Getal & Ruimte (12e editie) - vwo wiskunde A
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({3 \over 2 a} + {6 \over 2 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 2 a} + {6 \over 2 a} = {9 \over 2 a}\) 1p 1p b \({5 \over x} - {8 \over 9 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({5 \over x} - {8 \over 9 x} = {45 \over 9 x} - {8 \over 9 x} = {37 \over 9 x}\) 1p 1p c \({5 \over 8 x} - {3 \over 2 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over 8 x} - {3 \over 2 y} = {5 y \over 8 x y} - {12 x \over 8 x y} = {5 y - 12 x \over 8 x y}\) 1p 1p d \(5 - {9 \over 4 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(5 - {9 \over 4 a} = {5 \over 1} - {9 \over 4 a} = {20 a \over 4 a} - {9 \over 4 a} = {20 a - 9 \over 4 a}\) 1p opgave 2Herleid tot één breuk. 1p \({7 p \over q} - {8 \over 3 q}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({7 p \over q} - {8 \over 3 q} = {21 p \over 3 q} - {8 \over 3 q} = {21 p - 8 \over 3 q}\) 1p opgave 3Herleid. 1p a \({9 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 a \over a} = {9 \over 1} = 9\) 1p 1p b \({p \over 4 p}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 4 p} = {1 \over 4}\) 1p 1p c \({4 a \over 18 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({4 a \over 18 a} = \frac{2}{9}\) 1p 1p d \({8 x \over -2 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({8 x \over -2 x} = -4\) 1p opgave 4Herleid. 1p a \({-15 x y \over -21 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-15 x y \over -21 x z} = {5 y \over 7 z}\) 1p 1p b \({-10 b \over -16 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-10 b \over -16 a b} = {5 \over 8 a}\) 1p 1p c \({-20 p q r \over -5 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-20 p q r \over -5 q r} = 4 p\) 1p 1p d \({5 a b \over b} + {6 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({5 a b \over b} + {6 a c \over c} = 5 a + 6 a = 11 a\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(4 x + {6 \over 5 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(4 x + {6 \over 5 x} = {4 x \over 1} ⋅ {5 x \over 5 x} + {6 \over 5 x} = {20 x^{2} \over 5 x} + {6 \over 5 x} = {20 x^{2} + 6 \over 5 x}\) 1p 1p b \({6 b \over 9 a} + {4 a \over 8 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({6 b \over 9 a} + {4 a \over 8 b} = {48 b^{2} \over 72 a b} + {36 a^{2} \over 72 a b} = {36 a^{2} + 48 b^{2} \over 72 a b} = {3 a^{2} + 4 b^{2} \over 6 a b}\) 1p 1p c \({2 \over x} ⋅ {3 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({2 \over x} ⋅ {3 \over y} = {6 \over x y}\) 1p 1p d \({p \over 5} ⋅ {7 \over q}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({p \over 5} ⋅ {7 \over q} = {7 p \over 5 q}\) 1p opgave 2Herleid tot één breuk. 1p a \(-{6 \over 5} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{6 \over 5} ⋅ a = -{6 a \over 5}\) 1p 1p b \({7 b \over a} ⋅ {a - 9 \over 6}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({7 b \over a} ⋅ {a - 9 \over 6} = {7 b (a - 9) \over 6 a} = {7 a b - 63 b \over 6 a}\) 1p 1p c \({2 \over x} : {5 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({2 \over x} : {5 \over y} = {2 \over x} ⋅ {y \over 5} = {2 y \over 5 x}\) 1p 1p d \({4 \over 3} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \({4 \over 3} : p = {4 \over 3} : {p \over 1} = {4 \over 3} ⋅ {1 \over p} = {4 \over 3 p}\) 1p opgave 3Herleid tot één breuk. 1p a \({3 \over 8} : {a - 4 b \over b}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 8} : {a - 4 b \over b} = {3 \over 8} ⋅ {b \over a - 4 b} = {3 b \over 8 (a - 4 b)} = {3 b \over 8 a - 32 b}\) 1p 1p b \({9 x \over 4} + {x - 6 \over 3}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({9 x \over 4} + {x - 6 \over 3} = {27 x \over 12} + {4 (x - 6) \over 12} = {27 x + 4 (x - 6) \over 12} = {31 x - 24 \over 12}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-4 a - 8 \over -6 a - 2} + 3\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({-4 a - 8 \over -6 a - 2} + 3 = {-4 a - 8 \over -6 a - 2} - {-3 (-6 a - 2) \over -6 a - 2} = {-4 a - 8 + 3 (-6 a - 2) \over -6 a - 2} = {-4 a - 8 - 18 a - 6 \over -6 a - 2} = {-22 a - 14 \over -6 a - 2}\) 1p |
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| vwo wiskunde A | 13.3 Formules herschrijven |
opgave 1Deel uit. 1p \({8 a^{2} + 5 a - 2 \over 4 a^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 a^{2} + 5 a - 2 \over 4 a^{2}} = {8 a^{2} \over 4 a^{2}} + {5 a \over 4 a^{2}} - {2 \over 4 a^{2}} = 2 + {5 \over 4 a} - {1 \over 2 a^{2}}\) 1p |