Getal & Ruimte (13e editie) - vwo wiskunde C
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({4 \over 7 p} - {8 \over 7 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 7 p} - {8 \over 7 p} = -{4 \over 7 p}\) 1p 1p b \({8 \over a} - {4 \over 5 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({8 \over a} - {4 \over 5 a} = {40 \over 5 a} - {4 \over 5 a} = {36 \over 5 a}\) 1p 1p c \({5 \over 3 x} - {7 \over 2 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over 3 x} - {7 \over 2 y} = {10 y \over 6 x y} - {21 x \over 6 x y} = {10 y - 21 x \over 6 x y}\) 1p 1p d \(9 + {5 \over 3 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(9 + {5 \over 3 a} = {9 \over 1} + {5 \over 3 a} = {27 a \over 3 a} + {5 \over 3 a} = {27 a + 5 \over 3 a}\) 1p opgave 2Herleid tot één breuk. 1p \({8 x \over y} + {5 \over 2 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 x \over y} + {5 \over 2 y} = {16 x \over 2 y} + {5 \over 2 y} = {16 x + 5 \over 2 y}\) 1p opgave 3Herleid. 1p a \({9 x \over x}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 x \over x} = {9 \over 1} = 9\) 1p 1p b \({a \over 2 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 2 a} = {1 \over 2}\) 1p 1p c \({20 a \over 36 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({20 a \over 36 a} = \frac{5}{9}\) 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 \({-16 x y \over -36 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-16 x y \over -36 x z} = {4 y \over 9 z}\) 1p 1p b \({4 q \over 14 p q}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({4 q \over 14 p q} = {2 \over 7 p}\) 1p 1p c \({-24 x y z \over -3 y z}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-24 x y z \over -3 y z} = 8 x\) 1p 1p d \({7 a b \over b} - {3 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 a b \over b} - {3 a c \over c} = 7 a - 3 a = 4 a\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(7 x + {4 \over 9 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(7 x + {4 \over 9 x} = {7 x \over 1} ⋅ {9 x \over 9 x} + {4 \over 9 x} = {63 x^{2} \over 9 x} + {4 \over 9 x} = {63 x^{2} + 4 \over 9 x}\) 1p 1p b \({9 b \over 4 a} - {3 a \over 7 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({9 b \over 4 a} - {3 a \over 7 b} = {63 b^{2} \over 28 a b} - {12 a^{2} \over 28 a b} = {-12 a^{2} + 63 b^{2} \over 28 a b}\) 1p 1p c \({5 \over p} ⋅ {6 \over q}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over p} ⋅ {6 \over q} = {30 \over p q}\) 1p 1p d \({x \over 9} ⋅ {6 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({x \over 9} ⋅ {6 \over y} = {6 x \over 9 y} = {2 x \over 3 y}\) 1p opgave 2Herleid tot één breuk. 1p a \({1 \over 5} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({1 \over 5} ⋅ a = {a \over 5}\) 1p 1p b \({4 y \over x} ⋅ {x - 9 \over 3}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({4 y \over x} ⋅ {x - 9 \over 3} = {4 y (x - 9) \over 3 x} = {4 x y - 36 y \over 3 x}\) 1p 1p c \({7 \over p} : {4 \over q}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over p} : {4 \over q} = {7 \over p} ⋅ {q \over 4} = {7 q \over 4 p}\) 1p 1p d \(-{5 \over 3} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{5 \over 3} : x = -{5 \over 3} : {x \over 1} = -{5 \over 3} ⋅ {1 \over x} = -{5 \over 3 x}\) 1p opgave 3Herleid tot één breuk. 1p a \(-{8 \over 5} : {a - 9 b \over b}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{8 \over 5} : {a - 9 b \over b} = -{8 \over 5} ⋅ {b \over a - 9 b} = -{8 b \over 5 (a - 9 b)} = -{8 b \over 5 a - 45 b}\) 1p 1p b \({5 a \over 9} + {a + 8 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({5 a \over 9} + {a + 8 \over 7} = {35 a \over 63} + {9 (a + 8) \over 63} = {35 a + 9 (a + 8) \over 63} = {44 a + 72 \over 63}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-7 x + 3 \over 9 x + 4} - 8\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({-7 x + 3 \over 9 x + 4} - 8 = {-7 x + 3 \over 9 x + 4} - {8 (9 x + 4) \over 9 x + 4} = {-7 x + 3 - 8 (9 x + 4) \over 9 x + 4} = {-7 x + 3 - 72 x - 32 \over 9 x + 4} = {-79 x - 29 \over 9 x + 4}\) 1p |
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| vwo wiskunde A | 3.1 Breuken en verhoudingen |
opgave 1Deel uit. 1p a \({6 a^{2} + 2 a - 40 \over 2 a}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({6 a^{2} + 2 a - 40 \over 2 a} = {6 a^{2} \over 2 a} + {2 a \over 2 a} - {40 \over 2 a} = 3 a + 1 - {20 \over a}\) 1p 1p b \({6 a^{2} - 9 a - 7 \over 5 a^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({6 a^{2} - 9 a - 7 \over 5 a^{2}} = {6 a^{2} \over 5 a^{2}} - {9 a \over 5 a^{2}} - {7 \over 5 a^{2}} = 1\frac{1}{5} - {9 \over 5 a} - {7 \over 5 a^{2}}\) 1p |