Getal & Ruimte (13e editie) - havo wiskunde A
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({9 \over 7 p} + {4 \over 7 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({9 \over 7 p} + {4 \over 7 p} = {13 \over 7 p}\) 1p 1p b \({4 \over a} - {7 \over 6 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({4 \over a} - {7 \over 6 a} = {24 \over 6 a} - {7 \over 6 a} = {17 \over 6 a}\) 1p 1p c \({9 \over 2 x} + {6 \over 8 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over 2 x} + {6 \over 8 y} = {36 y \over 8 x y} + {6 x \over 8 x y} = {36 y + 6 x \over 8 x y} = {18 y + 3 x \over 4 x y}\) 1p 1p d \(7 - {5 \over 6 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(7 - {5 \over 6 x} = {7 \over 1} - {5 \over 6 x} = {42 x \over 6 x} - {5 \over 6 x} = {42 x - 5 \over 6 x}\) 1p opgave 2Herleid tot één breuk. 1p a \(6 a + {5 \over 8 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(6 a + {5 \over 8 a} = {6 a \over 1} ⋅ {8 a \over 8 a} + {5 \over 8 a} = {48 a^{2} \over 8 a} + {5 \over 8 a} = {48 a^{2} + 5 \over 8 a}\) 1p 1p b \({3 a \over b} + {9 \over 5 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({3 a \over b} + {9 \over 5 b} = {15 a \over 5 b} + {9 \over 5 b} = {15 a + 9 \over 5 b}\) 1p 1p c \({5 y \over 6 x} - {7 x \over 3 y}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({5 y \over 6 x} - {7 x \over 3 y} = {5 y^{2} \over 6 x y} - {14 x^{2} \over 6 x y} = {-14 x^{2} + 5 y^{2} \over 6 x y}\) 1p opgave 3Herleid. 1p a \({2 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 a \over a} = {2 \over 1} = 2\) 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 \({8 p \over -20 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 p \over -20 p} = -\frac{2}{5}\) 1p 1p d \({25 a \over -5 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({25 a \over -5 a} = -5\) 1p opgave 4Herleid. 1p a \({12 x y \over -20 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({12 x y \over -20 x z} = -{3 y \over 5 z}\) 1p 1p b \({-15 b \over 25 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-15 b \over 25 a b} = -{3 \over 5 a}\) 1p 1p c \({14 x y z \over 2 y z}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({14 x y z \over 2 y z} = 7 x\) 1p 1p d \({4 p q \over q} + {5 p r \over r}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({4 p q \over q} + {5 p r \over r} = 4 p + 5 p = 9 p\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({7 \over a} ⋅ {2 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({7 \over a} ⋅ {2 \over b} = {14 \over a b}\) 1p 1p b \({p \over 4} ⋅ {3 \over q}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 4} ⋅ {3 \over q} = {3 p \over 4 q}\) 1p 1p c \({4 \over 7} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({4 \over 7} ⋅ a = {4 a \over 7}\) 1p 1p d \({6 \over x} : {7 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({6 \over x} : {7 \over y} = {6 \over x} ⋅ {y \over 7} = {6 y \over 7 x}\) 1p opgave 2Herleid tot één breuk. 1p \(-{6 \over 5} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{6 \over 5} : x = -{6 \over 5} : {x \over 1} = -{6 \over 5} ⋅ {1 \over x} = -{6 \over 5 x}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({8 a \over 5} + {a + 1 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 a \over 5} + {a + 1 \over 7} = {56 a \over 35} + {5 (a + 1) \over 35} = {56 a + 5 (a + 1) \over 35} = {61 a + 5 \over 35}\) 1p |
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| havo wiskunde A | 6.2 Formules met breuken |
opgave 1Herleid tot één breuk. 1p a \({5 \over 4} : {x - 8 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 \over 4} : {x - 8 y \over y} = {5 \over 4} ⋅ {y \over x - 8 y} = {5 y \over 4 (x - 8 y)} = {5 y \over 4 x - 32 y}\) 1p 1p b \({-4 a + 1 \over -7 a + 6} - 3\) Optellen (9) 00eh - Breuken herleiden - basis - 1ms - dynamic variables b \({-4 a + 1 \over -7 a + 6} - 3 = {-4 a + 1 \over -7 a + 6} + {-3 (-7 a + 6) \over -7 a + 6} = {-4 a + 1 - 3 (-7 a + 6) \over -7 a + 6} = {-4 a + 1 + 21 a - 18 \over -7 a + 6} = {17 a - 17 \over -7 a + 6}\) 1p |