Getal & Ruimte (13e editie) - 3 havo
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({4 \over 2 x} - {8 \over 2 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 2 x} - {8 \over 2 x} = -{4 \over 2 x} = -{2 \over x}\) 1p 1p b \({4 \over x} - {9 \over 8 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({4 \over x} - {9 \over 8 x} = {32 \over 8 x} - {9 \over 8 x} = {23 \over 8 x}\) 1p 1p c \({6 \over 9 a} - {7 \over 4 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 9 a} - {7 \over 4 b} = {24 b \over 36 a b} - {63 a \over 36 a b} = {24 b - 63 a \over 36 a b} = {8 b - 21 a \over 12 a b}\) 1p 1p d \(4 - {6 \over 7 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(4 - {6 \over 7 p} = {4 \over 1} - {6 \over 7 p} = {28 p \over 7 p} - {6 \over 7 p} = {28 p - 6 \over 7 p}\) 1p opgave 2Herleid tot één breuk. 1p a \(9 a + {3 \over 2 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(9 a + {3 \over 2 a} = {9 a \over 1} ⋅ {2 a \over 2 a} + {3 \over 2 a} = {18 a^{2} \over 2 a} + {3 \over 2 a} = {18 a^{2} + 3 \over 2 a}\) 1p 1p b \({9 x \over y} - {4 \over 6 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({9 x \over y} - {4 \over 6 y} = {54 x \over 6 y} - {4 \over 6 y} = {54 x - 4 \over 6 y} = {27 x - 2 \over 3 y}\) 1p 1p c \({8 b \over 2 a} - {7 a \over 4 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 b \over 2 a} - {7 a \over 4 b} = {16 b^{2} \over 4 a b} - {7 a^{2} \over 4 a b} = {-7 a^{2} + 16 b^{2} \over 4 a b}\) 1p opgave 3Herleid. 1p a \({6 x \over x}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({6 x \over x} = {6 \over 1} = 6\) 1p 1p b \({a \over 5 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 5 a} = {1 \over 5}\) 1p 1p c \({40 p \over -45 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({40 p \over -45 p} = -\frac{8}{9}\) 1p 1p d \({9 a \over -3 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({9 a \over -3 a} = -3\) 1p opgave 4Herleid. 1p a \({-9 x y \over -24 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-9 x y \over -24 x z} = {3 y \over 8 z}\) 1p 1p b \({35 b \over -45 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({35 b \over -45 a b} = -{7 \over 9 a}\) 1p 1p c \({-24 p q r \over 3 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-24 p q r \over 3 q r} = -8 p\) 1p 1p d \({5 x y \over y} - {3 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({5 x y \over y} - {3 x z \over z} = 5 x - 3 x = 2 x\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({4 \over x} ⋅ {6 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over x} ⋅ {6 \over y} = {24 \over x y}\) 1p 1p b \({a \over 9} ⋅ {2 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 9} ⋅ {2 \over b} = {2 a \over 9 b}\) 1p 1p c \(-{1 \over 5} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{1 \over 5} ⋅ a = -{a \over 5}\) 1p 1p d \({9 \over p} : {6 \over q}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({9 \over p} : {6 \over q} = {9 \over p} ⋅ {q \over 6} = {9 q \over 6 p} = {3 q \over 2 p}\) 1p opgave 2Herleid tot één breuk. 1p \({5 \over 3} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({5 \over 3} : x = {5 \over 3} : {x \over 1} = {5 \over 3} ⋅ {1 \over x} = {5 \over 3 x}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({5 p \over 4} + {p - 7 \over 3}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({5 p \over 4} + {p - 7 \over 3} = {15 p \over 12} + {4 (p - 7) \over 12} = {15 p + 4 (p - 7) \over 12} = {19 p - 28 \over 12}\) 1p |