Getal & Ruimte (12e editie) - havo wiskunde B
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({4 \over 7 p} - {9 \over 7 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 7 p} - {9 \over 7 p} = -{5 \over 7 p}\) 1p 1p b \({6 \over x} - {3 \over 7 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over x} - {3 \over 7 x} = {42 \over 7 x} - {3 \over 7 x} = {39 \over 7 x}\) 1p 1p c \({8 \over 3 a} - {7 \over 2 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over 3 a} - {7 \over 2 b} = {16 b \over 6 a b} - {21 a \over 6 a b} = {16 b - 21 a \over 6 a b}\) 1p 1p d \(7 - {8 \over 3 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(7 - {8 \over 3 x} = {7 \over 1} - {8 \over 3 x} = {21 x \over 3 x} - {8 \over 3 x} = {21 x - 8 \over 3 x}\) 1p opgave 2Herleid tot één breuk. 1p a \(8 a + {5 \over 6 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(8 a + {5 \over 6 a} = {8 a \over 1} ⋅ {6 a \over 6 a} + {5 \over 6 a} = {48 a^{2} \over 6 a} + {5 \over 6 a} = {48 a^{2} + 5 \over 6 a}\) 1p 1p b \({6 x \over y} - {3 \over 9 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({6 x \over y} - {3 \over 9 y} = {54 x \over 9 y} - {3 \over 9 y} = {54 x - 3 \over 9 y} = {18 x - 1 \over 3 y}\) 1p 1p c \({7 b \over 6 a} + {4 a \over 8 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({7 b \over 6 a} + {4 a \over 8 b} = {28 b^{2} \over 24 a b} + {12 a^{2} \over 24 a b} = {12 a^{2} + 28 b^{2} \over 24 a b} = {3 a^{2} + 7 b^{2} \over 6 a b}\) 1p opgave 3Herleid. 1p a \({9 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 p \over p} = {9 \over 1} = 9\) 1p 1p b \({x \over 7 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 7 x} = {1 \over 7}\) 1p 1p c \({16 a \over -20 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({16 a \over -20 a} = -\frac{4}{5}\) 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 \({-12 p q \over -28 p r}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-12 p q \over -28 p r} = {3 q \over 7 r}\) 1p 1p b \({-21 y \over -27 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-21 y \over -27 x y} = {7 \over 9 x}\) 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 \({2 x y \over y} + {7 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({2 x y \over y} + {7 x z \over z} = 2 x + 7 x = 9 x\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({4 \over p} ⋅ {3 \over q}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over p} ⋅ {3 \over q} = {12 \over p q}\) 1p 1p b \({a \over 3} ⋅ {7 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 3} ⋅ {7 \over b} = {7 a \over 3 b}\) 1p 1p c \(-{2 \over 9} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{2 \over 9} ⋅ x = -{2 x \over 9}\) 1p 1p d \({3 \over a} : {9 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({3 \over a} : {9 \over b} = {3 \over a} ⋅ {b \over 9} = {3 b \over 9 a} = {b \over 3 a}\) 1p opgave 2Herleid tot één breuk. 1p \(-{3 \over 7} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{3 \over 7} : x = -{3 \over 7} : {x \over 1} = -{3 \over 7} ⋅ {1 \over x} = -{3 \over 7 x}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({5 p \over 2} + {p - 1 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({5 p \over 2} + {p - 1 \over 7} = {35 p \over 14} + {2 (p - 1) \over 14} = {35 p + 2 (p - 1) \over 14} = {37 p - 2 \over 14}\) 1p |
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| havo wiskunde B | 11.5 Gebroken functies |
opgave 1Herleid tot één breuk. 1p \({-2 x + 8 \over 4 x + 3} + 7\) Optellen (9) 00eh - Breuken herleiden - basis - 1ms - dynamic variables ○ \({-2 x + 8 \over 4 x + 3} + 7 = {-2 x + 8 \over 4 x + 3} + {7 (4 x + 3) \over 4 x + 3} = {-2 x + 8 + 7 (4 x + 3) \over 4 x + 3} = {-2 x + 8 + 28 x + 21 \over 4 x + 3} = {26 x + 29 \over 4 x + 3}\) 1p opgave 2Deel uit. 1p a \({2 a^{2} - a - 30 \over a}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({2 a^{2} - a - 30 \over a} = {2 a^{2} \over a} - {a \over a} - {30 \over a} = 2 a - 1 - {30 \over a}\) 1p 1p b \({8 p^{2} + 4 p - 3 \over 5 p^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({8 p^{2} + 4 p - 3 \over 5 p^{2}} = {8 p^{2} \over 5 p^{2}} + {4 p \over 5 p^{2}} - {3 \over 5 p^{2}} = 1\frac{3}{5} + {4 \over 5 p} - {3 \over 5 p^{2}}\) 1p |