Getal & Ruimte (13e editie) - vwo wiskunde B
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({9 \over 5 a} + {7 \over 5 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({9 \over 5 a} + {7 \over 5 a} = {16 \over 5 a}\) 1p 1p b \({7 \over x} + {8 \over 6 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({7 \over x} + {8 \over 6 x} = {42 \over 6 x} + {8 \over 6 x} = {50 \over 6 x} = {25 \over 3 x}\) 1p 1p c \({6 \over 3 p} - {8 \over 7 q}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 3 p} - {8 \over 7 q} = {42 q \over 21 p q} - {24 p \over 21 p q} = {42 q - 24 p \over 21 p q} = {14 q - 8 p \over 7 p q}\) 1p 1p d \(6 + {2 \over 3 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(6 + {2 \over 3 x} = {6 \over 1} + {2 \over 3 x} = {18 x \over 3 x} + {2 \over 3 x} = {18 x + 2 \over 3 x}\) 1p opgave 2Herleid tot één breuk. 1p \({7 a \over b} + {4 \over 2 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({7 a \over b} + {4 \over 2 b} = {14 a \over 2 b} + {4 \over 2 b} = {14 a + 4 \over 2 b} = {7 a + 2 \over b}\) 1p opgave 3Herleid. 1p a \({2 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 a \over a} = {2 \over 1} = 2\) 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 \({-20 a \over 24 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-20 a \over 24 a} = -\frac{5}{6}\) 1p 1p d \({-25 x \over -5 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-25 x \over -5 x} = 5\) 1p opgave 4Herleid. 1p a \({-8 p q \over -20 p r}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-8 p q \over -20 p r} = {2 q \over 5 r}\) 1p 1p b \({-20 b \over -45 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-20 b \over -45 a b} = {4 \over 9 a}\) 1p 1p c \({-40 p q r \over -5 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-40 p q r \over -5 q r} = 8 p\) 1p 1p d \({7 x y \over y} - {4 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 x y \over y} - {4 x z \over z} = 7 x - 4 x = 3 x\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(6 p + {2 \over 3 p}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(6 p + {2 \over 3 p} = {6 p \over 1} ⋅ {3 p \over 3 p} + {2 \over 3 p} = {18 p^{2} \over 3 p} + {2 \over 3 p} = {18 p^{2} + 2 \over 3 p}\) 1p 1p b \({9 y \over 2 x} + {8 x \over 7 y}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({9 y \over 2 x} + {8 x \over 7 y} = {63 y^{2} \over 14 x y} + {16 x^{2} \over 14 x y} = {16 x^{2} + 63 y^{2} \over 14 x y}\) 1p 1p c \({8 \over a} ⋅ -{7 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over a} ⋅ -{7 \over b} = -{56 \over a b}\) 1p 1p d \({x \over 7} ⋅ -{2 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({x \over 7} ⋅ -{2 \over y} = -{2 x \over 7 y}\) 1p opgave 2Herleid tot één breuk. 1p a \(-{1 \over 6} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{1 \over 6} ⋅ a = -{a \over 6}\) 1p 1p b \({3 b \over a} ⋅ {a - 7 \over 5}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 b \over a} ⋅ {a - 7 \over 5} = {3 b (a - 7) \over 5 a} = {3 a b - 21 b \over 5 a}\) 1p 1p c \({5 \over a} : {4 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over a} : {4 \over b} = {5 \over a} ⋅ {b \over 4} = {5 b \over 4 a}\) 1p 1p d \({4 \over 9} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \({4 \over 9} : x = {4 \over 9} : {x \over 1} = {4 \over 9} ⋅ {1 \over x} = {4 \over 9 x}\) 1p opgave 3Herleid tot één breuk. 1p a \(-{9 \over 5} : {x - 6 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{9 \over 5} : {x - 6 y \over y} = -{9 \over 5} ⋅ {y \over x - 6 y} = -{9 y \over 5 (x - 6 y)} = -{9 y \over 5 x - 30 y}\) 1p 1p b \({3 p \over 5} + {p - 4 \over 9}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 p \over 5} + {p - 4 \over 9} = {27 p \over 45} + {5 (p - 4) \over 45} = {27 p + 5 (p - 4) \over 45} = {32 p - 20 \over 45}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({4 x + 1 \over 6 x + 5} - 8\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({4 x + 1 \over 6 x + 5} - 8 = {4 x + 1 \over 6 x + 5} - {8 (6 x + 5) \over 6 x + 5} = {4 x + 1 - 8 (6 x + 5) \over 6 x + 5} = {4 x + 1 - 48 x - 40 \over 6 x + 5} = {-44 x - 39 \over 6 x + 5}\) 1p |
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| vwo wiskunde B | 4.4 Formules met breuken herleiden |
opgave 1Deel uit. 1p a \({6 a^{2} + 9 a + 30 \over 3 a}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({6 a^{2} + 9 a + 30 \over 3 a} = {6 a^{2} \over 3 a} + {9 a \over 3 a} + {30 \over 3 a} = 2 a + 3 + {10 \over a}\) 1p 1p b \({6 p^{2} - 3 p - 2 \over p^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({6 p^{2} - 3 p - 2 \over p^{2}} = {6 p^{2} \over p^{2}} - {3 p \over p^{2}} - {2 \over p^{2}} = 6 - {3 \over p} - {2 \over p^{2}}\) 1p |