Getal & Ruimte (13e editie) - havo wiskunde A
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({4 \over 7 x} - {2 \over 7 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 7 x} - {2 \over 7 x} = {2 \over 7 x}\) 1p 1p b \({7 \over a} + {9 \over 5 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({7 \over a} + {9 \over 5 a} = {35 \over 5 a} + {9 \over 5 a} = {44 \over 5 a}\) 1p 1p c \({5 \over 7 a} + {3 \over 2 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over 7 a} + {3 \over 2 b} = {10 b \over 14 a b} + {21 a \over 14 a b} = {10 b + 21 a \over 14 a b}\) 1p 1p d \(9 - {2 \over 3 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(9 - {2 \over 3 p} = {9 \over 1} - {2 \over 3 p} = {27 p \over 3 p} - {2 \over 3 p} = {27 p - 2 \over 3 p}\) 1p opgave 2Herleid tot één breuk. 1p a \(6 x - {7 \over 9 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(6 x - {7 \over 9 x} = {6 x \over 1} ⋅ {9 x \over 9 x} - {7 \over 9 x} = {54 x^{2} \over 9 x} - {7 \over 9 x} = {54 x^{2} - 7 \over 9 x}\) 1p 1p b \({3 x \over y} + {8 \over 6 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({3 x \over y} + {8 \over 6 y} = {18 x \over 6 y} + {8 \over 6 y} = {18 x + 8 \over 6 y} = {9 x + 4 \over 3 y}\) 1p 1p c \({6 b \over 9 a} - {2 a \over 5 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 b \over 9 a} - {2 a \over 5 b} = {30 b^{2} \over 45 a b} - {18 a^{2} \over 45 a b} = {-18 a^{2} + 30 b^{2} \over 45 a b} = {-6 a^{2} + 10 b^{2} \over 15 a b}\) 1p opgave 3Herleid. 1p a \({4 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 a \over a} = {4 \over 1} = 4\) 1p 1p b \({p \over 3 p}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 3 p} = {1 \over 3}\) 1p 1p c \({28 x \over -32 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({28 x \over -32 x} = -\frac{7}{8}\) 1p 1p d \({12 a \over -4 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({12 a \over -4 a} = -3\) 1p opgave 4Herleid. 1p a \({-16 p q \over -18 p r}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-16 p q \over -18 p r} = {8 q \over 9 r}\) 1p 1p b \({-16 y \over -18 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-16 y \over -18 x y} = {8 \over 9 x}\) 1p 1p c \({-6 a b c \over -2 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-6 a b c \over -2 b c} = 3 a\) 1p 1p d \({5 x y \over y} + {6 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({5 x y \over y} + {6 x z \over z} = 5 x + 6 x = 11 x\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({8 \over a} ⋅ -{7 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over a} ⋅ -{7 \over b} = -{56 \over a b}\) 1p 1p b \({a \over 4} ⋅ {9 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 4} ⋅ {9 \over b} = {9 a \over 4 b}\) 1p 1p c \({8 \over 9} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over 9} ⋅ x = {8 x \over 9}\) 1p 1p d \({5 \over p} : {7 \over q}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({5 \over p} : {7 \over q} = {5 \over p} ⋅ {q \over 7} = {5 q \over 7 p}\) 1p opgave 2Herleid tot één breuk. 1p \({4 \over 9} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({4 \over 9} : x = {4 \over 9} : {x \over 1} = {4 \over 9} ⋅ {1 \over x} = {4 \over 9 x}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({4 a \over 3} + {a + 9 \over 5}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({4 a \over 3} + {a + 9 \over 5} = {20 a \over 15} + {3 (a + 9) \over 15} = {20 a + 3 (a + 9) \over 15} = {23 a + 27 \over 15}\) 1p |
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| havo wiskunde A | 6.2 Formules met breuken |
opgave 1Herleid tot één breuk. 1p a \(-{5 \over 6} : {a + 8 b \over b}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{5 \over 6} : {a + 8 b \over b} = -{5 \over 6} ⋅ {b \over a + 8 b} = -{5 b \over 6 (a + 8 b)} = -{5 b \over 6 a + 48 b}\) 1p 1p b \({-9 x - 4 \over -2 x - 6} - 8\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables b \({-9 x - 4 \over -2 x - 6} - 8 = {-9 x - 4 \over -2 x - 6} + {-8 (-2 x - 6) \over -2 x - 6} = {-9 x - 4 - 8 (-2 x - 6) \over -2 x - 6} = {-9 x - 4 + 16 x + 48 \over -2 x - 6} = {7 x + 44 \over -2 x - 6}\) 1p |