Getal & Ruimte (13e editie) - 3 vwo
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({8 \over 4 x} + {2 \over 4 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over 4 x} + {2 \over 4 x} = {10 \over 4 x} = {5 \over 2 x}\) 1p 1p b \({4 \over x} + {8 \over 7 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({4 \over x} + {8 \over 7 x} = {28 \over 7 x} + {8 \over 7 x} = {36 \over 7 x}\) 1p 1p c \({4 \over 6 a} - {3 \over 7 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({4 \over 6 a} - {3 \over 7 b} = {28 b \over 42 a b} - {18 a \over 42 a b} = {28 b - 18 a \over 42 a b} = {14 b - 9 a \over 21 a b}\) 1p 1p d \(6 - {5 \over 9 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(6 - {5 \over 9 p} = {6 \over 1} - {5 \over 9 p} = {54 p \over 9 p} - {5 \over 9 p} = {54 p - 5 \over 9 p}\) 1p opgave 2Herleid tot één breuk. 1p \({7 a \over b} + {4 \over 6 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({7 a \over b} + {4 \over 6 b} = {42 a \over 6 b} + {4 \over 6 b} = {42 a + 4 \over 6 b} = {21 a + 2 \over 3 b}\) 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 \({a \over 3 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 3 a} = {1 \over 3}\) 1p 1p c \({10 a \over -18 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({10 a \over -18 a} = -\frac{5}{9}\) 1p 1p d \({-9 x \over -3 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-9 x \over -3 x} = 3\) 1p opgave 4Herleid. 1p a \({-16 x y \over 28 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-16 x y \over 28 x z} = -{4 y \over 7 z}\) 1p 1p b \({6 b \over -9 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({6 b \over -9 a b} = -{2 \over 3 a}\) 1p 1p c \({12 p q r \over 2 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({12 p q r \over 2 q r} = 6 p\) 1p 1p d \({7 a b \over b} + {6 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 a b \over b} + {6 a c \over c} = 7 a + 6 a = 13 a\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(6 a + {9 \over 5 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(6 a + {9 \over 5 a} = {6 a \over 1} ⋅ {5 a \over 5 a} + {9 \over 5 a} = {30 a^{2} \over 5 a} + {9 \over 5 a} = {30 a^{2} + 9 \over 5 a}\) 1p 1p b \({6 b \over 9 a} + {7 a \over 8 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({6 b \over 9 a} + {7 a \over 8 b} = {48 b^{2} \over 72 a b} + {63 a^{2} \over 72 a b} = {63 a^{2} + 48 b^{2} \over 72 a b} = {21 a^{2} + 16 b^{2} \over 24 a b}\) 1p 1p c \({7 \over x} ⋅ {4 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over x} ⋅ {4 \over y} = {28 \over x y}\) 1p 1p d \({x \over 7} ⋅ {9 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({x \over 7} ⋅ {9 \over y} = {9 x \over 7 y}\) 1p opgave 2Herleid tot één breuk. 1p a \({8 \over 9} ⋅ p\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over 9} ⋅ p = {8 p \over 9}\) 1p 1p b \({5 y \over x} ⋅ {x - 6 \over 4}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({5 y \over x} ⋅ {x - 6 \over 4} = {5 y (x - 6) \over 4 x} = {5 x y - 30 y \over 4 x}\) 1p 1p c \({4 \over p} : {9 \over q}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({4 \over p} : {9 \over q} = {4 \over p} ⋅ {q \over 9} = {4 q \over 9 p}\) 1p 1p d \(-{9 \over 5} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{9 \over 5} : a = -{9 \over 5} : {a \over 1} = -{9 \over 5} ⋅ {1 \over a} = -{9 \over 5 a}\) 1p opgave 3Herleid tot één breuk. 1p a \({1 \over 4} : {x - 6 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({1 \over 4} : {x - 6 y \over y} = {1 \over 4} ⋅ {y \over x - 6 y} = {y \over 4 (x - 6 y)} = {y \over 4 x - 24 y}\) 1p 1p b \({5 a \over 6} + {a + 1 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({5 a \over 6} + {a + 1 \over 7} = {35 a \over 42} + {6 (a + 1) \over 42} = {35 a + 6 (a + 1) \over 42} = {41 a + 6 \over 42}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-7 p + 2 \over 4 p - 5} - 8\) Optellen (9) 00eh - Breuken herleiden - basis - 1ms - dynamic variables ○ \({-7 p + 2 \over 4 p - 5} - 8 = {-7 p + 2 \over 4 p - 5} - {8 (4 p - 5) \over 4 p - 5} = {-7 p + 2 - 8 (4 p - 5) \over 4 p - 5} = {-7 p + 2 - 32 p + 40 \over 4 p - 5} = {-39 p + 42 \over 4 p - 5}\) 1p |