Getal & Ruimte (13e editie) - 3 havo
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({9 \over 3 p} - {8 \over 3 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({9 \over 3 p} - {8 \over 3 p} = {1 \over 3 p}\) 1p 1p b \({6 \over a} + {9 \over 4 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over a} + {9 \over 4 a} = {24 \over 4 a} + {9 \over 4 a} = {33 \over 4 a}\) 1p 1p c \({5 \over 4 a} + {3 \over 2 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over 4 a} + {3 \over 2 b} = {5 b \over 4 a b} + {6 a \over 4 a b} = {5 b + 6 a \over 4 a b}\) 1p 1p d \(2 + {3 \over 5 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(2 + {3 \over 5 x} = {2 \over 1} + {3 \over 5 x} = {10 x \over 5 x} + {3 \over 5 x} = {10 x + 3 \over 5 x}\) 1p opgave 2Herleid tot één breuk. 1p a \(6 x + {5 \over 8 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(6 x + {5 \over 8 x} = {6 x \over 1} ⋅ {8 x \over 8 x} + {5 \over 8 x} = {48 x^{2} \over 8 x} + {5 \over 8 x} = {48 x^{2} + 5 \over 8 x}\) 1p 1p b \({4 a \over b} - {5 \over 7 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({4 a \over b} - {5 \over 7 b} = {28 a \over 7 b} - {5 \over 7 b} = {28 a - 5 \over 7 b}\) 1p 1p c \({3 y \over 6 x} - {8 x \over 2 y}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({3 y \over 6 x} - {8 x \over 2 y} = {3 y^{2} \over 6 x y} - {24 x^{2} \over 6 x y} = {-24 x^{2} + 3 y^{2} \over 6 x y} = {-8 x^{2} + y^{2} \over 2 x y}\) 1p opgave 3Herleid. 1p a \({7 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({7 a \over a} = {7 \over 1} = 7\) 1p 1p b \({x \over 5 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 5 x} = {1 \over 5}\) 1p 1p c \({10 p \over -45 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({10 p \over -45 p} = -\frac{2}{9}\) 1p 1p d \({10 x \over 5 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({10 x \over 5 x} = 2\) 1p opgave 4Herleid. 1p a \({12 a b \over 28 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({12 a b \over 28 a c} = {3 b \over 7 c}\) 1p 1p b \({15 q \over 40 p q}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({15 q \over 40 p q} = {3 \over 8 p}\) 1p 1p c \({-24 a b c \over 4 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-24 a b c \over 4 b c} = -6 a\) 1p 1p d \({2 x y \over y} - {6 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({2 x y \over y} - {6 x z \over z} = 2 x - 6 x = -4 x\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({3 \over x} ⋅ {7 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over x} ⋅ {7 \over y} = {21 \over x y}\) 1p 1p b \({a \over 2} ⋅ {9 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 2} ⋅ {9 \over b} = {9 a \over 2 b}\) 1p 1p c \(-{6 \over 7} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{6 \over 7} ⋅ x = -{6 x \over 7}\) 1p 1p d \({2 \over a} : {8 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({2 \over a} : {8 \over b} = {2 \over a} ⋅ {b \over 8} = {2 b \over 8 a} = {b \over 4 a}\) 1p opgave 2Herleid tot één breuk. 1p \(-{8 \over 7} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{8 \over 7} : p = -{8 \over 7} : {p \over 1} = -{8 \over 7} ⋅ {1 \over p} = -{8 \over 7 p}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({7 a \over 3} + {a - 9 \over 5}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({7 a \over 3} + {a - 9 \over 5} = {35 a \over 15} + {3 (a - 9) \over 15} = {35 a + 3 (a - 9) \over 15} = {38 a - 27 \over 15}\) 1p |