Завдання 1268
1) (3 1/4 + 0,25 – 1 5/24) : (2 3/4 – 4 1/2 – 0,75) : (–4 7/12) = 1/5
а) 3 1/4 + 0,25 – 1 5/24 = 3 1/4 + 1/4 – 1 5/24 = 3 2/4 – 1 5/24 = 3 12/24 – 1 5/24 = 2 7/24
b) 2 3/4 – 4 1/2 – 3/4 = 2 3/4 – 3/4 – 4 1/2 = 2 – 4 2/4 = –2 2/4 = –2 1/2
c) 2 7/24 : (–2 1/2) = –55/24 : 5/2 = –55/24 • 2/5 = –11/12
d) – 11/12 : (–4 7/12) = –11/12 : (–55/12) = 11/12 • 12/55 = 1/5
2) –24,6 : (–2,35 + 0,7 : 2 1/3) – 15,36 = –3,36
a) 0,7 : 2 1/3 = 7/10 : 7/3 = 7/10 • 3/7 = 3/10
b) –2,35 + 3/10 = –2,35 + 0,3 = –2,05
c) –24,6 : (–2,05) = 12
d) 12 – 15,36 = –3,36
3) (5 5/28 – 5 1/3 • 1,25 – 1 16/21) : (–1,5) = 2 1/6
a) 5 1/3 • 1,25 = 5 1/3 • 1 1/4 = 16/3 • 5/4 = 20/3 = 6 2/3
b) 5 5/28 – 6 2/3 – 1 16/21 = 5 15/84 – 6 56/84 – 1 64/84 = 5 15/84 – 7 120/84 = 5 15/84 – 8 36/84 = –3 21/84 =
= –3 1/4
c) –3 1/4 : (–1,5) = –3 1/4 : (–1 1/2) = 13/4 : 3/2 = 13/4 • 2/3 = 13/6 = 2 1/6
d) (–3 1/3 • 1,9 + 19,5 : 4 1/3) : (0,16 – 62/75) =
= (–10/3 • 19/10 + 195/10 : 13/3) : (16/100 – 62/75) =
= (–19/3 + 195/10 • 3/13) : (4/25 – 62/75) = (–6 1/3 + 4 1/2) : (12/75 – 62/75) =
= (–6 3/6 + 4 3/6) : (–2/3) = 11/6 • 3/2 = 11/4 = 2 3/4
8) (–13,6 + 5,1) • 1 3/17 + (2 7/23 – 1 45/46) : 1 7/23 = –85/10 • 20/17 + (2 14/16 – 1 45/46) : 1 7/23 =
= –10 + 15/46 : 30/23 = –10 + 15/46 • 23/30 = –10 + 1/4 = –9 3/4
Завдання 1269
1) (3 1/3 + 2,5) : (3 1/3 – 2,5) = (3 1/3 + 2 1/2) : (3 1/3 – 2 1/2) =
= (3 2/6 + 2 3/6) : (3 2/6 – 2 3/6) = 5 5/6 : 5/6 = 35/6 : 5/6 = 35/6 • 6/5 = 7
40% від 7 – це 7 • 0,4 = 2,8
2) (3 1/3 : 10 + 0,175 : 0,35) : (1,75 – 1 11/17 • 51/56) =
= (10/3 : 10 + 0,5) : (1 3/4 – 28/17 • 51/56) = (10/3 • 1/10 + 1/2) : (1 3/4 – 3/2) =
= (1/3 + 1/2) : (1 3/4 – 1 2/4) = 5/6 : 1/4 = 5/6 • 4/1 = 10/3 = 3 1/3
54% від 3 1/3 – це 3 1/3 • 54 : 100 = 10/3 • 54 : 100 = 10/3 • 54/100 = 18/10 = 1,8
Завдання 1270
1) (3 7/12 – 2 11/18 + 2 1/24) • 1 5/31 = (3 42/72 – 2 44/72 + 2 3/72) • 1 5/31 =
= 3 1/72 • 1 5/31 = 217/72 • 36/31 = 7/2 = 3,5
3 1/2 : 28/100 = 7/2 : 7/25 = 7/2 • 25/7 = 25/2 = 12,5
2) (0,5 : 1 1/4 + 1 2/5 : 1 4/7 – 3/11) : (1,5 + 1/4) : 2 13/32 =
= (1/2 : 5/4 + 7/5 : 11/7 – 3/11) : ((1 1/2 + 1/4) : 77/32) =
= (2/5 + 7/5 • 7/11 – 3/11) : (7/4 : 77/32) = (2/5 + 49/55 – 3/11) : (7/4 • 32/77) =
= 56/55 : 8/11 = 56/55 • 11/8 = 7/5 = 1,4
1,4 : 0,35 = 4
Завдання 1271
1) (8 7/12 – 5 19/36) • 1 4/5 = (8 21/36 – 5 19/36) • 1 4/5 = 3 2/36 • 1 4/5 = 55/18 • 9/5 = 11/2 = 5 1/2
(39,375 – 5 5/8) : 2 5/11 = (39,375 – 5,625) : 2 5/11 = 33 75/100 : 2 5/11 = 33 3/4 : 2 5/11 =
= 135/4 • 11/27 = 55/4
(11/2 : 55/4) • 100% = 11/2 • 4/55 • 100 = 40%
2) – 0,75 : (–1 1/4 : 3 + 1/6) = –0,75 : (–5/4 : 3 + 1/6) = –0,75 : (–5/12 + 1/6) =
= –0,75 : (–5/12 + 2/12) = 0,75 : (–3/12) = 75/100 • 12/3 = 3
(17,5 : 3,5 + 1 : 0,5) : (12,68 – 11,18) • 1/3 = (5 + 2) : (1,5 • 1/3) = 7 : 1/2 = 14
(3 : 14) • 100% = 3/14 • 100% = 21 3/7%
Завдання 1272
а = (5 2/3 – (–2 1/9)) • (–1 7/20) = (5 2/3 + 2 1/9) • (–1 7/20) = (5 6/9 + 2 1/9) • (–1 7/20) =
= 7 7/9 • (–1 7/20) = –70/9 • 27/20 = –21/3 = –10,5
b = (–2 2/5 – 1 1/3) : (–1 1/20) = –3 11/15 : (–1 1/20) = 56/15 : 21/20 = 56/15 • 20/21 = 3 5/9
с = (–6 5/12 – (–7 3/16)) • (–4,8) = (–6 5/12 + 7 3/16) • (–4,8) = (–6 20/48 + 7 9/48) • (–4,8) =
= (–6 20/48 + 6 57/48) • (–48/10) = –37/48 • 48/10 = –37/10 = –3,7
d = (7 1/6 + (–8 3/8)) • (–2 2/29) = (7 4/24 – 8 9/24) • (–2 2/29) = (–1 5/24) • (–2 2/29) =
= –29/24 • (–60/29) = 29/24 • 60/29 = 60/24 = 2,5
Отже, найменше число – це а.