Getal & Ruimte (13e editie) - vwo wiskunde C
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({6 \over 2 a} - {8 \over 2 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({6 \over 2 a} - {8 \over 2 a} = -{2 \over 2 a} = -{1 \over a}\) 1p 1p b \({7 \over p} - {6 \over 4 p}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({7 \over p} - {6 \over 4 p} = {28 \over 4 p} - {6 \over 4 p} = {22 \over 4 p} = {11 \over 2 p}\) 1p 1p c \({7 \over 5 x} - {8 \over 2 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 5 x} - {8 \over 2 y} = {14 y \over 10 x y} - {40 x \over 10 x y} = {14 y - 40 x \over 10 x y} = {7 y - 20 x \over 5 x y}\) 1p 1p d \(2 + {5 \over 8 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(2 + {5 \over 8 x} = {2 \over 1} + {5 \over 8 x} = {16 x \over 8 x} + {5 \over 8 x} = {16 x + 5 \over 8 x}\) 1p opgave 2Herleid tot één breuk. 1p \({4 a \over b} + {3 \over 9 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({4 a \over b} + {3 \over 9 b} = {36 a \over 9 b} + {3 \over 9 b} = {36 a + 3 \over 9 b} = {12 a + 1 \over 3 b}\) 1p opgave 3Herleid. 1p a \({8 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 p \over p} = {8 \over 1} = 8\) 1p 1p b \({a \over 2 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 2 a} = {1 \over 2}\) 1p 1p c \({12 x \over 16 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({12 x \over 16 x} = \frac{3}{4}\) 1p 1p d \({-28 a \over 4 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-28 a \over 4 a} = -7\) 1p opgave 4Herleid. 1p a \({-8 x y \over 28 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-8 x y \over 28 x z} = -{2 y \over 7 z}\) 1p 1p b \({6 y \over 15 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({6 y \over 15 x y} = {2 \over 5 x}\) 1p 1p c \({10 a b c \over 5 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({10 a b c \over 5 b c} = 2 a\) 1p 1p d \({3 x y \over y} + {5 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({3 x y \over y} + {5 x z \over z} = 3 x + 5 x = 8 x\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(2 a + {5 \over 8 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(2 a + {5 \over 8 a} = {2 a \over 1} ⋅ {8 a \over 8 a} + {5 \over 8 a} = {16 a^{2} \over 8 a} + {5 \over 8 a} = {16 a^{2} + 5 \over 8 a}\) 1p 1p b \({7 q \over 4 p} - {5 p \over 2 q}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({7 q \over 4 p} - {5 p \over 2 q} = {7 q^{2} \over 4 p q} - {10 p^{2} \over 4 p q} = {-10 p^{2} + 7 q^{2} \over 4 p q}\) 1p 1p c \({7 \over x} ⋅ {3 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over x} ⋅ {3 \over y} = {21 \over x y}\) 1p 1p d \({x \over 2} ⋅ -{7 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({x \over 2} ⋅ -{7 \over y} = -{7 x \over 2 y}\) 1p opgave 2Herleid tot één breuk. 1p a \({8 \over 3} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over 3} ⋅ a = {8 a \over 3}\) 1p 1p b \({6 b \over a} ⋅ {a - 3 \over 8}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({6 b \over a} ⋅ {a - 3 \over 8} = {6 b (a - 3) \over 8 a} = {3 b (a - 3) \over 4 a} = {3 a b - 9 b \over 4 a}\) 1p 1p c \({3 \over x} : {8 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({3 \over x} : {8 \over y} = {3 \over x} ⋅ {y \over 8} = {3 y \over 8 x}\) 1p 1p d \(-{2 \over 7} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{2 \over 7} : a = -{2 \over 7} : {a \over 1} = -{2 \over 7} ⋅ {1 \over a} = -{2 \over 7 a}\) 1p opgave 3Herleid tot één breuk. 1p a \(-{4 \over 3} : {p - 6 q \over q}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{4 \over 3} : {p - 6 q \over q} = -{4 \over 3} ⋅ {q \over p - 6 q} = -{4 q \over 3 (p - 6 q)} = -{4 q \over 3 p - 18 q}\) 1p 1p b \({3 x \over 7} + {x + 5 \over 9}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 x \over 7} + {x + 5 \over 9} = {27 x \over 63} + {7 (x + 5) \over 63} = {27 x + 7 (x + 5) \over 63} = {34 x + 35 \over 63}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-8 a + 9 \over -3 a + 4} - 2\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({-8 a + 9 \over -3 a + 4} - 2 = {-8 a + 9 \over -3 a + 4} + {-2 (-3 a + 4) \over -3 a + 4} = {-8 a + 9 - 2 (-3 a + 4) \over -3 a + 4} = {-8 a + 9 + 6 a - 8 \over -3 a + 4} = {-2 a + 1 \over -3 a + 4}\) 1p |
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| vwo wiskunde A | 3.1 Breuken en verhoudingen |
opgave 1Deel uit. 1p a \({3 p^{2} + 6 p + 90 \over 3 p}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({3 p^{2} + 6 p + 90 \over 3 p} = {3 p^{2} \over 3 p} + {6 p \over 3 p} + {90 \over 3 p} = p + 2 + {30 \over p}\) 1p 1p b \({9 x^{2} - 7 x - 2 \over 6 x^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({9 x^{2} - 7 x - 2 \over 6 x^{2}} = {9 x^{2} \over 6 x^{2}} - {7 x \over 6 x^{2}} - {2 \over 6 x^{2}} = 1\frac{1}{2} - {7 \over 6 x} - {1 \over 3 x^{2}}\) 1p |