Getal & Ruimte (13e editie) - 2 havo/vwo
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({4 \over 8 a} + {6 \over 8 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 8 a} + {6 \over 8 a} = {10 \over 8 a} = {5 \over 4 a}\) 1p 1p b \({9 \over x} - {2 \over 7 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({9 \over x} - {2 \over 7 x} = {63 \over 7 x} - {2 \over 7 x} = {61 \over 7 x}\) 1p 1p c \({5 \over 3 p} + {4 \over 7 q}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over 3 p} + {4 \over 7 q} = {35 q \over 21 p q} + {12 p \over 21 p q} = {35 q + 12 p \over 21 p q}\) 1p 1p d \(5 - {7 \over 6 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(5 - {7 \over 6 x} = {5 \over 1} - {7 \over 6 x} = {30 x \over 6 x} - {7 \over 6 x} = {30 x - 7 \over 6 x}\) 1p opgave 2Herleid tot één breuk. 1p a \(5 a - {2 \over 9 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(5 a - {2 \over 9 a} = {5 a \over 1} ⋅ {9 a \over 9 a} - {2 \over 9 a} = {45 a^{2} \over 9 a} - {2 \over 9 a} = {45 a^{2} - 2 \over 9 a}\) 1p 1p b \({9 p \over q} + {3 \over 4 q}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({9 p \over q} + {3 \over 4 q} = {36 p \over 4 q} + {3 \over 4 q} = {36 p + 3 \over 4 q}\) 1p 1p c \({4 b \over 8 a} - {2 a \over 6 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({4 b \over 8 a} - {2 a \over 6 b} = {12 b^{2} \over 24 a b} - {8 a^{2} \over 24 a b} = {-8 a^{2} + 12 b^{2} \over 24 a b} = {-2 a^{2} + 3 b^{2} \over 6 a b}\) 1p opgave 3Herleid. 1p a \({5 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 a \over a} = {5 \over 1} = 5\) 1p 1p b \({x \over 3 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 3 x} = {1 \over 3}\) 1p 1p c \({20 x \over 24 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({20 x \over 24 x} = \frac{5}{6}\) 1p 1p d \({-6 a \over 2 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-6 a \over 2 a} = -3\) 1p opgave 4Herleid. 1p a \({10 x y \over 18 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({10 x y \over 18 x z} = {5 y \over 9 z}\) 1p 1p b \({-9 q \over 15 p q}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-9 q \over 15 p q} = -{3 \over 5 p}\) 1p 1p c \({-8 a b c \over 2 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-8 a b c \over 2 b c} = -4 a\) 1p 1p d \({4 x y \over y} - {5 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({4 x y \over y} - {5 x z \over z} = 4 x - 5 x = -x\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({2 \over a} ⋅ {9 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 \over a} ⋅ {9 \over b} = {18 \over a b}\) 1p 1p b \({a \over 6} ⋅ -{3 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 6} ⋅ -{3 \over b} = -{3 a \over 6 b} = -{a \over 2 b}\) 1p 1p c \(-{9 \over 5} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{9 \over 5} ⋅ x = -{9 x \over 5}\) 1p 1p d \({3 \over x} : {4 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({3 \over x} : {4 \over y} = {3 \over x} ⋅ {y \over 4} = {3 y \over 4 x}\) 1p opgave 2Herleid tot één breuk. 1p \(-{2 \over 5} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{2 \over 5} : p = -{2 \over 5} : {p \over 1} = -{2 \over 5} ⋅ {1 \over p} = -{2 \over 5 p}\) 1p |