Getal & Ruimte (12e editie) - havo wiskunde A
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({6 \over 8 a} + {2 \over 8 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({6 \over 8 a} + {2 \over 8 a} = {8 \over 8 a} = {1 \over a}\) 1p 1p b \({8 \over p} + {3 \over 7 p}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({8 \over p} + {3 \over 7 p} = {56 \over 7 p} + {3 \over 7 p} = {59 \over 7 p}\) 1p 1p c \({8 \over 7 x} - {2 \over 4 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over 7 x} - {2 \over 4 y} = {32 y \over 28 x y} - {14 x \over 28 x y} = {32 y - 14 x \over 28 x y} = {16 y - 7 x \over 14 x y}\) 1p 1p d \(3 + {8 \over 9 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(3 + {8 \over 9 a} = {3 \over 1} + {8 \over 9 a} = {27 a \over 9 a} + {8 \over 9 a} = {27 a + 8 \over 9 a}\) 1p opgave 2Herleid tot één breuk. 1p a \(8 x + {9 \over 5 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(8 x + {9 \over 5 x} = {8 x \over 1} ⋅ {5 x \over 5 x} + {9 \over 5 x} = {40 x^{2} \over 5 x} + {9 \over 5 x} = {40 x^{2} + 9 \over 5 x}\) 1p 1p b \({8 x \over y} - {5 \over 3 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({8 x \over y} - {5 \over 3 y} = {24 x \over 3 y} - {5 \over 3 y} = {24 x - 5 \over 3 y}\) 1p 1p c \({8 b \over 5 a} + {2 a \over 9 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 b \over 5 a} + {2 a \over 9 b} = {72 b^{2} \over 45 a b} + {10 a^{2} \over 45 a b} = {10 a^{2} + 72 b^{2} \over 45 a b}\) 1p opgave 3Herleid. 1p a \({5 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 a \over a} = {5 \over 1} = 5\) 1p 1p b \({x \over 9 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 9 x} = {1 \over 9}\) 1p 1p c \({30 p \over -35 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({30 p \over -35 p} = -\frac{6}{7}\) 1p 1p d \({15 a \over 3 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({15 a \over 3 a} = 5\) 1p opgave 4Herleid. 1p a \({-15 p q \over -20 p r}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-15 p q \over -20 p r} = {3 q \over 4 r}\) 1p 1p b \({25 y \over -35 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({25 y \over -35 x y} = -{5 \over 7 x}\) 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 \({4 a b \over b} - {3 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({4 a b \over b} - {3 a c \over c} = 4 a - 3 a = a\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({4 \over x} ⋅ -{3 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over x} ⋅ -{3 \over y} = -{12 \over x y}\) 1p 1p b \({a \over 2} ⋅ -{7 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 2} ⋅ -{7 \over b} = -{7 a \over 2 b}\) 1p 1p c \(-{4 \over 3} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{4 \over 3} ⋅ a = -{4 a \over 3}\) 1p 1p d \({7 \over x} : {4 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({7 \over x} : {4 \over y} = {7 \over x} ⋅ {y \over 4} = {7 y \over 4 x}\) 1p opgave 2Herleid tot één breuk. 1p \(-{7 \over 9} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{7 \over 9} : p = -{7 \over 9} : {p \over 1} = -{7 \over 9} ⋅ {1 \over p} = -{7 \over 9 p}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({a \over 6} + {a + 3 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 1ms - dynamic variables ○ \({a \over 6} + {a + 3 \over 7} = {7 a \over 42} + {6 (a + 3) \over 42} = {7 a + 6 (a + 3) \over 42} = {13 a + 18 \over 42}\) 1p |
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| havo wiskunde A | 6.3 Formules met breuken |
opgave 1Herleid tot één breuk. 1p a \({5 y \over x} ⋅ {x - 9 \over 8}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 y \over x} ⋅ {x - 9 \over 8} = {5 y (x - 9) \over 8 x} = {5 x y - 45 y \over 8 x}\) 1p 1p b \(-{5 \over 2} : {a - 3 b \over b}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables b \(-{5 \over 2} : {a - 3 b \over b} = -{5 \over 2} ⋅ {b \over a - 3 b} = -{5 b \over 2 (a - 3 b)} = -{5 b \over 2 a - 6 b}\) 1p |
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| havo wiskunde A | 11.2 Herleiden en combineren van formules |
opgave 1Deel uit. 1p a \({9 x^{2} - 6 x + 30 \over 3 x}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({9 x^{2} - 6 x + 30 \over 3 x} = {9 x^{2} \over 3 x} - {6 x \over 3 x} + {30 \over 3 x} = 3 x - 2 + {10 \over x}\) 1p 1p b \({6 x^{2} - 3 x - 9 \over x^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({6 x^{2} - 3 x - 9 \over x^{2}} = {6 x^{2} \over x^{2}} - {3 x \over x^{2}} - {9 \over x^{2}} = 6 - {3 \over x} - {9 \over x^{2}}\) 1p |