Getal & Ruimte (13e editie) - vwo wiskunde C
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({6 \over 8 x} + {2 \over 8 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({6 \over 8 x} + {2 \over 8 x} = {8 \over 8 x} = {1 \over x}\) 1p 1p b \({8 \over a} + {9 \over 5 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({8 \over a} + {9 \over 5 a} = {40 \over 5 a} + {9 \over 5 a} = {49 \over 5 a}\) 1p 1p c \({5 \over 9 x} - {7 \over 8 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over 9 x} - {7 \over 8 y} = {40 y \over 72 x y} - {63 x \over 72 x y} = {40 y - 63 x \over 72 x y}\) 1p 1p d \(7 + {4 \over 9 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(7 + {4 \over 9 a} = {7 \over 1} + {4 \over 9 a} = {63 a \over 9 a} + {4 \over 9 a} = {63 a + 4 \over 9 a}\) 1p opgave 2Herleid tot één breuk. 1p \({3 p \over q} - {2 \over 8 q}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({3 p \over q} - {2 \over 8 q} = {24 p \over 8 q} - {2 \over 8 q} = {24 p - 2 \over 8 q} = {12 p - 1 \over 4 q}\) 1p opgave 3Herleid. 1p a \({7 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({7 a \over a} = {7 \over 1} = 7\) 1p 1p b \({a \over 6 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 6 a} = {1 \over 6}\) 1p 1p c \({20 p \over -25 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({20 p \over -25 p} = -\frac{4}{5}\) 1p 1p d \({25 x \over -5 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({25 x \over -5 x} = -5\) 1p opgave 4Herleid. 1p a \({20 x y \over -32 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({20 x y \over -32 x z} = -{5 y \over 8 z}\) 1p 1p b \({-16 y \over 20 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-16 y \over 20 x y} = -{4 \over 5 x}\) 1p 1p c \({-25 a b c \over 5 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-25 a b c \over 5 b c} = -5 a\) 1p 1p d \({2 p q \over q} + {7 p r \over r}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({2 p q \over q} + {7 p r \over r} = 2 p + 7 p = 9 p\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(4 x - {3 \over 7 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(4 x - {3 \over 7 x} = {4 x \over 1} ⋅ {7 x \over 7 x} - {3 \over 7 x} = {28 x^{2} \over 7 x} - {3 \over 7 x} = {28 x^{2} - 3 \over 7 x}\) 1p 1p b \({3 b \over 2 a} - {4 a \over 7 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 b \over 2 a} - {4 a \over 7 b} = {21 b^{2} \over 14 a b} - {8 a^{2} \over 14 a b} = {-8 a^{2} + 21 b^{2} \over 14 a b}\) 1p 1p c \({2 \over p} ⋅ -{5 \over q}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({2 \over p} ⋅ -{5 \over q} = -{10 \over p q}\) 1p 1p d \({a \over 7} ⋅ {4 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({a \over 7} ⋅ {4 \over b} = {4 a \over 7 b}\) 1p opgave 2Herleid tot één breuk. 1p a \({3 \over 5} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 5} ⋅ x = {3 x \over 5}\) 1p 1p b \({9 y \over x} ⋅ {x + 2 \over 8}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({9 y \over x} ⋅ {x + 2 \over 8} = {9 y (x + 2) \over 8 x} = {9 x y + 18 y \over 8 x}\) 1p 1p c \({9 \over p} : {5 \over q}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over p} : {5 \over q} = {9 \over p} ⋅ {q \over 5} = {9 q \over 5 p}\) 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 \({6 \over 5} : {a - 7 b \over b}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({6 \over 5} : {a - 7 b \over b} = {6 \over 5} ⋅ {b \over a - 7 b} = {6 b \over 5 (a - 7 b)} = {6 b \over 5 a - 35 b}\) 1p 1p b \({3 a \over 4} + {a - 2 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 a \over 4} + {a - 2 \over 7} = {21 a \over 28} + {4 (a - 2) \over 28} = {21 a + 4 (a - 2) \over 28} = {25 a - 8 \over 28}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({4 a + 7 \over 2 a - 3} + 6\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({4 a + 7 \over 2 a - 3} + 6 = {4 a + 7 \over 2 a - 3} + {6 (2 a - 3) \over 2 a - 3} = {4 a + 7 + 6 (2 a - 3) \over 2 a - 3} = {4 a + 7 + 12 a - 18 \over 2 a - 3} = {16 a - 11 \over 2 a - 3}\) 1p |
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| vwo wiskunde A | 3.1 Breuken en verhoudingen |
opgave 1Deel uit. 1p a \({3 a^{2} - a + 20 \over a}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({3 a^{2} - a + 20 \over a} = {3 a^{2} \over a} - {a \over a} + {20 \over a} = 3 a - 1 + {20 \over a}\) 1p 1p b \({4 x^{2} - 9 x + 3 \over 5 x^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({4 x^{2} - 9 x + 3 \over 5 x^{2}} = {4 x^{2} \over 5 x^{2}} - {9 x \over 5 x^{2}} + {3 \over 5 x^{2}} = \frac{4}{5} - {9 \over 5 x} + {3 \over 5 x^{2}}\) 1p |