Getal & Ruimte (13e editie) - vwo wiskunde A
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({6 \over 7 p} - {2 \over 7 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({6 \over 7 p} - {2 \over 7 p} = {4 \over 7 p}\) 1p 1p b \({6 \over x} + {3 \over 5 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over x} + {3 \over 5 x} = {30 \over 5 x} + {3 \over 5 x} = {33 \over 5 x}\) 1p 1p c \({9 \over 3 a} + {6 \over 5 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over 3 a} + {6 \over 5 b} = {45 b \over 15 a b} + {18 a \over 15 a b} = {45 b + 18 a \over 15 a b} = {15 b + 6 a \over 5 a b}\) 1p 1p d \(4 + {7 \over 5 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(4 + {7 \over 5 a} = {4 \over 1} + {7 \over 5 a} = {20 a \over 5 a} + {7 \over 5 a} = {20 a + 7 \over 5 a}\) 1p opgave 2Herleid tot één breuk. 1p \({8 x \over y} + {3 \over 4 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 x \over y} + {3 \over 4 y} = {32 x \over 4 y} + {3 \over 4 y} = {32 x + 3 \over 4 y}\) 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 \({x \over 5 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 5 x} = {1 \over 5}\) 1p 1p c \({-8 p \over -18 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-8 p \over -18 p} = \frac{4}{9}\) 1p 1p d \({10 a \over -5 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({10 a \over -5 a} = -2\) 1p opgave 4Herleid. 1p a \({-20 x y \over 36 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-20 x y \over 36 x z} = -{5 y \over 9 z}\) 1p 1p b \({-8 b \over -12 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-8 b \over -12 a b} = {2 \over 3 a}\) 1p 1p c \({15 a b c \over -3 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({15 a b c \over -3 b c} = -5 a\) 1p 1p d \({7 x y \over y} + {2 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 x y \over y} + {2 x z \over z} = 7 x + 2 x = 9 x\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(7 p + {4 \over 3 p}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(7 p + {4 \over 3 p} = {7 p \over 1} ⋅ {3 p \over 3 p} + {4 \over 3 p} = {21 p^{2} \over 3 p} + {4 \over 3 p} = {21 p^{2} + 4 \over 3 p}\) 1p 1p b \({2 b \over 9 a} + {4 a \over 5 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({2 b \over 9 a} + {4 a \over 5 b} = {10 b^{2} \over 45 a b} + {36 a^{2} \over 45 a b} = {36 a^{2} + 10 b^{2} \over 45 a b}\) 1p 1p c \({9 \over x} ⋅ {5 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over x} ⋅ {5 \over y} = {45 \over x y}\) 1p 1p d \({x \over 8} ⋅ -{2 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({x \over 8} ⋅ -{2 \over y} = -{2 x \over 8 y} = -{x \over 4 y}\) 1p opgave 2Herleid tot één breuk. 1p a \({1 \over 3} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({1 \over 3} ⋅ a = {a \over 3}\) 1p 1p b \({3 b \over a} ⋅ {a + 9 \over 8}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 b \over a} ⋅ {a + 9 \over 8} = {3 b (a + 9) \over 8 a} = {3 a b + 27 b \over 8 a}\) 1p 1p c \({8 \over x} : {6 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over x} : {6 \over y} = {8 \over x} ⋅ {y \over 6} = {8 y \over 6 x} = {4 y \over 3 x}\) 1p 1p d \({8 \over 9} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \({8 \over 9} : a = {8 \over 9} : {a \over 1} = {8 \over 9} ⋅ {1 \over a} = {8 \over 9 a}\) 1p opgave 3Herleid tot één breuk. 1p a \({6 \over 7} : {x + 2 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({6 \over 7} : {x + 2 y \over y} = {6 \over 7} ⋅ {y \over x + 2 y} = {6 y \over 7 (x + 2 y)} = {6 y \over 7 x + 14 y}\) 1p 1p b \({7 p \over 9} + {p + 8 \over 4}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({7 p \over 9} + {p + 8 \over 4} = {28 p \over 36} + {9 (p + 8) \over 36} = {28 p + 9 (p + 8) \over 36} = {37 p + 72 \over 36}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-5 x + 8 \over 9 x - 3} - 1\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({-5 x + 8 \over 9 x - 3} - 1 = {-5 x + 8 \over 9 x - 3} - {1 (9 x - 3) \over 9 x - 3} = {-5 x + 8 - 1 (9 x - 3) \over 9 x - 3} = {-5 x + 8 - 9 x + 3 \over 9 x - 3} = {-14 x + 11 \over 9 x - 3}\) 1p |
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| vwo wiskunde A | 3.1 Breuken en verhoudingen |
opgave 1Deel uit. 1p a \({2 a^{2} - 4 a - 60 \over 2 a}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({2 a^{2} - 4 a - 60 \over 2 a} = {2 a^{2} \over 2 a} - {4 a \over 2 a} - {60 \over 2 a} = a - 2 - {30 \over a}\) 1p 1p b \({6 x^{2} - 7 x - 4 \over 8 x^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({6 x^{2} - 7 x - 4 \over 8 x^{2}} = {6 x^{2} \over 8 x^{2}} - {7 x \over 8 x^{2}} - {4 \over 8 x^{2}} = \frac{3}{4} - {7 \over 8 x} - {1 \over 2 x^{2}}\) 1p |