Getal & Ruimte (13e editie) - 2 havo/vwo
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({9 \over 8 x} + {7 \over 8 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({9 \over 8 x} + {7 \over 8 x} = {16 \over 8 x} = {2 \over x}\) 1p 1p b \({9 \over x} - {3 \over 8 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({9 \over x} - {3 \over 8 x} = {72 \over 8 x} - {3 \over 8 x} = {69 \over 8 x}\) 1p 1p c \({3 \over 6 p} + {8 \over 2 q}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({3 \over 6 p} + {8 \over 2 q} = {3 q \over 6 p q} + {24 p \over 6 p q} = {3 q + 24 p \over 6 p q} = {q + 8 p \over 2 p q}\) 1p 1p d \(6 - {8 \over 3 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(6 - {8 \over 3 a} = {6 \over 1} - {8 \over 3 a} = {18 a \over 3 a} - {8 \over 3 a} = {18 a - 8 \over 3 a}\) 1p opgave 2Herleid tot één breuk. 1p a \(3 a - {9 \over 8 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(3 a - {9 \over 8 a} = {3 a \over 1} ⋅ {8 a \over 8 a} - {9 \over 8 a} = {24 a^{2} \over 8 a} - {9 \over 8 a} = {24 a^{2} - 9 \over 8 a}\) 1p 1p b \({6 x \over y} - {4 \over 8 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({6 x \over y} - {4 \over 8 y} = {48 x \over 8 y} - {4 \over 8 y} = {48 x - 4 \over 8 y} = {12 x - 1 \over 2 y}\) 1p 1p c \({5 y \over 3 x} - {2 x \over 8 y}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({5 y \over 3 x} - {2 x \over 8 y} = {40 y^{2} \over 24 x y} - {6 x^{2} \over 24 x y} = {-6 x^{2} + 40 y^{2} \over 24 x y} = {-3 x^{2} + 20 y^{2} \over 12 x y}\) 1p opgave 3Herleid. 1p a \({5 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 p \over p} = {5 \over 1} = 5\) 1p 1p b \({a \over 8 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 8 a} = {1 \over 8}\) 1p 1p c \({-8 a \over 20 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-8 a \over 20 a} = -\frac{2}{5}\) 1p 1p d \({-16 a \over 2 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-16 a \over 2 a} = -8\) 1p opgave 4Herleid. 1p a \({-25 x y \over -40 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-25 x y \over -40 x z} = {5 y \over 8 z}\) 1p 1p b \({14 q \over 18 p q}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({14 q \over 18 p q} = {7 \over 9 p}\) 1p 1p c \({16 a b c \over -4 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({16 a b c \over -4 b c} = -4 a\) 1p 1p d \({6 x y \over y} + {4 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({6 x y \over y} + {4 x z \over z} = 6 x + 4 x = 10 x\) 1p |
|
| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({3 \over p} ⋅ -{8 \over q}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over p} ⋅ -{8 \over q} = -{24 \over p q}\) 1p 1p b \({x \over 2} ⋅ -{3 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 2} ⋅ -{3 \over y} = -{3 x \over 2 y}\) 1p 1p c \({7 \over 9} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 9} ⋅ a = {7 a \over 9}\) 1p 1p d \({4 \over a} : {8 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({4 \over a} : {8 \over b} = {4 \over a} ⋅ {b \over 8} = {4 b \over 8 a} = {b \over 2 a}\) 1p opgave 2Herleid tot één breuk. 1p \(-{8 \over 7} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{8 \over 7} : x = -{8 \over 7} : {x \over 1} = -{8 \over 7} ⋅ {1 \over x} = -{8 \over 7 x}\) 1p |