Getal & Ruimte (13e editie) - havo wiskunde A
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({8 \over 5 a} - {7 \over 5 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over 5 a} - {7 \over 5 a} = {1 \over 5 a}\) 1p 1p b \({4 \over x} - {6 \over 5 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({4 \over x} - {6 \over 5 x} = {20 \over 5 x} - {6 \over 5 x} = {14 \over 5 x}\) 1p 1p c \({5 \over 3 a} - {4 \over 8 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over 3 a} - {4 \over 8 b} = {40 b \over 24 a b} - {12 a \over 24 a b} = {40 b - 12 a \over 24 a b} = {10 b - 3 a \over 6 a b}\) 1p 1p d \(8 + {4 \over 3 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(8 + {4 \over 3 x} = {8 \over 1} + {4 \over 3 x} = {24 x \over 3 x} + {4 \over 3 x} = {24 x + 4 \over 3 x}\) 1p opgave 2Herleid tot één breuk. 1p a \(2 p + {5 \over 9 p}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(2 p + {5 \over 9 p} = {2 p \over 1} ⋅ {9 p \over 9 p} + {5 \over 9 p} = {18 p^{2} \over 9 p} + {5 \over 9 p} = {18 p^{2} + 5 \over 9 p}\) 1p 1p b \({7 x \over y} + {9 \over 3 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({7 x \over y} + {9 \over 3 y} = {21 x \over 3 y} + {9 \over 3 y} = {21 x + 9 \over 3 y} = {7 x + 3 \over y}\) 1p 1p c \({9 b \over 2 a} + {7 a \over 3 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 b \over 2 a} + {7 a \over 3 b} = {27 b^{2} \over 6 a b} + {14 a^{2} \over 6 a b} = {14 a^{2} + 27 b^{2} \over 6 a b}\) 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 \({p \over 4 p}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 4 p} = {1 \over 4}\) 1p 1p c \({-4 a \over 18 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-4 a \over 18 a} = -\frac{2}{9}\) 1p 1p d \({12 x \over 2 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({12 x \over 2 x} = 6\) 1p opgave 4Herleid. 1p a \({12 a b \over 20 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({12 a b \over 20 a c} = {3 b \over 5 c}\) 1p 1p b \({32 b \over -36 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({32 b \over -36 a b} = -{8 \over 9 a}\) 1p 1p c \({-6 x y z \over -3 y z}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-6 x y z \over -3 y z} = 2 x\) 1p 1p d \({5 p q \over q} - {2 p r \over r}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({5 p q \over q} - {2 p r \over r} = 5 p - 2 p = 3 p\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({9 \over p} ⋅ {2 \over q}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 \over p} ⋅ {2 \over q} = {18 \over p q}\) 1p 1p b \({x \over 7} ⋅ {9 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 7} ⋅ {9 \over y} = {9 x \over 7 y}\) 1p 1p c \(-{6 \over 7} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{6 \over 7} ⋅ a = -{6 a \over 7}\) 1p 1p d \({8 \over a} : {4 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({8 \over a} : {4 \over b} = {8 \over a} ⋅ {b \over 4} = {8 b \over 4 a} = {2 b \over a}\) 1p opgave 2Herleid tot één breuk. 1p \(-{2 \over 3} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{2 \over 3} : x = -{2 \over 3} : {x \over 1} = -{2 \over 3} ⋅ {1 \over x} = -{2 \over 3 x}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({9 a \over 5} + {a + 6 \over 2}\) Optellen (8) 0098 - Breuken herleiden - basis - 1ms - dynamic variables ○ \({9 a \over 5} + {a + 6 \over 2} = {18 a \over 10} + {5 (a + 6) \over 10} = {18 a + 5 (a + 6) \over 10} = {23 a + 30 \over 10}\) 1p |
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| havo wiskunde A | 6.2 Formules met breuken |
opgave 1Herleid tot één breuk. 1p a \({3 \over 2} : {x - 8 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 2} : {x - 8 y \over y} = {3 \over 2} ⋅ {y \over x - 8 y} = {3 y \over 2 (x - 8 y)} = {3 y \over 2 x - 16 y}\) 1p 1p b \({-2 p - 6 \over 3 p - 5} - 8\) Optellen (9) 00eh - Breuken herleiden - basis - 1ms - dynamic variables b \({-2 p - 6 \over 3 p - 5} - 8 = {-2 p - 6 \over 3 p - 5} - {8 (3 p - 5) \over 3 p - 5} = {-2 p - 6 - 8 (3 p - 5) \over 3 p - 5} = {-2 p - 6 - 24 p + 40 \over 3 p - 5} = {-26 p + 34 \over 3 p - 5}\) 1p |