Getal & Ruimte (13e editie) - 2 havo/vwo
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({3 \over 8 a} - {2 \over 8 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 8 a} - {2 \over 8 a} = {1 \over 8 a}\) 1p 1p b \({3 \over x} - {9 \over 6 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({3 \over x} - {9 \over 6 x} = {18 \over 6 x} - {9 \over 6 x} = {9 \over 6 x} = {3 \over 2 x}\) 1p 1p c \({6 \over 7 x} - {2 \over 5 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 7 x} - {2 \over 5 y} = {30 y \over 35 x y} - {14 x \over 35 x y} = {30 y - 14 x \over 35 x y}\) 1p 1p d \(7 + {8 \over 9 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(7 + {8 \over 9 p} = {7 \over 1} + {8 \over 9 p} = {63 p \over 9 p} + {8 \over 9 p} = {63 p + 8 \over 9 p}\) 1p opgave 2Herleid tot één breuk. 1p a \(4 a - {7 \over 2 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(4 a - {7 \over 2 a} = {4 a \over 1} ⋅ {2 a \over 2 a} - {7 \over 2 a} = {8 a^{2} \over 2 a} - {7 \over 2 a} = {8 a^{2} - 7 \over 2 a}\) 1p 1p b \({4 p \over q} + {2 \over 3 q}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({4 p \over q} + {2 \over 3 q} = {12 p \over 3 q} + {2 \over 3 q} = {12 p + 2 \over 3 q}\) 1p 1p c \({9 b \over 6 a} + {5 a \over 2 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 b \over 6 a} + {5 a \over 2 b} = {9 b^{2} \over 6 a b} + {15 a^{2} \over 6 a b} = {15 a^{2} + 9 b^{2} \over 6 a b} = {5 a^{2} + 3 b^{2} \over 2 a b}\) 1p opgave 3Herleid. 1p a \({3 x \over x}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 x \over x} = {3 \over 1} = 3\) 1p 1p b \({a \over 3 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 3 a} = {1 \over 3}\) 1p 1p c \({10 x \over -45 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({10 x \over -45 x} = -\frac{2}{9}\) 1p 1p d \({-15 a \over -3 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-15 a \over -3 a} = 5\) 1p opgave 4Herleid. 1p a \({-12 x y \over 15 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-12 x y \over 15 x z} = -{4 y \over 5 z}\) 1p 1p b \({-20 q \over 25 p q}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-20 q \over 25 p q} = -{4 \over 5 p}\) 1p 1p c \({12 a b c \over 3 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({12 a b c \over 3 b c} = 4 a\) 1p 1p d \({2 x y \over y} - {3 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({2 x y \over y} - {3 x z \over z} = 2 x - 3 x = -x\) 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 \({x \over 8} ⋅ {5 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 8} ⋅ {5 \over y} = {5 x \over 8 y}\) 1p 1p c \({1 \over 8} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({1 \over 8} ⋅ a = {a \over 8}\) 1p 1p d \({3 \over p} : {2 \over q}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({3 \over p} : {2 \over q} = {3 \over p} ⋅ {q \over 2} = {3 q \over 2 p}\) 1p opgave 2Herleid tot één breuk. 1p \(-{6 \over 7} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{6 \over 7} : a = -{6 \over 7} : {a \over 1} = -{6 \over 7} ⋅ {1 \over a} = -{6 \over 7 a}\) 1p |