Getal & Ruimte (13e editie) - 3 vwo
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({9 \over 8 a} - {3 \over 8 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({9 \over 8 a} - {3 \over 8 a} = {6 \over 8 a} = {3 \over 4 a}\) 1p 1p b \({6 \over p} + {5 \over 9 p}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over p} + {5 \over 9 p} = {54 \over 9 p} + {5 \over 9 p} = {59 \over 9 p}\) 1p 1p c \({7 \over 4 x} - {6 \over 5 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 4 x} - {6 \over 5 y} = {35 y \over 20 x y} - {24 x \over 20 x y} = {35 y - 24 x \over 20 x y}\) 1p 1p d \(2 - {7 \over 6 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(2 - {7 \over 6 a} = {2 \over 1} - {7 \over 6 a} = {12 a \over 6 a} - {7 \over 6 a} = {12 a - 7 \over 6 a}\) 1p opgave 2Herleid tot één breuk. 1p \({6 x \over y} - {2 \over 4 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({6 x \over y} - {2 \over 4 y} = {24 x \over 4 y} - {2 \over 4 y} = {24 x - 2 \over 4 y} = {12 x - 1 \over 2 y}\) 1p opgave 3Herleid. 1p a \({6 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({6 a \over a} = {6 \over 1} = 6\) 1p 1p b \({x \over 6 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 6 x} = {1 \over 6}\) 1p 1p c \({6 p \over -14 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 p \over -14 p} = -\frac{3}{7}\) 1p 1p d \({25 a \over 5 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({25 a \over 5 a} = 5\) 1p opgave 4Herleid. 1p a \({20 x y \over -35 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({20 x y \over -35 x z} = -{4 y \over 7 z}\) 1p 1p b \({-6 b \over -21 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-6 b \over -21 a b} = {2 \over 7 a}\) 1p 1p c \({-18 x y z \over 3 y z}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-18 x y z \over 3 y z} = -6 x\) 1p 1p d \({4 a b \over b} + {2 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({4 a b \over b} + {2 a c \over c} = 4 a + 2 a = 6 a\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(5 p - {8 \over 9 p}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(5 p - {8 \over 9 p} = {5 p \over 1} ⋅ {9 p \over 9 p} - {8 \over 9 p} = {45 p^{2} \over 9 p} - {8 \over 9 p} = {45 p^{2} - 8 \over 9 p}\) 1p 1p b \({5 b \over 8 a} - {3 a \over 6 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({5 b \over 8 a} - {3 a \over 6 b} = {15 b^{2} \over 24 a b} - {12 a^{2} \over 24 a b} = {-12 a^{2} + 15 b^{2} \over 24 a b} = {-4 a^{2} + 5 b^{2} \over 8 a b}\) 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 \({a \over 5} ⋅ {3 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({a \over 5} ⋅ {3 \over b} = {3 a \over 5 b}\) 1p opgave 2Herleid tot één breuk. 1p a \(-{9 \over 7} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{9 \over 7} ⋅ x = -{9 x \over 7}\) 1p 1p b \({6 y \over x} ⋅ {x + 2 \over 9}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({6 y \over x} ⋅ {x + 2 \over 9} = {6 y (x + 2) \over 9 x} = {2 y (x + 2) \over 3 x} = {2 x y + 4 y \over 3 x}\) 1p 1p c \({9 \over a} : {4 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over a} : {4 \over b} = {9 \over a} ⋅ {b \over 4} = {9 b \over 4 a}\) 1p 1p d \(-{7 \over 6} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{7 \over 6} : x = -{7 \over 6} : {x \over 1} = -{7 \over 6} ⋅ {1 \over x} = -{7 \over 6 x}\) 1p opgave 3Herleid tot één breuk. 1p a \(-{5 \over 8} : {p - 3 q \over q}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{5 \over 8} : {p - 3 q \over q} = -{5 \over 8} ⋅ {q \over p - 3 q} = -{5 q \over 8 (p - 3 q)} = -{5 q \over 8 p - 24 q}\) 1p 1p b \({a \over 2} + {a + 9 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 2} + {a + 9 \over 7} = {7 a \over 14} + {2 (a + 9) \over 14} = {7 a + 2 (a + 9) \over 14} = {9 a + 18 \over 14}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({8 x + 3 \over 5 x + 7} - 1\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 x + 3 \over 5 x + 7} - 1 = {8 x + 3 \over 5 x + 7} - {1 (5 x + 7) \over 5 x + 7} = {8 x + 3 - 1 (5 x + 7) \over 5 x + 7} = {8 x + 3 - 5 x - 7 \over 5 x + 7} = {3 x - 4 \over 5 x + 7}\) 1p |