4.6 ÷ 2.3
= 1.3 × 5.4 + 1.3 × 5.6 – 1.3 × 1
= 1.3 × ( 5.4 + 5.6 – 1 )
= 1.3 × 10 = 13
問３１
43 × 15 + 92 ÷ 13 + 15 × 42 – 14 ÷ 13 =
- 答え
- 1131
- 解き方
- 43 × 15 + 92 ÷ 13 + 15 × 42 – 14 ÷ 13
= 15 × ( 43 + 42 ) + ( 92 – 14 ) ÷ 13
= 15 × 85 + 78 ÷ 13
= 15 × 15 × 5 + 6
= 225 × 5 + 6
= 1125 + 6 = 1131
問３２
34 – { 850 – 1150 ÷ ( 60 – 2 × 7 ) } ÷ 25 =
- 答え
- 1
- 解き方
- 34 – { 850 – 1150 ÷ ( 60 – 2 × 7 ) } ÷ 25
= 34 – { 850 – 1150 ÷ ( 60 – 14 ) } ÷ 25
= 34 – { ( 850 – 1150 ÷ 46 ) × \(\dfrac{1}{25}\) }
= 34 – ( \(\cancelto{34}{850}\) × \(\dfrac{1}{\cancel{25}}\) – \(\cancelto{\cancel{46}}{1150}\) × \(\dfrac{1}{\cancel{46}}\) × \(\dfrac{1}{\cancel{25}}\) )
= 34 – ( 34 – 1 ) = 34 – 33 = 1
問３３
{ ( 75 – 57 ) × 3 + 24 } ÷ 6 – 12 × 3 ÷ 6 =
- 答え
- 7
- 解き方
- { ( 75 – 57 ) × 3 + 24 } ÷ 6 – 12 × 3 ÷ 6
= ( 18 × 3 + 24 ) ÷ 6 – 6
= ( 54 + 24 ) ÷ 6 – 6
= ( 9 + 4 ) – 6 = 13 – 6 = 7
問３４
( 119 ÷ 17 – 51 ÷ 17 ) × { ( 119 – 51 ) ÷ 17 + 1 } =
- 答え
- 20
- 解き方
- ( 119 ÷ 17 – 51 ÷ 17 ) × { ( 119 – 51 ) ÷ 17 + 1 }
= ( 7 – 3 ) × { ( 7 – 3 ) + 1 }
= 4 × 5 = 20
問３５
1100 × 0.125 + 625 × 0.4 + 3.75 × 2 =
- ヒント
- 125 × 8 = 1000
- 答え
- 395
- 解き方
- 1100 × 0.125 + 625 × 0.4 + 3.75 × 2
= 1.1 × 125 + 125 × 5 × 0.4 + 125 × 0.03 × 2
= 125 × ( 1.1 + 2 + 0.06 )
= 125 × 3.16
=125 × 8 × 0.395 = 1000 × 0.395 = 395
問３６
781 × 5.6 + 45 × 2.1 – 63 × 3.2 – 1230 × 0.55 =
- 答え
- 3590
- 解き方
- 781 × 5.6 + 45 × 2.1 – 63 × 3.2 – 1230 × 0.55
= 4373.6 + 94.5 – 201.6 – 676.5
= ( 4373.6 – 201.6 ) – ( 676.5 – 94.5 )
= 4172 – 582 = 3590
問３７
65 × 2.1 + 72 × 3.5 – 0.31 × 50 + 45 ÷ 0.15 =
- 答え
- 673
- 解き方
- 65 × 2.1 + 72 × 3.5 – 0.31 × 50 + 45 ÷ 0.15
= 65 × 3 × 0.7 + 72 × 5 × 0.7 – 15.5 + 300
= ( 195 + 360 ) × 0.7 – 15.5 + 300
= 555 × 0.7 – 15.5 + 300
= 388.5 – 15.5 + 300
= 373 + 300 = 673
問３８
150 – 56 ÷ 0.7 × 0.25 + 420 × 0.55 =
- 答え
- 361
- 解き方
- 150 – 56 ÷ 0.7 × 0.25 + 420 × 0.55
= 150 – 80 × 0.125 × 2 + 420 × ( 0.5 + 0.05 )
= 150 – 10 × 2 + 420 × 0.5 + 420 × 0.05
= 150 – 20 + 210 + 21 = 361
問３９
( 1.4 – 2.94 ÷ 21 ) × 2.5 =
- 答え
- 3.15
- 解き方
- ( 1.4 – 2.94 ÷ 21 ) × 2.5
= ( 1.4 – 0.14 ) × 2.5
= { 1.4 × ( 1 – 0.1 ) } × 2.5
= 1.4 × 0.9 × 2.5
