Getal & Ruimte (12e editie) - vwo wiskunde A

'Breuken herleiden'.

1 vwo	6.6 Herleiden van breuken
Breuken herleiden (13)	opgave 1 Herleid tot één breuk. 1p a \({6 \over 8 a} + {7 \over 8 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({6 \over 8 a} + {7 \over 8 a} = {13 \over 8 a}\) 1p 1p b \({8 \over x} - {6 \over 9 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({8 \over x} - {6 \over 9 x} = {72 \over 9 x} - {6 \over 9 x} = {66 \over 9 x} = {22 \over 3 x}\) 1p 1p c \({9 \over 4 x} + {2 \over 3 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over 4 x} + {2 \over 3 y} = {27 y \over 12 x y} + {8 x \over 12 x y} = {27 y + 8 x \over 12 x y}\) 1p 1p d \(8 + {3 \over 2 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(8 + {3 \over 2 p} = {8 \over 1} + {3 \over 2 p} = {16 p \over 2 p} + {3 \over 2 p} = {16 p + 3 \over 2 p}\) 1p opgave 2 Herleid tot één breuk. 1p \({3 a \over b} - {7 \over 6 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({3 a \over b} - {7 \over 6 b} = {18 a \over 6 b} - {7 \over 6 b} = {18 a - 7 \over 6 b}\) 1p opgave 3 Herleid. 1p a \({8 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 p \over p} = {8 \over 1} = 8\) 1p 1p b \({a \over 8 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 8 a} = {1 \over 8}\) 1p 1p c \({-10 a \over 12 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-10 a \over 12 a} = -\frac{5}{6}\) 1p 1p d \({-36 x \over 4 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-36 x \over 4 x} = -9\) 1p opgave 4 Herleid. 1p a \({-20 x y \over 25 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-20 x y \over 25 x z} = -{4 y \over 5 z}\) 1p 1p b \({6 b \over 10 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({6 b \over 10 a b} = {3 \over 5 a}\) 1p 1p c \({-15 x y z \over 5 y z}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-15 x y z \over 5 y z} = -3 x\) 1p 1p d \({4 x y \over y} + {7 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({4 x y \over y} + {7 x z \over z} = 4 x + 7 x = 11 x\) 1p
2 vwo	1.2 Herleiden van breuken
Breuken herleiden (10)	opgave 1 Herleid tot één breuk. 1p a \(6 x - {9 \over 2 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(6 x - {9 \over 2 x} = {6 x \over 1} ⋅ {2 x \over 2 x} - {9 \over 2 x} = {12 x^{2} \over 2 x} - {9 \over 2 x} = {12 x^{2} - 9 \over 2 x}\) 1p 1p b \({9 q \over 8 p} - {3 p \over 5 q}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({9 q \over 8 p} - {3 p \over 5 q} = {45 q^{2} \over 40 p q} - {24 p^{2} \over 40 p q} = {-24 p^{2} + 45 q^{2} \over 40 p q}\) 1p 1p c \({5 \over a} ⋅ {3 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over a} ⋅ {3 \over b} = {15 \over a b}\) 1p 1p d \({a \over 9} ⋅ -{6 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({a \over 9} ⋅ -{6 \over b} = -{6 a \over 9 b} = -{2 a \over 3 b}\) 1p opgave 2 Herleid tot één breuk. 1p a \({4 \over 9} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 9} ⋅ x = {4 x \over 9}\) 1p 1p b \({7 y \over x} ⋅ {x + 5 \over 4}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({7 y \over x} ⋅ {x + 5 \over 4} = {7 y (x + 5) \over 4 x} = {7 x y + 35 y \over 4 x}\) 1p 1p c \({7 \over a} : {6 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over a} : {6 \over b} = {7 \over a} ⋅ {b \over 6} = {7 b \over 6 a}\) 1p 1p d \(-{6 \over 7} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{6 \over 7} : a = -{6 \over 7} : {a \over 1} = -{6 \over 7} ⋅ {1 \over a} = -{6 \over 7 a}\) 1p opgave 3 Herleid tot één breuk. 1p a \(-{3 \over 8} : {p + 4 q \over q}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{3 \over 8} : {p + 4 q \over q} = -{3 \over 8} ⋅ {q \over p + 4 q} = -{3 q \over 8 (p + 4 q)} = -{3 q \over 8 p + 32 q}\) 1p 1p b \({8 x \over 9} + {x + 1 \over 2}\) Optellen (8) 0098 - Breuken herleiden - basis - 1ms - dynamic variables b \({8 x \over 9} + {x + 1 \over 2} = {16 x \over 18} + {9 (x + 1) \over 18} = {16 x + 9 (x + 1) \over 18} = {25 x + 9 \over 18}\) 1p
3 vwo	5.3 Breuken met letters herleiden
Breuken herleiden (1)	opgave 1 Herleid tot één breuk. 1p \({-8 x + 4 \over -6 x - 7} - 5\) Optellen (9) 00eh - Breuken herleiden - basis - 1ms - dynamic variables ○ \({-8 x + 4 \over -6 x - 7} - 5 = {-8 x + 4 \over -6 x - 7} + {-5 (-6 x - 7) \over -6 x - 7} = {-8 x + 4 - 5 (-6 x - 7) \over -6 x - 7} = {-8 x + 4 + 30 x + 35 \over -6 x - 7} = {22 x + 39 \over -6 x - 7}\) 1p
vwo wiskunde A	13.3 Formules herschrijven
Breuken herleiden (1)	opgave 1 Deel uit. 1p \({6 x^{2} + 5 x + 4 \over 2 x^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables ○ \({6 x^{2} + 5 x + 4 \over 2 x^{2}} = {6 x^{2} \over 2 x^{2}} + {5 x \over 2 x^{2}} + {4 \over 2 x^{2}} = 3 + {5 \over 2 x} + {2 \over x^{2}}\) 1p

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