Getal & Ruimte (13e editie) - 2 havo/vwo
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({5 \over 8 a} + {7 \over 8 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({5 \over 8 a} + {7 \over 8 a} = {12 \over 8 a} = {3 \over 2 a}\) 1p 1p b \({2 \over x} - {4 \over 6 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({2 \over x} - {4 \over 6 x} = {12 \over 6 x} - {4 \over 6 x} = {8 \over 6 x} = {4 \over 3 x}\) 1p 1p c \({2 \over 5 p} - {9 \over 8 q}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({2 \over 5 p} - {9 \over 8 q} = {16 q \over 40 p q} - {45 p \over 40 p q} = {16 q - 45 p \over 40 p q}\) 1p 1p d \(9 - {8 \over 3 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(9 - {8 \over 3 a} = {9 \over 1} - {8 \over 3 a} = {27 a \over 3 a} - {8 \over 3 a} = {27 a - 8 \over 3 a}\) 1p opgave 2Herleid tot één breuk. 1p a \(2 x - {9 \over 7 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(2 x - {9 \over 7 x} = {2 x \over 1} ⋅ {7 x \over 7 x} - {9 \over 7 x} = {14 x^{2} \over 7 x} - {9 \over 7 x} = {14 x^{2} - 9 \over 7 x}\) 1p 1p b \({6 p \over q} - {8 \over 7 q}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({6 p \over q} - {8 \over 7 q} = {42 p \over 7 q} - {8 \over 7 q} = {42 p - 8 \over 7 q}\) 1p 1p c \({6 b \over 4 a} - {5 a \over 9 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 b \over 4 a} - {5 a \over 9 b} = {54 b^{2} \over 36 a b} - {20 a^{2} \over 36 a b} = {-20 a^{2} + 54 b^{2} \over 36 a b} = {-10 a^{2} + 27 b^{2} \over 18 a b}\) 1p opgave 3Herleid. 1p a \({4 x \over x}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 x \over x} = {4 \over 1} = 4\) 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 \({21 a \over -24 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({21 a \over -24 a} = -\frac{7}{8}\) 1p 1p d \({18 a \over 2 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({18 a \over 2 a} = 9\) 1p opgave 4Herleid. 1p a \({-6 x y \over 10 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-6 x y \over 10 x z} = -{3 y \over 5 z}\) 1p 1p b \({-28 b \over 32 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-28 b \over 32 a b} = -{7 \over 8 a}\) 1p 1p c \({-9 p q r \over 3 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-9 p q r \over 3 q r} = -3 p\) 1p 1p d \({7 x y \over y} + {6 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 x y \over y} + {6 x z \over z} = 7 x + 6 x = 13 x\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({3 \over a} ⋅ -{9 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over a} ⋅ -{9 \over b} = -{27 \over a b}\) 1p 1p b \({x \over 7} ⋅ -{6 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 7} ⋅ -{6 \over y} = -{6 x \over 7 y}\) 1p 1p c \({6 \over 5} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 5} ⋅ a = {6 a \over 5}\) 1p 1p d \({4 \over x} : {9 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({4 \over x} : {9 \over y} = {4 \over x} ⋅ {y \over 9} = {4 y \over 9 x}\) 1p opgave 2Herleid tot één breuk. 1p \(-{4 \over 3} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{4 \over 3} : p = -{4 \over 3} : {p \over 1} = -{4 \over 3} ⋅ {1 \over p} = -{4 \over 3 p}\) 1p |