Getal & Ruimte (12e editie) - havo wiskunde B
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({3 \over 7 x} + {8 \over 7 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 7 x} + {8 \over 7 x} = {11 \over 7 x}\) 1p 1p b \({8 \over a} - {6 \over 4 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({8 \over a} - {6 \over 4 a} = {32 \over 4 a} - {6 \over 4 a} = {26 \over 4 a} = {13 \over 2 a}\) 1p 1p c \({3 \over 9 a} + {2 \over 6 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({3 \over 9 a} + {2 \over 6 b} = {6 b \over 18 a b} + {6 a \over 18 a b} = {6 b + 6 a \over 18 a b} = {b + a \over 3 a b}\) 1p 1p d \(7 + {9 \over 4 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(7 + {9 \over 4 p} = {7 \over 1} + {9 \over 4 p} = {28 p \over 4 p} + {9 \over 4 p} = {28 p + 9 \over 4 p}\) 1p opgave 2Herleid tot één breuk. 1p a \(2 x + {5 \over 6 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(2 x + {5 \over 6 x} = {2 x \over 1} ⋅ {6 x \over 6 x} + {5 \over 6 x} = {12 x^{2} \over 6 x} + {5 \over 6 x} = {12 x^{2} + 5 \over 6 x}\) 1p 1p b \({8 a \over b} - {4 \over 2 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({8 a \over b} - {4 \over 2 b} = {16 a \over 2 b} - {4 \over 2 b} = {16 a - 4 \over 2 b} = {8 a - 2 \over b}\) 1p 1p c \({8 q \over 6 p} - {9 p \over 4 q}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 q \over 6 p} - {9 p \over 4 q} = {16 q^{2} \over 12 p q} - {27 p^{2} \over 12 p q} = {-27 p^{2} + 16 q^{2} \over 12 p q}\) 1p opgave 3Herleid. 1p a \({5 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 a \over a} = {5 \over 1} = 5\) 1p 1p b \({x \over 8 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 8 x} = {1 \over 8}\) 1p 1p c \({-12 x \over 14 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-12 x \over 14 x} = -\frac{6}{7}\) 1p 1p d \({-28 a \over 4 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-28 a \over 4 a} = -7\) 1p opgave 4Herleid. 1p a \({12 x y \over -27 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({12 x y \over -27 x z} = -{4 y \over 9 z}\) 1p 1p b \({16 b \over -18 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({16 b \over -18 a b} = -{8 \over 9 a}\) 1p 1p c \({15 p q r \over 5 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({15 p q r \over 5 q r} = 3 p\) 1p 1p d \({5 x y \over y} - {7 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({5 x y \over y} - {7 x z \over z} = 5 x - 7 x = -2 x\) 1p |
|
| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({2 \over a} ⋅ -{9 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 \over a} ⋅ -{9 \over b} = -{18 \over a b}\) 1p 1p b \({x \over 3} ⋅ {6 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 3} ⋅ {6 \over y} = {6 x \over 3 y} = {2 x \over y}\) 1p 1p c \(-{2 \over 9} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{2 \over 9} ⋅ a = -{2 a \over 9}\) 1p 1p d \({3 \over x} : {8 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({3 \over x} : {8 \over y} = {3 \over x} ⋅ {y \over 8} = {3 y \over 8 x}\) 1p opgave 2Herleid tot één breuk. 1p \({1 \over 4} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({1 \over 4} : p = {1 \over 4} : {p \over 1} = {1 \over 4} ⋅ {1 \over p} = {1 \over 4 p}\) 1p |
|
| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({9 p \over 4} + {p + 6 \over 5}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({9 p \over 4} + {p + 6 \over 5} = {45 p \over 20} + {4 (p + 6) \over 20} = {45 p + 4 (p + 6) \over 20} = {49 p + 24 \over 20}\) 1p |
|
| havo wiskunde B | 11.5 Gebroken functies |
opgave 1Herleid tot één breuk. 1p \({4 a + 6 \over -9 a - 8} - 1\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({4 a + 6 \over -9 a - 8} - 1 = {4 a + 6 \over -9 a - 8} + {-1 (-9 a - 8) \over -9 a - 8} = {4 a + 6 - 1 (-9 a - 8) \over -9 a - 8} = {4 a + 6 + 9 a + 8 \over -9 a - 8} = {13 a + 14 \over -9 a - 8}\) 1p opgave 2Deel uit. 1p a \({2 p^{2} + p - 30 \over p}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({2 p^{2} + p - 30 \over p} = {2 p^{2} \over p} + {p \over p} - {30 \over p} = 2 p + 1 - {30 \over p}\) 1p 1p b \({6 a^{2} - 7 a - 8 \over 2 a^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({6 a^{2} - 7 a - 8 \over 2 a^{2}} = {6 a^{2} \over 2 a^{2}} - {7 a \over 2 a^{2}} - {8 \over 2 a^{2}} = 3 - {7 \over 2 a} - {4 \over a^{2}}\) 1p |