Getal & Ruimte (13e editie) - vwo wiskunde A
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({4 \over 9 x} - {7 \over 9 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 9 x} - {7 \over 9 x} = -{3 \over 9 x} = -{1 \over 3 x}\) 1p 1p b \({7 \over p} + {8 \over 3 p}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({7 \over p} + {8 \over 3 p} = {21 \over 3 p} + {8 \over 3 p} = {29 \over 3 p}\) 1p 1p c \({3 \over 8 a} + {6 \over 7 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({3 \over 8 a} + {6 \over 7 b} = {21 b \over 56 a b} + {48 a \over 56 a b} = {21 b + 48 a \over 56 a b}\) 1p 1p d \(7 + {8 \over 5 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(7 + {8 \over 5 a} = {7 \over 1} + {8 \over 5 a} = {35 a \over 5 a} + {8 \over 5 a} = {35 a + 8 \over 5 a}\) 1p opgave 2Herleid tot één breuk. 1p \({8 x \over y} - {5 \over 4 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 x \over y} - {5 \over 4 y} = {32 x \over 4 y} - {5 \over 4 y} = {32 x - 5 \over 4 y}\) 1p opgave 3Herleid. 1p a \({9 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 p \over p} = {9 \over 1} = 9\) 1p 1p b \({a \over 8 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 8 a} = {1 \over 8}\) 1p 1p c \({-4 x \over 18 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-4 x \over 18 x} = -\frac{2}{9}\) 1p 1p d \({20 x \over -4 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({20 x \over -4 x} = -5\) 1p opgave 4Herleid. 1p a \({-20 a b \over -36 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-20 a b \over -36 a c} = {5 b \over 9 c}\) 1p 1p b \({-20 y \over 36 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-20 y \over 36 x y} = -{5 \over 9 x}\) 1p 1p c \({-45 a b c \over -5 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-45 a b c \over -5 b c} = 9 a\) 1p 1p d \({5 a b \over b} + {2 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({5 a b \over b} + {2 a c \over c} = 5 a + 2 a = 7 a\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(9 a + {7 \over 2 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(9 a + {7 \over 2 a} = {9 a \over 1} ⋅ {2 a \over 2 a} + {7 \over 2 a} = {18 a^{2} \over 2 a} + {7 \over 2 a} = {18 a^{2} + 7 \over 2 a}\) 1p 1p b \({3 b \over 7 a} + {2 a \over 8 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 b \over 7 a} + {2 a \over 8 b} = {24 b^{2} \over 56 a b} + {14 a^{2} \over 56 a b} = {14 a^{2} + 24 b^{2} \over 56 a b} = {7 a^{2} + 12 b^{2} \over 28 a b}\) 1p 1p c \({9 \over p} ⋅ {7 \over q}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over p} ⋅ {7 \over q} = {63 \over p q}\) 1p 1p d \({x \over 5} ⋅ -{3 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({x \over 5} ⋅ -{3 \over y} = -{3 x \over 5 y}\) 1p opgave 2Herleid tot één breuk. 1p a \(-{4 \over 9} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{4 \over 9} ⋅ x = -{4 x \over 9}\) 1p 1p b \({5 y \over x} ⋅ {x - 4 \over 3}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({5 y \over x} ⋅ {x - 4 \over 3} = {5 y (x - 4) \over 3 x} = {5 x y - 20 y \over 3 x}\) 1p 1p c \({8 \over a} : {3 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over a} : {3 \over b} = {8 \over a} ⋅ {b \over 3} = {8 b \over 3 a}\) 1p 1p d \(-{4 \over 7} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{4 \over 7} : p = -{4 \over 7} : {p \over 1} = -{4 \over 7} ⋅ {1 \over p} = -{4 \over 7 p}\) 1p opgave 3Herleid tot één breuk. 1p a \({7 \over 4} : {a + 2 b \over b}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({7 \over 4} : {a + 2 b \over b} = {7 \over 4} ⋅ {b \over a + 2 b} = {7 b \over 4 (a + 2 b)} = {7 b \over 4 a + 8 b}\) 1p 1p b \({9 x \over 5} + {x - 4 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({9 x \over 5} + {x - 4 \over 7} = {63 x \over 35} + {5 (x - 4) \over 35} = {63 x + 5 (x - 4) \over 35} = {68 x - 20 \over 35}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-4 x - 2 \over -9 x + 6} - 3\) Optellen (9) 00eh - Breuken herleiden - basis - 1ms - dynamic variables ○ \({-4 x - 2 \over -9 x + 6} - 3 = {-4 x - 2 \over -9 x + 6} + {-3 (-9 x + 6) \over -9 x + 6} = {-4 x - 2 - 3 (-9 x + 6) \over -9 x + 6} = {-4 x - 2 + 27 x - 18 \over -9 x + 6} = {23 x - 20 \over -9 x + 6}\) 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 \({9 x^{2} + 7 x + 1 \over 2 x^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({9 x^{2} + 7 x + 1 \over 2 x^{2}} = {9 x^{2} \over 2 x^{2}} + {7 x \over 2 x^{2}} + {1 \over 2 x^{2}} = 4\frac{1}{2} + {7 \over 2 x} + {1 \over 2 x^{2}}\) 1p |