Getal & Ruimte (13e editie) - vwo wiskunde A
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({3 \over 8 a} - {2 \over 8 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 8 a} - {2 \over 8 a} = {1 \over 8 a}\) 1p 1p b \({2 \over p} + {8 \over 4 p}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({2 \over p} + {8 \over 4 p} = {8 \over 4 p} + {8 \over 4 p} = {16 \over 4 p} = {4 \over p}\) 1p 1p c \({7 \over 3 a} - {8 \over 6 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 3 a} - {8 \over 6 b} = {14 b \over 6 a b} - {8 a \over 6 a b} = {14 b - 8 a \over 6 a b} = {7 b - 4 a \over 3 a b}\) 1p 1p d \(9 - {7 \over 2 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(9 - {7 \over 2 x} = {9 \over 1} - {7 \over 2 x} = {18 x \over 2 x} - {7 \over 2 x} = {18 x - 7 \over 2 x}\) 1p opgave 2Herleid tot één breuk. 1p \({9 x \over y} - {8 \over 4 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({9 x \over y} - {8 \over 4 y} = {36 x \over 4 y} - {8 \over 4 y} = {36 x - 8 \over 4 y} = {9 x - 2 \over y}\) 1p opgave 3Herleid. 1p a \({4 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 p \over p} = {4 \over 1} = 4\) 1p 1p b \({x \over 7 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 7 x} = {1 \over 7}\) 1p 1p c \({10 a \over 25 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({10 a \over 25 a} = \frac{2}{5}\) 1p 1p d \({-12 x \over -2 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-12 x \over -2 x} = 6\) 1p opgave 4Herleid. 1p a \({-35 a b \over -45 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-35 a b \over -45 a c} = {7 b \over 9 c}\) 1p 1p b \({-15 y \over -35 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-15 y \over -35 x y} = {3 \over 7 x}\) 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 \({4 a b \over b} - {3 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({4 a b \over b} - {3 a c \over c} = 4 a - 3 a = a\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(5 p + {3 \over 8 p}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(5 p + {3 \over 8 p} = {5 p \over 1} ⋅ {8 p \over 8 p} + {3 \over 8 p} = {40 p^{2} \over 8 p} + {3 \over 8 p} = {40 p^{2} + 3 \over 8 p}\) 1p 1p b \({8 b \over 6 a} - {4 a \over 3 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({8 b \over 6 a} - {4 a \over 3 b} = {8 b^{2} \over 6 a b} - {8 a^{2} \over 6 a b} = {-8 a^{2} + 8 b^{2} \over 6 a b} = {-4 a^{2} + 4 b^{2} \over 3 a b}\) 1p 1p c \({6 \over x} ⋅ -{5 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over x} ⋅ -{5 \over y} = -{30 \over x y}\) 1p 1p d \({a \over 2} ⋅ {4 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({a \over 2} ⋅ {4 \over b} = {4 a \over 2 b} = {2 a \over b}\) 1p opgave 2Herleid tot één breuk. 1p a \(-{9 \over 4} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{9 \over 4} ⋅ x = -{9 x \over 4}\) 1p 1p b \({9 b \over a} ⋅ {a + 8 \over 6}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({9 b \over a} ⋅ {a + 8 \over 6} = {9 b (a + 8) \over 6 a} = {3 b (a + 8) \over 2 a} = {3 a b + 24 b \over 2 a}\) 1p 1p c \({7 \over a} : {9 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over a} : {9 \over b} = {7 \over a} ⋅ {b \over 9} = {7 b \over 9 a}\) 1p 1p d \(-{9 \over 2} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{9 \over 2} : x = -{9 \over 2} : {x \over 1} = -{9 \over 2} ⋅ {1 \over x} = -{9 \over 2 x}\) 1p opgave 3Herleid tot één breuk. 1p a \(-{6 \over 7} : {x - 9 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{6 \over 7} : {x - 9 y \over y} = -{6 \over 7} ⋅ {y \over x - 9 y} = -{6 y \over 7 (x - 9 y)} = -{6 y \over 7 x - 63 y}\) 1p 1p b \({3 p \over 2} + {p + 6 \over 5}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 p \over 2} + {p + 6 \over 5} = {15 p \over 10} + {2 (p + 6) \over 10} = {15 p + 2 (p + 6) \over 10} = {17 p + 12 \over 10}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-9 x - 7 \over 2 x - 4} + 3\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({-9 x - 7 \over 2 x - 4} + 3 = {-9 x - 7 \over 2 x - 4} + {3 (2 x - 4) \over 2 x - 4} = {-9 x - 7 + 3 (2 x - 4) \over 2 x - 4} = {-9 x - 7 + 6 x - 12 \over 2 x - 4} = {-3 x - 19 \over 2 x - 4}\) 1p |
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| vwo wiskunde A | 3.1 Breuken en verhoudingen |
opgave 1Deel uit. 1p a \({6 a^{2} - 2 a - 40 \over 2 a}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({6 a^{2} - 2 a - 40 \over 2 a} = {6 a^{2} \over 2 a} - {2 a \over 2 a} - {40 \over 2 a} = 3 a - 1 - {20 \over a}\) 1p 1p b \({a^{2} - 5 a + 8 \over 4 a^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({a^{2} - 5 a + 8 \over 4 a^{2}} = {a^{2} \over 4 a^{2}} - {5 a \over 4 a^{2}} + {8 \over 4 a^{2}} = \frac{1}{4} - {5 \over 4 a} + {2 \over a^{2}}\) 1p |