Getal & Ruimte (13e editie) - vwo wiskunde B
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({9 \over 7 a} + {5 \over 7 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({9 \over 7 a} + {5 \over 7 a} = {14 \over 7 a} = {2 \over a}\) 1p 1p b \({4 \over x} - {5 \over 3 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({4 \over x} - {5 \over 3 x} = {12 \over 3 x} - {5 \over 3 x} = {7 \over 3 x}\) 1p 1p c \({4 \over 9 a} - {5 \over 7 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({4 \over 9 a} - {5 \over 7 b} = {28 b \over 63 a b} - {45 a \over 63 a b} = {28 b - 45 a \over 63 a b}\) 1p 1p d \(6 + {9 \over 4 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(6 + {9 \over 4 x} = {6 \over 1} + {9 \over 4 x} = {24 x \over 4 x} + {9 \over 4 x} = {24 x + 9 \over 4 x}\) 1p opgave 2Herleid tot één breuk. 1p \({4 p \over q} + {3 \over 2 q}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({4 p \over q} + {3 \over 2 q} = {8 p \over 2 q} + {3 \over 2 q} = {8 p + 3 \over 2 q}\) 1p opgave 3Herleid. 1p a \({5 x \over x}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 x \over x} = {5 \over 1} = 5\) 1p 1p b \({x \over 2 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 2 x} = {1 \over 2}\) 1p 1p c \({-10 p \over 45 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-10 p \over 45 p} = -\frac{2}{9}\) 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 \({30 a b \over 35 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({30 a b \over 35 a c} = {6 b \over 7 c}\) 1p 1p b \({9 y \over -21 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({9 y \over -21 x y} = -{3 \over 7 x}\) 1p 1p c \({21 a b c \over -3 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({21 a b c \over -3 b c} = -7 a\) 1p 1p d \({7 a b \over b} - {2 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 a b \over b} - {2 a c \over c} = 7 a - 2 a = 5 a\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(4 x - {9 \over 2 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(4 x - {9 \over 2 x} = {4 x \over 1} ⋅ {2 x \over 2 x} - {9 \over 2 x} = {8 x^{2} \over 2 x} - {9 \over 2 x} = {8 x^{2} - 9 \over 2 x}\) 1p 1p b \({3 b \over 5 a} + {8 a \over 6 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 b \over 5 a} + {8 a \over 6 b} = {18 b^{2} \over 30 a b} + {40 a^{2} \over 30 a b} = {40 a^{2} + 18 b^{2} \over 30 a b} = {20 a^{2} + 9 b^{2} \over 15 a b}\) 1p 1p c \({6 \over p} ⋅ -{2 \over q}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over p} ⋅ -{2 \over q} = -{12 \over p q}\) 1p 1p d \({x \over 3} ⋅ -{5 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({x \over 3} ⋅ -{5 \over y} = -{5 x \over 3 y}\) 1p opgave 2Herleid tot één breuk. 1p a \({5 \over 8} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 \over 8} ⋅ a = {5 a \over 8}\) 1p 1p b \({3 b \over a} ⋅ {a - 9 \over 2}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 b \over a} ⋅ {a - 9 \over 2} = {3 b (a - 9) \over 2 a} = {3 a b - 27 b \over 2 a}\) 1p 1p c \({2 \over x} : {6 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({2 \over x} : {6 \over y} = {2 \over x} ⋅ {y \over 6} = {2 y \over 6 x} = {y \over 3 x}\) 1p 1p d \(-{9 \over 2} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{9 \over 2} : p = -{9 \over 2} : {p \over 1} = -{9 \over 2} ⋅ {1 \over p} = -{9 \over 2 p}\) 1p opgave 3Herleid tot één breuk. 1p a \({5 \over 4} : {x + 9 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 \over 4} : {x + 9 y \over y} = {5 \over 4} ⋅ {y \over x + 9 y} = {5 y \over 4 (x + 9 y)} = {5 y \over 4 x + 36 y}\) 1p 1p b \({7 a \over 9} + {a + 4 \over 5}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({7 a \over 9} + {a + 4 \over 5} = {35 a \over 45} + {9 (a + 4) \over 45} = {35 a + 9 (a + 4) \over 45} = {44 a + 36 \over 45}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-8 x + 2 \over 6 x - 4} - 3\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({-8 x + 2 \over 6 x - 4} - 3 = {-8 x + 2 \over 6 x - 4} - {3 (6 x - 4) \over 6 x - 4} = {-8 x + 2 - 3 (6 x - 4) \over 6 x - 4} = {-8 x + 2 - 18 x + 12 \over 6 x - 4} = {-26 x + 14 \over 6 x - 4}\) 1p |
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| vwo wiskunde B | 4.4 Formules met breuken herleiden |
opgave 1Deel uit. 1p a \({3 x^{2} + 9 x + 60 \over 3 x}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({3 x^{2} + 9 x + 60 \over 3 x} = {3 x^{2} \over 3 x} + {9 x \over 3 x} + {60 \over 3 x} = x + 3 + {20 \over x}\) 1p 1p b \({3 x^{2} - 8 x - 7 \over x^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({3 x^{2} - 8 x - 7 \over x^{2}} = {3 x^{2} \over x^{2}} - {8 x \over x^{2}} - {7 \over x^{2}} = 3 - {8 \over x} - {7 \over x^{2}}\) 1p |