= \(\dfrac{\cancelto{7}{14}}{10}\) × \(\dfrac{9}{10}\) × \(\dfrac{\cancelto{5}{25}}{\cancelto{2}{5}}\)
= \(\dfrac{315}{100}\) = 3.15
問４０
20.22 × 4.7 + 1.011 × 26 – 2.022 × 10 =
- 答え
- 101.1
- 解き方
- 20.22 × 4.7 + 1.011 × 26 – 2.022 × 10
= 2.022 × 10 × 4.7 + 1.011 × 2 × 13 – 2.02 × 10
= 2.022 × 47 + 2.022 × 13 – 2.022 × 10
= 2.022 × ( 47 + 13 – 10 )
= 2.022 × 50 = 101.1
問４１
( 1 + 0.5 + 0.25 + 0.125 ) ÷ 0.625 =
- ヒント
- 分数に変える
- 答え
- 3
- 解き方
- ( 1 + 0.5 + 0.25 + 0.125 ) ÷ 0.625
= ( 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) ) ÷ \(\dfrac{5}{8}\)
= ( 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) ) × \(\dfrac{8}{5}\)
= ( 8 + 4 + 2 + 1 ) × \(\dfrac{1}{5}\)
= \(\dfrac{15}{5}\) = 3
問４２
2.24 × 2.24 + 2.24 × 0.76 – 2.24 × 0.74 – 0.76 × 0.74 =
- 答え
- 4.5
- 解き方
2.24 × 2.24 + 2.24 × 0.76 – 2.24 × 0.74 – 0.76 × 0.74
= 0.76 × ( 2.24 – 0.74 ) + 2.24 × ( 2.24 – 0.74 )
= 0.76 × 1.5 + 2.24 × 1.5
= 1.5 × ( 0.76 + 2.24 )
= 1.5 × 3 = 4.5
問４３
43 × 0.29 – 0.56 ÷ 0.08 × 0.31 =
- 答え
- 10.3
- 解き方
- 43 × 0.29 – 0.56 ÷ 0.08 × 0.31
= 43 × ( 0.3 – 0.01 ) – { 7 × ( 0.3 + 0.01 ) }
= 43 × 0.3 – 43 × 0.01 – ( 7 × 0.3 + 7 × 0.01 )
= 43 × 0.3 – 43 × 0.01 – 7 × 0.3 – 7 × 0.01
= 43 × 0.3 – 7 × 0.3 – ( 43 × 0.01 + 7 × 0.01 )
= ( 43 – 7 ) × 0.3 – { ( 43 + 7 ) × 0.01 }
= 36 × 0.3 – 50 × 0.01
= 10.8 – 0.5 = 10.3
問４４
3.14 + 6.28 – 9.42 – 12.54 + 15.7 =
- 答え
- 3.16
- 解き方
- 3.14 + 6.28 – 9.42 – 12.54 + 15.7
= 3.14 × (1 + 2 – 3 + 5) – 12.54
= 3.14 × 5 -12.54
=15.7 – 12.54 = 3.16
問４５
{ \(\dfrac{2}{15}\) + \(\dfrac{2}{35}\) – ( \(\dfrac{2}{63}\) + \(\dfrac{2}{99}\) ) } × \(1\dfrac{3}{4}\) =
- 答え
- \(\dfrac{8}{33}\)
- 解き方
- { \(\dfrac{2}{15}\) + \(\dfrac{2}{35}\) – ( \(\dfrac{2}{63}\) + \(\dfrac{2}{99}\) ) } × \(1\dfrac{3}{4}\)
= [ ( \(\dfrac{1}{3}\) -\(\cancel{\dfrac{1}{5}}\) ) + \(\cancel{\dfrac{1}{5}}\) -\(\dfrac{1}{7}\) ) – { ( \(\dfrac{1}{7}\) – \(\cancel{\dfrac{1}{9}}\) ) + ( \(\cancel{\dfrac{1}{9}}\) – \(\dfrac{1}{11}\) ) } ] × \(\dfrac{7}{4}\)
= { ( \(\dfrac{1}{3}\) – \(\dfrac{1}{7}\) ) – ( \(\dfrac{1}{7}\) – \(\dfrac{1}{11}\) ) } × \(\dfrac{7}{4}\)
= ( \(\dfrac{4}{21}\) – \(\dfrac{4}{77}\) ) × \(\dfrac{7}{4}\)
