Getal & Ruimte (12e editie) - havo wiskunde A
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({8 \over 2 x} + {9 \over 2 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over 2 x} + {9 \over 2 x} = {17 \over 2 x}\) 1p 1p b \({9 \over x} - {5 \over 2 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({9 \over x} - {5 \over 2 x} = {18 \over 2 x} - {5 \over 2 x} = {13 \over 2 x}\) 1p 1p c \({2 \over 7 a} - {5 \over 3 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({2 \over 7 a} - {5 \over 3 b} = {6 b \over 21 a b} - {35 a \over 21 a b} = {6 b - 35 a \over 21 a b}\) 1p 1p d \(7 - {5 \over 6 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(7 - {5 \over 6 p} = {7 \over 1} - {5 \over 6 p} = {42 p \over 6 p} - {5 \over 6 p} = {42 p - 5 \over 6 p}\) 1p opgave 2Herleid tot één breuk. 1p a \(5 a + {7 \over 6 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(5 a + {7 \over 6 a} = {5 a \over 1} ⋅ {6 a \over 6 a} + {7 \over 6 a} = {30 a^{2} \over 6 a} + {7 \over 6 a} = {30 a^{2} + 7 \over 6 a}\) 1p 1p b \({7 x \over y} - {9 \over 2 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({7 x \over y} - {9 \over 2 y} = {14 x \over 2 y} - {9 \over 2 y} = {14 x - 9 \over 2 y}\) 1p 1p c \({7 b \over 2 a} - {5 a \over 3 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({7 b \over 2 a} - {5 a \over 3 b} = {21 b^{2} \over 6 a b} - {10 a^{2} \over 6 a b} = {-10 a^{2} + 21 b^{2} \over 6 a b}\) 1p opgave 3Herleid. 1p a \({6 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({6 a \over a} = {6 \over 1} = 6\) 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 \({-8 p \over -20 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-8 p \over -20 p} = \frac{2}{5}\) 1p 1p d \({-15 p \over -5 p}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-15 p \over -5 p} = 3\) 1p opgave 4Herleid. 1p a \({-8 a b \over -20 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-8 a b \over -20 a c} = {2 b \over 5 c}\) 1p 1p b \({6 y \over -27 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({6 y \over -27 x y} = -{2 \over 9 x}\) 1p 1p c \({45 a b c \over 5 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({45 a b c \over 5 b c} = 9 a\) 1p 1p d \({3 x y \over y} + {2 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({3 x y \over y} + {2 x z \over z} = 3 x + 2 x = 5 x\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({8 \over a} ⋅ {2 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over a} ⋅ {2 \over b} = {16 \over a b}\) 1p 1p b \({p \over 4} ⋅ -{5 \over q}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 4} ⋅ -{5 \over q} = -{5 p \over 4 q}\) 1p 1p c \({4 \over 9} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({4 \over 9} ⋅ a = {4 a \over 9}\) 1p 1p d \({8 \over x} : {5 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({8 \over x} : {5 \over y} = {8 \over x} ⋅ {y \over 5} = {8 y \over 5 x}\) 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 \({7 x \over 3} + {x + 5 \over 4}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({7 x \over 3} + {x + 5 \over 4} = {28 x \over 12} + {3 (x + 5) \over 12} = {28 x + 3 (x + 5) \over 12} = {31 x + 15 \over 12}\) 1p |
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| havo wiskunde A | 6.3 Formules met breuken |
opgave 1Herleid tot één breuk. 1p a \({9 q \over p} ⋅ {p - 5 \over 8}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 q \over p} ⋅ {p - 5 \over 8} = {9 q (p - 5) \over 8 p} = {9 p q - 45 q \over 8 p}\) 1p 1p b \(-{6 \over 5} : {a + 2 b \over b}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables b \(-{6 \over 5} : {a + 2 b \over b} = -{6 \over 5} ⋅ {b \over a + 2 b} = -{6 b \over 5 (a + 2 b)} = -{6 b \over 5 a + 10 b}\) 1p |
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| havo wiskunde A | 11.2 Herleiden en combineren van formules |
opgave 1Deel uit. 1p a \({6 a^{2} + 9 a + 30 \over 3 a}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({6 a^{2} + 9 a + 30 \over 3 a} = {6 a^{2} \over 3 a} + {9 a \over 3 a} + {30 \over 3 a} = 2 a + 3 + {10 \over a}\) 1p 1p b \({7 x^{2} + 5 x + 9 \over 4 x^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({7 x^{2} + 5 x + 9 \over 4 x^{2}} = {7 x^{2} \over 4 x^{2}} + {5 x \over 4 x^{2}} + {9 \over 4 x^{2}} = 1\frac{3}{4} + {5 \over 4 x} + {9 \over 4 x^{2}}\) 1p |