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GMAT -  Глава #1 - Дроби, десятичные числа и проценты - #2: Дроби
Словарь
fraction дробь
1 / 3
[frækʃn]
numerator числитель
1 / 3
[ˈnjuːməreɪtə]
denominator знаменатель
1 / 3
[ˈnjuːməreɪtə]
simplify упрощать

сокращать
4 / 8 = 2 / 4 = 1 / 2
[ˈsɪmplɪfaɪ]
factor множитель
10 = 2 х 5
[ˈfæktə]
common
factor
общий

множитель
10 = 2 х 5, 15 = 3 х 5
[ˈkɔmən ˈfæktə]
cancel сокращать
10 = 2 х 5, 15 = 3 х 5
[ˈkænsəl]
10 / 15 = (2 х 5) / (3 х 5) = 2 / 3
reciprocal обратный(ая)
2 / 3 ~> 3 / 2
[rɪˈsɪprəkəl]
Теория
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
6 7
|
13/2
6.5 = 6 + 0.5 = 13 / 2 = 6 + 1/2
правильные дроби неправильные дроби
0 <= x < 1 x >= 1
1/2
3/4
8/13
…
12/2
121/11
9/7
…
знаменатель > числитель знаменатель <= числитель
~ >смешанный тип неправильные дроби
8
2
_
3
=
3 x 8 + 2
_
3
=
26
_
3
сокращение / упрощение дроби
45 / 180 = (3 х 3 х 5) / (2 х 2 х 3 х 3 х 5) = 1 / (2 х 2) = 1 / 4
45 = 3 х 3 х 5
180 = 2 х 2 х 3 х 3 х 5
несократимая дробь
НОД(45, 180) = 45
умножение и упрощение дробей
26
_
3
12
_
30
х =
26
_
3
2 х 2 х 3
______
2 х 3 х 5
х =
26
_
3
2
_
5
х =
26 х 2
____
3 х 5
52
__
15
=
7
3 __
15
=
сложение / вычитание дробей
26
_
3
12
_
30
+ =
26 х НОК(3,5) / 3 + 12 х НОК(3,5) / 5
_____________________
НОК (3,5)
26
_
3
2 х 2 х 3
______
2 х 3 х 5
+ =
26
_
3
2
_
5
+ = =
=
26 х 5+ 2 х 3
__________
15
=
136
___
15
21 + 5
___
3
=
21
_
3
5
_
3
+
21
___
1 + 2
=
21
_
1
21
_
2
+
15 + 6
___
1 + 2
=
15
_
1
6
_
2
+
«разделение» числителя и знаменателя
обратная дробь: в шаге от деления
26
_
3
х
a
_
b
= 1
a х b = 1
обратное значение «а» это такое значение «b» при котором 

соблюдается условие выше
деление дробей
26
_
3
12
_
30
/ =
26
_
3
2 х 2 х 3
______
2 х 3 х 5
/ =
26
_
3
5
_
2
x =
26 х 5
____
3 х 2
65
__
3
=
2
21 _
3
=
обратная дробь!
сменили знак!
сравнение дробей
8
_
13
15
_
17
?
(8 х 17) = 136 (15 х 13) = 195
8
_
13
15
_
17
8
_
13
15
_
17
<
Практика
Задание №1
Определите, изменит ли указанное действие начальное значение

в сторону увеличения, уменьшения или равенства.
Умножили числитель положительной правильной дроби на 3/2.
(А) Уменьшилось (B) Осталось прежним (С) Увеличилось
Задание №2
Определите, изменит ли указанное действие начальное значение

в сторону увеличения, уменьшения или равенства.
Добавили +1 к числителю положительной правильной дроби и

вычли -1 из знаменателя.
(А) Уменьшилось (B) Осталось прежним (С) Увеличилось
Задание №3
Определите, изменит ли указанное действие начальное значение

в сторону увеличения, уменьшения или равенства.
Умножили и числитель и знаменатель правильной дроби

на 3 целых 1/2 (или в виде неправильной дроби - 7/2).
(А) Уменьшилось (B) Осталось прежним (С) Увеличилось
Задание №4
Определите, изменит ли указанное действие начальное значение

в сторону увеличения, уменьшения или равенства.
Умножили положительную правильную дробь на 3/8.
(А) Уменьшилось (B) Осталось прежним (С) Увеличилось
Задание №5
Определите, изменит ли указанное действие начальное значение

в сторону увеличения, уменьшения или равенства.
Поделили положительную правильную дробь на 3/13.
(А) Уменьшилось (B) Осталось прежним (С) Увеличилось
Задание №6
Упростите выражения.
10 х Y
___
5 + Y
Задание №7
Упростите выражения.
8 x 3 x Y2 x 3
________
6 x Y
Задание №8
Упростите выражения.
3

_
5
1

_
3
2

_
3
2

_
5
_________
+
+
Задание №9
Упростите выражения.
12ab3 - 6a2b
_________
3ab
ab != 0
Задание №10
Являются ли значения обратными?
GMAT -  Глава #1 - Дроби, десятичные числа и проценты - #2: Дроби

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GMAT - Глава #1 - Дроби, десятичные числа и проценты - #2: Дроби