Getal & Ruimte (12e editie) - havo wiskunde A
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({4 \over 8 x} - {9 \over 8 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 8 x} - {9 \over 8 x} = -{5 \over 8 x}\) 1p 1p b \({6 \over a} + {9 \over 5 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over a} + {9 \over 5 a} = {30 \over 5 a} + {9 \over 5 a} = {39 \over 5 a}\) 1p 1p c \({6 \over 2 a} + {9 \over 7 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 2 a} + {9 \over 7 b} = {42 b \over 14 a b} + {18 a \over 14 a b} = {42 b + 18 a \over 14 a b} = {21 b + 9 a \over 7 a b}\) 1p 1p d \(8 + {5 \over 9 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(8 + {5 \over 9 p} = {8 \over 1} + {5 \over 9 p} = {72 p \over 9 p} + {5 \over 9 p} = {72 p + 5 \over 9 p}\) 1p opgave 2Herleid tot één breuk. 1p a \(2 x - {7 \over 4 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(2 x - {7 \over 4 x} = {2 x \over 1} ⋅ {4 x \over 4 x} - {7 \over 4 x} = {8 x^{2} \over 4 x} - {7 \over 4 x} = {8 x^{2} - 7 \over 4 x}\) 1p 1p b \({5 a \over b} + {7 \over 8 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({5 a \over b} + {7 \over 8 b} = {40 a \over 8 b} + {7 \over 8 b} = {40 a + 7 \over 8 b}\) 1p 1p c \({9 y \over 5 x} + {7 x \over 8 y}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 y \over 5 x} + {7 x \over 8 y} = {72 y^{2} \over 40 x y} + {35 x^{2} \over 40 x y} = {35 x^{2} + 72 y^{2} \over 40 x y}\) 1p opgave 3Herleid. 1p a \({7 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({7 p \over p} = {7 \over 1} = 7\) 1p 1p b \({a \over 8 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 8 a} = {1 \over 8}\) 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 \({-14 a \over 2 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-14 a \over 2 a} = -7\) 1p opgave 4Herleid. 1p a \({-6 p q \over -21 p r}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-6 p q \over -21 p r} = {2 q \over 7 r}\) 1p 1p b \({20 y \over 28 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({20 y \over 28 x y} = {5 \over 7 x}\) 1p 1p c \({-40 a b c \over 5 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-40 a b c \over 5 b c} = -8 a\) 1p 1p d \({2 x y \over y} + {4 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({2 x y \over y} + {4 x z \over z} = 2 x + 4 x = 6 x\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({7 \over x} ⋅ {9 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({7 \over x} ⋅ {9 \over y} = {63 \over x y}\) 1p 1p b \({x \over 8} ⋅ -{2 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 8} ⋅ -{2 \over y} = -{2 x \over 8 y} = -{x \over 4 y}\) 1p 1p c \({1 \over 2} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({1 \over 2} ⋅ a = {a \over 2}\) 1p 1p d \({2 \over a} : {8 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({2 \over a} : {8 \over b} = {2 \over a} ⋅ {b \over 8} = {2 b \over 8 a} = {b \over 4 a}\) 1p opgave 2Herleid tot één breuk. 1p \(-{4 \over 5} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{4 \over 5} : p = -{4 \over 5} : {p \over 1} = -{4 \over 5} ⋅ {1 \over p} = -{4 \over 5 p}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({8 p \over 3} + {p - 1 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 p \over 3} + {p - 1 \over 7} = {56 p \over 21} + {3 (p - 1) \over 21} = {56 p + 3 (p - 1) \over 21} = {59 p - 3 \over 21}\) 1p |
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| havo wiskunde A | 6.3 Formules met breuken |
opgave 1Herleid tot één breuk. 1p a \({9 y \over x} ⋅ {x - 7 \over 3}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 y \over x} ⋅ {x - 7 \over 3} = {9 y (x - 7) \over 3 x} = {3 y (x - 7) \over x} = {3 x y - 21 y \over x}\) 1p 1p b \({6 \over 5} : {a + 8 b \over b}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over 5} : {a + 8 b \over b} = {6 \over 5} ⋅ {b \over a + 8 b} = {6 b \over 5 (a + 8 b)} = {6 b \over 5 a + 40 b}\) 1p |
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| havo wiskunde A | 11.2 Herleiden en combineren van formules |
opgave 1Deel uit. 1p a \({a^{2} - 3 a - 20 \over a}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({a^{2} - 3 a - 20 \over a} = {a^{2} \over a} - {3 a \over a} - {20 \over a} = a - 3 - {20 \over a}\) 1p 1p b \({5 a^{2} + 4 a - 6 \over 3 a^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({5 a^{2} + 4 a - 6 \over 3 a^{2}} = {5 a^{2} \over 3 a^{2}} + {4 a \over 3 a^{2}} - {6 \over 3 a^{2}} = 1\frac{2}{3} + {4 \over 3 a} - {2 \over a^{2}}\) 1p |