= \(\dfrac{4}{21}\) × \(\dfrac{7}{4}\) – \(\dfrac{4}{77}\) × \(\dfrac{7}{4}\)
= \(\dfrac{1}{3}\) – \(\dfrac{1}{11}\) = \(\dfrac{11\ -\ 3}{33}\) = \(\dfrac{8}{33}\)
問４６
( \(\dfrac{3}{8}\) + \(\dfrac{1}{40}\) + \(\dfrac{6}{35}\) ) × ( \(\dfrac{5}{6}\) – \(\dfrac{7}{12}\) + \(\dfrac{1}{20}\) ) =
- 答え
- \(\dfrac{6}{35}\)
- 解き方
- ( \(\dfrac{3}{8}\) + \(\dfrac{1}{40}\) + \(\dfrac{6}{35}\) ) × ( \(\dfrac{5}{6}\) – \(\dfrac{7}{12}\) + \(\dfrac{1}{20}\) )
= \(\dfrac{1}{2}\) × ( \(\dfrac{3}{4}\) + \(\dfrac{1}{20}\) + \(\dfrac{12}{35}\) ) × ( \(\dfrac{5}{6}\) – \(\dfrac{7}{12}\) + \(\dfrac{1}{20}\) )= \(\dfrac{1}{2}\) × { ( \(\dfrac{1}{1}\) – \(\cancel{\dfrac{1}{4}}\) ) + ( \(\cancel{\dfrac{1}{4}}\) – \(\cancel{\dfrac{1}{5}}\) ) + ( \(\cancel{\dfrac{1}{5}}\) + \(\dfrac{1}{7}\) ) } × { ( \(\dfrac{1}{2}\) + \(\cancel{\dfrac{1}{3}}\) ) – ( \(\cancel{\dfrac{1}{3}}\) + \(\cancel{\dfrac{1}{4}}\) ) + ( \(\cancel{\dfrac{1}{4}}\) – \(\dfrac{1}{5}\) ) }
= \(\dfrac{1}{2}\) × ( 1 + \(\dfrac{1}{7}\) ) × ( \(\dfrac{1}{2}\) – \(\dfrac{1}{5}\) )
= \(\dfrac{1}{\cancel{2}}\) × \(\dfrac{\cancelto{\cancelto{2}{4}}{8}}{7}\) × \(\dfrac{3}{\cancelto{5}{10}}\) = \(\dfrac{6}{35}\)
問４７
( \(\dfrac{7}{24}\) – \(\dfrac{9}{40}\) + \(\dfrac{1}{42}\) ) ÷ \(\dfrac{57}{70}\) =
- 答え
- \(\dfrac{1}{9}\)
- 解き方
- ( \(\dfrac{7}{24}\) – \(\dfrac{9}{40}\) + \(\dfrac{1}{42}\) ) ÷ \(\dfrac{57}{70}\)
= \(\dfrac{1}{2}\) × ( \(\dfrac{7}{12}\) – \(\dfrac{9}{20}\) + \(\dfrac{1}{21}\) ) × \(\dfrac{70}{57}\)
= \(\dfrac{1}{2}\) × { ( \(\dfrac{1}{3}\) + \(\cancel{\dfrac{1}{4}}\) ) – ( \(\cancel{\dfrac{1}{4}}\) + \(\dfrac{1}{5}\) ) + \(\dfrac{1}{21}\) } × \(\dfrac{70}{57}\)
= \(\dfrac{1}{2}\) × ( \(\dfrac{1}{3}\) – \(\dfrac{1}{5}\) + \(\dfrac{1}{21}\) ) × \(\dfrac{70}{57}\)
= \(\dfrac{1}{\cancel{2}}\) × \(\dfrac{\cancel{19}}{\cancelto{3}{105}}\) × \(\dfrac{\cancelto{\cancel{35}}{70}}{\cancelto{3}{57}}\) = \(\dfrac{1}{9}\)
問４８
( \(2\displaystyle\frac{11}{40}\) + \(\displaystyle\frac{3}{16}\) ) ÷ 1.25 – \(\displaystyle\frac{7}{12}\) =
- 答え
- \(1\displaystyle\frac{29}{75}\)
- 解き方
- ( \(2\displaystyle\frac{11}{40}\) + \(\displaystyle\frac{3}{16}\) ) ÷ 1.25 – \(\displaystyle\frac{7}{12}\)
