Getal & Ruimte (13e editie) - 2 vwo
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({3 \over 9 p} - {2 \over 9 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 9 p} - {2 \over 9 p} = {1 \over 9 p}\) 1p 1p b \({6 \over a} - {9 \over 4 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over a} - {9 \over 4 a} = {24 \over 4 a} - {9 \over 4 a} = {15 \over 4 a}\) 1p 1p c \({2 \over 4 x} + {7 \over 8 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({2 \over 4 x} + {7 \over 8 y} = {4 y \over 8 x y} + {7 x \over 8 x y} = {4 y + 7 x \over 8 x y}\) 1p 1p d \(6 - {8 \over 5 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(6 - {8 \over 5 a} = {6 \over 1} - {8 \over 5 a} = {30 a \over 5 a} - {8 \over 5 a} = {30 a - 8 \over 5 a}\) 1p opgave 2Herleid tot één breuk. 1p \({4 x \over y} + {2 \over 3 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({4 x \over y} + {2 \over 3 y} = {12 x \over 3 y} + {2 \over 3 y} = {12 x + 2 \over 3 y}\) 1p opgave 3Herleid. 1p a \({2 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 a \over a} = {2 \over 1} = 2\) 1p 1p b \({p \over 7 p}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 7 p} = {1 \over 7}\) 1p 1p c \({9 a \over -12 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 a \over -12 a} = -\frac{3}{4}\) 1p 1p d \({-28 x \over -4 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-28 x \over -4 x} = 7\) 1p opgave 4Herleid. 1p a \({-9 x y \over 21 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-9 x y \over 21 x z} = -{3 y \over 7 z}\) 1p 1p b \({35 y \over -45 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({35 y \over -45 x y} = -{7 \over 9 x}\) 1p 1p c \({24 x y z \over -3 y z}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({24 x y z \over -3 y z} = -8 x\) 1p 1p d \({3 a b \over b} - {4 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({3 a b \over b} - {4 a c \over c} = 3 a - 4 a = -a\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(9 p + {8 \over 5 p}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(9 p + {8 \over 5 p} = {9 p \over 1} ⋅ {5 p \over 5 p} + {8 \over 5 p} = {45 p^{2} \over 5 p} + {8 \over 5 p} = {45 p^{2} + 8 \over 5 p}\) 1p 1p b \({3 b \over 6 a} + {9 a \over 7 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 b \over 6 a} + {9 a \over 7 b} = {21 b^{2} \over 42 a b} + {54 a^{2} \over 42 a b} = {54 a^{2} + 21 b^{2} \over 42 a b} = {18 a^{2} + 7 b^{2} \over 14 a b}\) 1p 1p c \({7 \over x} ⋅ {2 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over x} ⋅ {2 \over y} = {14 \over x y}\) 1p 1p d \({a \over 8} ⋅ -{4 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({a \over 8} ⋅ -{4 \over b} = -{4 a \over 8 b} = -{a \over 2 b}\) 1p opgave 2Herleid tot één breuk. 1p a \({8 \over 5} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over 5} ⋅ x = {8 x \over 5}\) 1p 1p b \({3 b \over a} ⋅ {a - 8 \over 9}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({3 b \over a} ⋅ {a - 8 \over 9} = {3 b (a - 8) \over 9 a} = {b (a - 8) \over 3 a} = {a b - 8 b \over 3 a}\) 1p 1p c \({8 \over a} : {4 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over a} : {4 \over b} = {8 \over a} ⋅ {b \over 4} = {8 b \over 4 a} = {2 b \over a}\) 1p 1p d \({2 \over 3} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \({2 \over 3} : p = {2 \over 3} : {p \over 1} = {2 \over 3} ⋅ {1 \over p} = {2 \over 3 p}\) 1p opgave 3Herleid tot één breuk. 1p a \({1 \over 6} : {x - 8 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({1 \over 6} : {x - 8 y \over y} = {1 \over 6} ⋅ {y \over x - 8 y} = {y \over 6 (x - 8 y)} = {y \over 6 x - 48 y}\) 1p 1p b \({x \over 4} + {x + 5 \over 9}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 4} + {x + 5 \over 9} = {9 x \over 36} + {4 (x + 5) \over 36} = {9 x + 4 (x + 5) \over 36} = {13 x + 20 \over 36}\) 1p |