Getal & Ruimte (13e editie) - havo wiskunde A
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({9 \over 4 a} - {6 \over 4 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({9 \over 4 a} - {6 \over 4 a} = {3 \over 4 a}\) 1p 1p b \({2 \over p} + {8 \over 9 p}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({2 \over p} + {8 \over 9 p} = {18 \over 9 p} + {8 \over 9 p} = {26 \over 9 p}\) 1p 1p c \({6 \over 8 x} - {7 \over 4 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 8 x} - {7 \over 4 y} = {6 y \over 8 x y} - {14 x \over 8 x y} = {6 y - 14 x \over 8 x y} = {3 y - 7 x \over 4 x y}\) 1p 1p d \(4 - {5 \over 8 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(4 - {5 \over 8 x} = {4 \over 1} - {5 \over 8 x} = {32 x \over 8 x} - {5 \over 8 x} = {32 x - 5 \over 8 x}\) 1p opgave 2Herleid tot één breuk. 1p a \(4 a + {6 \over 7 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(4 a + {6 \over 7 a} = {4 a \over 1} ⋅ {7 a \over 7 a} + {6 \over 7 a} = {28 a^{2} \over 7 a} + {6 \over 7 a} = {28 a^{2} + 6 \over 7 a}\) 1p 1p b \({3 x \over y} + {4 \over 2 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({3 x \over y} + {4 \over 2 y} = {6 x \over 2 y} + {4 \over 2 y} = {6 x + 4 \over 2 y} = {3 x + 2 \over y}\) 1p 1p c \({7 b \over 5 a} - {8 a \over 4 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({7 b \over 5 a} - {8 a \over 4 b} = {28 b^{2} \over 20 a b} - {40 a^{2} \over 20 a b} = {-40 a^{2} + 28 b^{2} \over 20 a b} = {-10 a^{2} + 7 b^{2} \over 5 a b}\) 1p opgave 3Herleid. 1p a \({6 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({6 p \over p} = {6 \over 1} = 6\) 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 \({-32 x \over -36 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-32 x \over -36 x} = \frac{8}{9}\) 1p 1p d \({24 p \over 3 p}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({24 p \over 3 p} = 8\) 1p opgave 4Herleid. 1p a \({-10 x y \over -45 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-10 x y \over -45 x z} = {2 y \over 9 z}\) 1p 1p b \({6 b \over 16 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({6 b \over 16 a b} = {3 \over 8 a}\) 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 \({7 a b \over b} - {6 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 a b \over b} - {6 a c \over c} = 7 a - 6 a = a\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({7 \over a} ⋅ {3 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({7 \over a} ⋅ {3 \over b} = {21 \over a b}\) 1p 1p b \({p \over 8} ⋅ -{3 \over q}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 8} ⋅ -{3 \over q} = -{3 p \over 8 q}\) 1p 1p c \({6 \over 7} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 7} ⋅ x = {6 x \over 7}\) 1p 1p d \({9 \over x} : {7 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({9 \over x} : {7 \over y} = {9 \over x} ⋅ {y \over 7} = {9 y \over 7 x}\) 1p opgave 2Herleid tot één breuk. 1p \({8 \over 9} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 \over 9} : a = {8 \over 9} : {a \over 1} = {8 \over 9} ⋅ {1 \over a} = {8 \over 9 a}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({5 x \over 9} + {x - 3 \over 8}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({5 x \over 9} + {x - 3 \over 8} = {40 x \over 72} + {9 (x - 3) \over 72} = {40 x + 9 (x - 3) \over 72} = {49 x - 27 \over 72}\) 1p |
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| havo wiskunde A | 6.2 Formules met breuken |
opgave 1Herleid tot één breuk. 1p a \({8 \over 3} : {a - b \over b}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over 3} : {a - b \over b} = {8 \over 3} ⋅ {b \over a - b} = {8 b \over 3 (a - b)} = {8 b \over 3 a - 3 b}\) 1p 1p b \({4 x + 8 \over 7 x - 2} - 9\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables b \({4 x + 8 \over 7 x - 2} - 9 = {4 x + 8 \over 7 x - 2} - {9 (7 x - 2) \over 7 x - 2} = {4 x + 8 - 9 (7 x - 2) \over 7 x - 2} = {4 x + 8 - 63 x + 18 \over 7 x - 2} = {-59 x + 26 \over 7 x - 2}\) 1p |