= ( \(\displaystyle\frac{91}{40}\) + \(\displaystyle\frac{3}{16}\) ) ÷ \(\dfrac{5}{4}\) – \(\displaystyle\frac{7}{12}\)
= ( \(\displaystyle\frac{91}{5}\) + \(\displaystyle\frac{3}{2}\) ) × \(\dfrac{1}{8}\) × \(\dfrac{4}{5}\) – \(\displaystyle\frac{7}{12}\)
= ( \(\displaystyle\frac{182}{10}\) + \(\displaystyle\frac{15}{10}\) ) × \(\dfrac{1}{\cancelto{2}{8}}\) × \(\dfrac{\cancel{4}}{5}\) – \(\displaystyle\frac{7}{12}\)
= \(\displaystyle\frac{197}{10}\) × \(\dfrac{1}{10}\) – \(\displaystyle\frac{7}{12}\)
= \(\displaystyle\frac{197}{100}\) – \(\displaystyle\frac{7}{12}\)
= \(\dfrac{1}{4}\) × ( \(\displaystyle\frac{197}{25}\) – \(\displaystyle\frac{7}{3}\) )
= \(\dfrac{1}{4}\) × ( \(\displaystyle\frac{591}{75}\) – \(\displaystyle\frac{175}{75}\) )
= \(\dfrac{1}{\cancel{4}}\) × \(\displaystyle\frac{\cancelto{104}{416}}{75}\) = \(1\dfrac{29}{75}\)
問４９
\(1\dfrac{1}{5}\) × ( \(2\dfrac{1}{3}\) – 1.75 ) ÷ \(2\dfrac{1}{3}\) + \(\dfrac{1}{4}\) =
- 答え
- \(\displaystyle\frac{11}{20}\) または 0.55
- 解き方
- \(1\dfrac{1}{5}\) × ( \(2\dfrac{1}{3}\) – 1.75 ) ÷ \(2\dfrac{1}{3}\) + \(\dfrac{1}{4}\)
= \(\dfrac{6}{5}\) × ( \(\dfrac{7}{3}\) – \(\dfrac{7}{4}\) ) ÷ \(\dfrac{7}{3}\) + \(\dfrac{1}{4}\)
= \(\dfrac{6}{5}\) × ( \(\dfrac{7}{3}\) – \(\dfrac{7}{4}\) ) × \(\dfrac{3}{7}\) + \(\dfrac{1}{4}\)
= \(\dfrac{6}{5}\) × ( \(\dfrac{1}{3}\) – \(\dfrac{1}{4}\) ) × 3 + \(\dfrac{1}{4}\)
= \(\dfrac{\cancel{6}}{5}\) × \(\dfrac{1}{\cancelto{2}{12}}\) × 3 + \(\dfrac{1}{4}\)
= \(\dfrac{3}{10}\) + \(\dfrac{1}{4}\)
= \(\dfrac{6}{20}\) + \(\dfrac{5}{20}\) = \(\dfrac{11}{20}\)
問５０
4.2 × ( \(\dfrac{5}{6}\) – \(\dfrac{5}{7}\) ) + \(\dfrac{5}{8}\) ÷ 0.5 =
- 答え
- \(1\dfrac{3}{4}\) または 1.75
- 解き方
- 4.2 × ( \(\dfrac{5}{6}\) – \(\dfrac{5}{7}\) ) + \(\dfrac{5}{8}\) ÷ 0.5
= \(\dfrac{21}{5}\) × ( \(\dfrac{5}{6}\) – \(\dfrac{5}{7}\) ) + \(\dfrac{5}{8}\) ÷ \(\dfrac{1}{2}\)
= 21 × ( \(\dfrac{1}{6}\) – \(\dfrac{1}{7}\) ) + \(\dfrac{5}{8}\) × 2
= \(\cancel{21}\) × \(\dfrac{1}{\cancelto{2}{42}}\) + \(\dfrac{5}{\cancelto{4}{8}}\) × \(\cancel{2}\)
= \(\dfrac{2}{4}\) + \(\dfrac{5}{4}\) = \(\dfrac{7}{4}\) = \(1\dfrac{3}{4}\)