Getal & Ruimte (12e editie) - vwo wiskunde B
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({4 \over 6 x} + {8 \over 6 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 6 x} + {8 \over 6 x} = {12 \over 6 x} = {2 \over x}\) 1p 1p b \({6 \over x} - {3 \over 7 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over x} - {3 \over 7 x} = {42 \over 7 x} - {3 \over 7 x} = {39 \over 7 x}\) 1p 1p c \({2 \over 3 p} + {7 \over 5 q}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({2 \over 3 p} + {7 \over 5 q} = {10 q \over 15 p q} + {21 p \over 15 p q} = {10 q + 21 p \over 15 p q}\) 1p 1p d \(5 + {2 \over 3 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(5 + {2 \over 3 a} = {5 \over 1} + {2 \over 3 a} = {15 a \over 3 a} + {2 \over 3 a} = {15 a + 2 \over 3 a}\) 1p opgave 2Herleid tot één breuk. 1p \({5 a \over b} - {7 \over 3 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({5 a \over b} - {7 \over 3 b} = {15 a \over 3 b} - {7 \over 3 b} = {15 a - 7 \over 3 b}\) 1p opgave 3Herleid. 1p a \({7 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({7 a \over a} = {7 \over 1} = 7\) 1p 1p b \({a \over 6 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 6 a} = {1 \over 6}\) 1p 1p c \({10 x \over -35 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({10 x \over -35 x} = -\frac{2}{7}\) 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 \({15 x y \over 21 x z}\) 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 \({8 y \over 12 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({8 y \over 12 x y} = {2 \over 3 x}\) 1p 1p c \({24 p q r \over 4 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({24 p q r \over 4 q r} = 6 p\) 1p 1p d \({7 a b \over b} - {2 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 a b \over b} - {2 a c \over c} = 7 a - 2 a = 5 a\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(6 p + {5 \over 9 p}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(6 p + {5 \over 9 p} = {6 p \over 1} ⋅ {9 p \over 9 p} + {5 \over 9 p} = {54 p^{2} \over 9 p} + {5 \over 9 p} = {54 p^{2} + 5 \over 9 p}\) 1p 1p b \({7 b \over 8 a} + {5 a \over 9 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({7 b \over 8 a} + {5 a \over 9 b} = {63 b^{2} \over 72 a b} + {40 a^{2} \over 72 a b} = {40 a^{2} + 63 b^{2} \over 72 a b}\) 1p 1p c \({9 \over x} ⋅ -{6 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over x} ⋅ -{6 \over y} = -{54 \over x y}\) 1p 1p d \({x \over 6} ⋅ {5 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({x \over 6} ⋅ {5 \over y} = {5 x \over 6 y}\) 1p opgave 2Herleid tot één breuk. 1p a \({2 \over 3} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 \over 3} ⋅ a = {2 a \over 3}\) 1p 1p b \({2 b \over a} ⋅ {a + 8 \over 5}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({2 b \over a} ⋅ {a + 8 \over 5} = {2 b (a + 8) \over 5 a} = {2 a b + 16 b \over 5 a}\) 1p 1p c \({5 \over x} : {2 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over x} : {2 \over y} = {5 \over x} ⋅ {y \over 2} = {5 y \over 2 x}\) 1p 1p d \({7 \over 3} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \({7 \over 3} : p = {7 \over 3} : {p \over 1} = {7 \over 3} ⋅ {1 \over p} = {7 \over 3 p}\) 1p opgave 3Herleid tot één breuk. 1p a \(-{5 \over 9} : {x + 7 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{5 \over 9} : {x + 7 y \over y} = -{5 \over 9} ⋅ {y \over x + 7 y} = -{5 y \over 9 (x + 7 y)} = -{5 y \over 9 x + 63 y}\) 1p 1p b \({a \over 6} + {a + 3 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 1ms - dynamic variables b \({a \over 6} + {a + 3 \over 7} = {7 a \over 42} + {6 (a + 3) \over 42} = {7 a + 6 (a + 3) \over 42} = {13 a + 18 \over 42}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-7 p - 4 \over 9 p - 2} - 3\) Optellen (9) 00eh - Breuken herleiden - basis - 1ms - dynamic variables ○ \({-7 p - 4 \over 9 p - 2} - 3 = {-7 p - 4 \over 9 p - 2} - {3 (9 p - 2) \over 9 p - 2} = {-7 p - 4 - 3 (9 p - 2) \over 9 p - 2} = {-7 p - 4 - 27 p + 6 \over 9 p - 2} = {-34 p + 2 \over 9 p - 2}\) 1p |
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| vwo wiskunde B | 4.4 Herleidingen en inverse functies |
opgave 1Deel uit. 1p a \({2 a^{2} - a - 30 \over a}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({2 a^{2} - a - 30 \over a} = {2 a^{2} \over a} - {a \over a} - {30 \over a} = 2 a - 1 - {30 \over a}\) 1p 1p b \({6 x^{2} + 5 x - 8 \over 2 x^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({6 x^{2} + 5 x - 8 \over 2 x^{2}} = {6 x^{2} \over 2 x^{2}} + {5 x \over 2 x^{2}} - {8 \over 2 x^{2}} = 3 + {5 \over 2 x} - {4 \over x^{2}}\) 1p |