Getal & Ruimte (12e editie) - havo wiskunde B
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({7 \over 8 a} - {9 \over 8 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({7 \over 8 a} - {9 \over 8 a} = -{2 \over 8 a} = -{1 \over 4 a}\) 1p 1p b \({7 \over x} + {6 \over 4 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({7 \over x} + {6 \over 4 x} = {28 \over 4 x} + {6 \over 4 x} = {34 \over 4 x} = {17 \over 2 x}\) 1p 1p c \({6 \over 7 p} - {5 \over 3 q}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 7 p} - {5 \over 3 q} = {18 q \over 21 p q} - {35 p \over 21 p q} = {18 q - 35 p \over 21 p q}\) 1p 1p d \(3 - {9 \over 2 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(3 - {9 \over 2 x} = {3 \over 1} - {9 \over 2 x} = {6 x \over 2 x} - {9 \over 2 x} = {6 x - 9 \over 2 x}\) 1p opgave 2Herleid tot één breuk. 1p a \(6 a - {8 \over 9 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(6 a - {8 \over 9 a} = {6 a \over 1} ⋅ {9 a \over 9 a} - {8 \over 9 a} = {54 a^{2} \over 9 a} - {8 \over 9 a} = {54 a^{2} - 8 \over 9 a}\) 1p 1p b \({3 x \over y} + {4 \over 7 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({3 x \over y} + {4 \over 7 y} = {21 x \over 7 y} + {4 \over 7 y} = {21 x + 4 \over 7 y}\) 1p 1p c \({6 b \over 8 a} + {3 a \over 2 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 b \over 8 a} + {3 a \over 2 b} = {6 b^{2} \over 8 a b} + {12 a^{2} \over 8 a b} = {12 a^{2} + 6 b^{2} \over 8 a b} = {6 a^{2} + 3 b^{2} \over 4 a b}\) 1p opgave 3Herleid. 1p a \({5 x \over x}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 x \over x} = {5 \over 1} = 5\) 1p 1p b \({p \over 4 p}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 4 p} = {1 \over 4}\) 1p 1p c \({6 a \over 9 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 a \over 9 a} = \frac{2}{3}\) 1p 1p d \({4 a \over 2 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({4 a \over 2 a} = 2\) 1p opgave 4Herleid. 1p a \({-16 a b \over -18 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-16 a b \over -18 a c} = {8 b \over 9 c}\) 1p 1p b \({25 y \over 45 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({25 y \over 45 x y} = {5 \over 9 x}\) 1p 1p c \({16 p q r \over 2 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({16 p q r \over 2 q r} = 8 p\) 1p 1p d \({2 x y \over y} - {4 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({2 x y \over y} - {4 x z \over z} = 2 x - 4 x = -2 x\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({5 \over x} ⋅ {6 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 \over x} ⋅ {6 \over y} = {30 \over x y}\) 1p 1p b \({p \over 3} ⋅ {7 \over q}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 3} ⋅ {7 \over q} = {7 p \over 3 q}\) 1p 1p c \({4 \over 3} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({4 \over 3} ⋅ a = {4 a \over 3}\) 1p 1p d \({9 \over a} : {5 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({9 \over a} : {5 \over b} = {9 \over a} ⋅ {b \over 5} = {9 b \over 5 a}\) 1p opgave 2Herleid tot één breuk. 1p \({8 \over 3} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 \over 3} : x = {8 \over 3} : {x \over 1} = {8 \over 3} ⋅ {1 \over x} = {8 \over 3 x}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({4 a \over 7} + {a - 6 \over 5}\) Optellen (8) 0098 - Breuken herleiden - basis - 1ms - dynamic variables ○ \({4 a \over 7} + {a - 6 \over 5} = {20 a \over 35} + {7 (a - 6) \over 35} = {20 a + 7 (a - 6) \over 35} = {27 a - 42 \over 35}\) 1p |
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| havo wiskunde B | 11.5 Gebroken functies |
opgave 1Herleid tot één breuk. 1p \({5 a + 6 \over -2 a + 8} - 9\) Optellen (9) 00eh - Breuken herleiden - basis - 1ms - dynamic variables ○ \({5 a + 6 \over -2 a + 8} - 9 = {5 a + 6 \over -2 a + 8} + {-9 (-2 a + 8) \over -2 a + 8} = {5 a + 6 - 9 (-2 a + 8) \over -2 a + 8} = {5 a + 6 + 18 a - 72 \over -2 a + 8} = {23 a - 66 \over -2 a + 8}\) 1p opgave 2Deel uit. 1p a \({9 p^{2} - 3 p + 60 \over 3 p}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({9 p^{2} - 3 p + 60 \over 3 p} = {9 p^{2} \over 3 p} - {3 p \over 3 p} + {60 \over 3 p} = 3 p - 1 + {20 \over p}\) 1p 1p b \({6 x^{2} - 5 x + 9 \over x^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({6 x^{2} - 5 x + 9 \over x^{2}} = {6 x^{2} \over x^{2}} - {5 x \over x^{2}} + {9 \over x^{2}} = 6 - {5 \over x} + {9 \over x^{2}}\) 1p |