Getal & Ruimte (13e editie) - 2 vwo
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({9 \over 7 p} + {2 \over 7 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({9 \over 7 p} + {2 \over 7 p} = {11 \over 7 p}\) 1p 1p b \({5 \over a} - {4 \over 2 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({5 \over a} - {4 \over 2 a} = {10 \over 2 a} - {4 \over 2 a} = {6 \over 2 a} = {3 \over a}\) 1p 1p c \({6 \over 9 x} - {8 \over 4 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 9 x} - {8 \over 4 y} = {24 y \over 36 x y} - {72 x \over 36 x y} = {24 y - 72 x \over 36 x y} = {2 y - 6 x \over 3 x y}\) 1p 1p d \(8 - {5 \over 2 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(8 - {5 \over 2 a} = {8 \over 1} - {5 \over 2 a} = {16 a \over 2 a} - {5 \over 2 a} = {16 a - 5 \over 2 a}\) 1p opgave 2Herleid tot één breuk. 1p \({9 x \over y} - {6 \over 4 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({9 x \over y} - {6 \over 4 y} = {36 x \over 4 y} - {6 \over 4 y} = {36 x - 6 \over 4 y} = {18 x - 3 \over 2 y}\) 1p opgave 3Herleid. 1p a \({6 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({6 a \over a} = {6 \over 1} = 6\) 1p 1p b \({a \over 5 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 5 a} = {1 \over 5}\) 1p 1p c \({21 x \over 24 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({21 x \over 24 x} = \frac{7}{8}\) 1p 1p d \({30 p \over -5 p}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({30 p \over -5 p} = -6\) 1p opgave 4Herleid. 1p a \({14 x y \over 16 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({14 x y \over 16 x z} = {7 y \over 8 z}\) 1p 1p b \({12 y \over -28 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({12 y \over -28 x y} = -{3 \over 7 x}\) 1p 1p c \({35 a b c \over 5 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({35 a b c \over 5 b c} = 7 a\) 1p 1p d \({2 x y \over y} + {5 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({2 x y \over y} + {5 x z \over z} = 2 x + 5 x = 7 x\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(5 a + {8 \over 3 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(5 a + {8 \over 3 a} = {5 a \over 1} ⋅ {3 a \over 3 a} + {8 \over 3 a} = {15 a^{2} \over 3 a} + {8 \over 3 a} = {15 a^{2} + 8 \over 3 a}\) 1p 1p b \({9 b \over 5 a} - {4 a \over 6 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({9 b \over 5 a} - {4 a \over 6 b} = {54 b^{2} \over 30 a b} - {20 a^{2} \over 30 a b} = {-20 a^{2} + 54 b^{2} \over 30 a b} = {-10 a^{2} + 27 b^{2} \over 15 a b}\) 1p 1p c \({6 \over x} ⋅ -{4 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over x} ⋅ -{4 \over y} = -{24 \over x y}\) 1p 1p d \({x \over 8} ⋅ {7 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({x \over 8} ⋅ {7 \over y} = {7 x \over 8 y}\) 1p opgave 2Herleid tot één breuk. 1p a \({3 \over 8} ⋅ p\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 8} ⋅ p = {3 p \over 8}\) 1p 1p b \({4 b \over a} ⋅ {a - 7 \over 6}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({4 b \over a} ⋅ {a - 7 \over 6} = {4 b (a - 7) \over 6 a} = {2 b (a - 7) \over 3 a} = {2 a b - 14 b \over 3 a}\) 1p 1p c \({3 \over a} : {8 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({3 \over a} : {8 \over b} = {3 \over a} ⋅ {b \over 8} = {3 b \over 8 a}\) 1p 1p d \(-{6 \over 5} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{6 \over 5} : x = -{6 \over 5} : {x \over 1} = -{6 \over 5} ⋅ {1 \over x} = -{6 \over 5 x}\) 1p opgave 3Herleid tot één breuk. 1p a \({5 \over 2} : {x - 6 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 \over 2} : {x - 6 y \over y} = {5 \over 2} ⋅ {y \over x - 6 y} = {5 y \over 2 (x - 6 y)} = {5 y \over 2 x - 12 y}\) 1p 1p b \({7 p \over 6} + {p + 4 \over 5}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({7 p \over 6} + {p + 4 \over 5} = {35 p \over 30} + {6 (p + 4) \over 30} = {35 p + 6 (p + 4) \over 30} = {41 p + 24 \over 30}\) 1p |