Getal & Ruimte (12e editie) - vwo wiskunde C
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({7 \over 8 p} + {4 \over 8 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({7 \over 8 p} + {4 \over 8 p} = {11 \over 8 p}\) 1p 1p b \({2 \over x} - {4 \over 9 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({2 \over x} - {4 \over 9 x} = {18 \over 9 x} - {4 \over 9 x} = {14 \over 9 x}\) 1p 1p c \({7 \over 9 x} + {5 \over 3 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 9 x} + {5 \over 3 y} = {7 y \over 9 x y} + {15 x \over 9 x y} = {7 y + 15 x \over 9 x y}\) 1p 1p d \(2 - {3 \over 4 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(2 - {3 \over 4 a} = {2 \over 1} - {3 \over 4 a} = {8 a \over 4 a} - {3 \over 4 a} = {8 a - 3 \over 4 a}\) 1p opgave 2Herleid tot één breuk. 1p \({2 a \over b} + {6 \over 5 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({2 a \over b} + {6 \over 5 b} = {10 a \over 5 b} + {6 \over 5 b} = {10 a + 6 \over 5 b}\) 1p opgave 3Herleid. 1p a \({9 x \over x}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 x \over x} = {9 \over 1} = 9\) 1p 1p b \({p \over 6 p}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 6 p} = {1 \over 6}\) 1p 1p c \({8 x \over 12 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 x \over 12 x} = \frac{2}{3}\) 1p 1p d \({-15 a \over -3 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-15 a \over -3 a} = 5\) 1p opgave 4Herleid. 1p a \({-15 a b \over 27 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-15 a b \over 27 a c} = -{5 b \over 9 c}\) 1p 1p b \({8 y \over 28 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({8 y \over 28 x y} = {2 \over 7 x}\) 1p 1p c \({24 x y z \over -4 y z}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({24 x y z \over -4 y z} = -6 x\) 1p 1p d \({5 a b \over b} - {7 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({5 a b \over b} - {7 a c \over c} = 5 a - 7 a = -2 a\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(2 x - {7 \over 4 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(2 x - {7 \over 4 x} = {2 x \over 1} ⋅ {4 x \over 4 x} - {7 \over 4 x} = {8 x^{2} \over 4 x} - {7 \over 4 x} = {8 x^{2} - 7 \over 4 x}\) 1p 1p b \({3 b \over 4 a} - {2 a \over 9 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 b \over 4 a} - {2 a \over 9 b} = {27 b^{2} \over 36 a b} - {8 a^{2} \over 36 a b} = {-8 a^{2} + 27 b^{2} \over 36 a b}\) 1p 1p c \({9 \over a} ⋅ -{7 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over a} ⋅ -{7 \over b} = -{63 \over a b}\) 1p 1p d \({p \over 3} ⋅ -{4 \over q}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({p \over 3} ⋅ -{4 \over q} = -{4 p \over 3 q}\) 1p opgave 2Herleid tot één breuk. 1p a \({2 \over 3} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 \over 3} ⋅ x = {2 x \over 3}\) 1p 1p b \({8 y \over x} ⋅ {x + 5 \over 4}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({8 y \over x} ⋅ {x + 5 \over 4} = {8 y (x + 5) \over 4 x} = {2 y (x + 5) \over x} = {2 x y + 10 y \over x}\) 1p 1p c \({6 \over a} : {4 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over a} : {4 \over b} = {6 \over a} ⋅ {b \over 4} = {6 b \over 4 a} = {3 b \over 2 a}\) 1p 1p d \(-{4 \over 3} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{4 \over 3} : x = -{4 \over 3} : {x \over 1} = -{4 \over 3} ⋅ {1 \over x} = -{4 \over 3 x}\) 1p opgave 3Herleid tot één breuk. 1p a \({2 \over 9} : {a - b \over b}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 \over 9} : {a - b \over b} = {2 \over 9} ⋅ {b \over a - b} = {2 b \over 9 (a - b)} = {2 b \over 9 a - 9 b}\) 1p 1p b \({2 p \over 3} + {p - 6 \over 5}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({2 p \over 3} + {p - 6 \over 5} = {10 p \over 15} + {3 (p - 6) \over 15} = {10 p + 3 (p - 6) \over 15} = {13 p - 18 \over 15}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-4 p + 5 \over 2 p + 3} - 7\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({-4 p + 5 \over 2 p + 3} - 7 = {-4 p + 5 \over 2 p + 3} - {7 (2 p + 3) \over 2 p + 3} = {-4 p + 5 - 7 (2 p + 3) \over 2 p + 3} = {-4 p + 5 - 14 p - 21 \over 2 p + 3} = {-18 p - 16 \over 2 p + 3}\) 1p |