Getal & Ruimte (13e editie) - havo wiskunde A
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({3 \over 5 p} + {2 \over 5 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 5 p} + {2 \over 5 p} = {5 \over 5 p} = {1 \over p}\) 1p 1p b \({8 \over x} + {2 \over 9 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({8 \over x} + {2 \over 9 x} = {72 \over 9 x} + {2 \over 9 x} = {74 \over 9 x}\) 1p 1p c \({9 \over 5 x} + {6 \over 2 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over 5 x} + {6 \over 2 y} = {18 y \over 10 x y} + {30 x \over 10 x y} = {18 y + 30 x \over 10 x y} = {9 y + 15 x \over 5 x y}\) 1p 1p d \(2 - {5 \over 8 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(2 - {5 \over 8 a} = {2 \over 1} - {5 \over 8 a} = {16 a \over 8 a} - {5 \over 8 a} = {16 a - 5 \over 8 a}\) 1p opgave 2Herleid tot één breuk. 1p a \(4 a - {7 \over 2 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(4 a - {7 \over 2 a} = {4 a \over 1} ⋅ {2 a \over 2 a} - {7 \over 2 a} = {8 a^{2} \over 2 a} - {7 \over 2 a} = {8 a^{2} - 7 \over 2 a}\) 1p 1p b \({5 x \over y} - {4 \over 6 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({5 x \over y} - {4 \over 6 y} = {30 x \over 6 y} - {4 \over 6 y} = {30 x - 4 \over 6 y} = {15 x - 2 \over 3 y}\) 1p 1p c \({9 y \over 2 x} + {3 x \over 7 y}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 y \over 2 x} + {3 x \over 7 y} = {63 y^{2} \over 14 x y} + {6 x^{2} \over 14 x y} = {6 x^{2} + 63 y^{2} \over 14 x y}\) 1p opgave 3Herleid. 1p a \({4 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 p \over p} = {4 \over 1} = 4\) 1p 1p b \({a \over 9 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 9 a} = {1 \over 9}\) 1p 1p c \({-10 a \over -45 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-10 a \over -45 a} = \frac{2}{9}\) 1p 1p d \({-6 a \over -3 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-6 a \over -3 a} = 2\) 1p opgave 4Herleid. 1p a \({-6 p q \over 10 p r}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-6 p q \over 10 p r} = -{3 q \over 5 r}\) 1p 1p b \({-4 y \over 6 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-4 y \over 6 x y} = -{2 \over 3 x}\) 1p 1p c \({15 x y z \over -5 y z}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({15 x y z \over -5 y z} = -3 x\) 1p 1p d \({6 a b \over b} + {4 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({6 a b \over b} + {4 a c \over c} = 6 a + 4 a = 10 a\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({3 \over x} ⋅ -{8 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over x} ⋅ -{8 \over y} = -{24 \over x y}\) 1p 1p b \({a \over 7} ⋅ -{4 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 7} ⋅ -{4 \over b} = -{4 a \over 7 b}\) 1p 1p c \(-{9 \over 7} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{9 \over 7} ⋅ x = -{9 x \over 7}\) 1p 1p d \({7 \over p} : {4 \over q}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({7 \over p} : {4 \over q} = {7 \over p} ⋅ {q \over 4} = {7 q \over 4 p}\) 1p opgave 2Herleid tot één breuk. 1p \(-{7 \over 8} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{7 \over 8} : a = -{7 \over 8} : {a \over 1} = -{7 \over 8} ⋅ {1 \over a} = -{7 \over 8 a}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({8 a \over 3} + {a - 6 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 a \over 3} + {a - 6 \over 7} = {56 a \over 21} + {3 (a - 6) \over 21} = {56 a + 3 (a - 6) \over 21} = {59 a - 18 \over 21}\) 1p |
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| havo wiskunde A | 6.2 Formules met breuken |
opgave 1Herleid tot één breuk. 1p a \(-{9 \over 4} : {p - 8 q \over q}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{9 \over 4} : {p - 8 q \over q} = -{9 \over 4} ⋅ {q \over p - 8 q} = -{9 q \over 4 (p - 8 q)} = -{9 q \over 4 p - 32 q}\) 1p 1p b \({-9 a - 8 \over -4 a + 1} + 5\) Optellen (9) 00eh - Breuken herleiden - basis - 1ms - dynamic variables b \({-9 a - 8 \over -4 a + 1} + 5 = {-9 a - 8 \over -4 a + 1} - {-5 (-4 a + 1) \over -4 a + 1} = {-9 a - 8 + 5 (-4 a + 1) \over -4 a + 1} = {-9 a - 8 - 20 a + 5 \over -4 a + 1} = {-29 a - 3 \over -4 a + 1}\) 1p |