Getal & Ruimte (12e editie) - havo wiskunde A
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({5 \over 8 p} - {3 \over 8 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({5 \over 8 p} - {3 \over 8 p} = {2 \over 8 p} = {1 \over 4 p}\) 1p 1p b \({6 \over a} - {9 \over 4 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over a} - {9 \over 4 a} = {24 \over 4 a} - {9 \over 4 a} = {15 \over 4 a}\) 1p 1p c \({2 \over 4 x} + {5 \over 8 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({2 \over 4 x} + {5 \over 8 y} = {4 y \over 8 x y} + {5 x \over 8 x y} = {4 y + 5 x \over 8 x y}\) 1p 1p d \(5 - {4 \over 3 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(5 - {4 \over 3 a} = {5 \over 1} - {4 \over 3 a} = {15 a \over 3 a} - {4 \over 3 a} = {15 a - 4 \over 3 a}\) 1p opgave 2Herleid tot één breuk. 1p a \(9 x + {7 \over 5 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(9 x + {7 \over 5 x} = {9 x \over 1} ⋅ {5 x \over 5 x} + {7 \over 5 x} = {45 x^{2} \over 5 x} + {7 \over 5 x} = {45 x^{2} + 7 \over 5 x}\) 1p 1p b \({8 x \over y} + {4 \over 2 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({8 x \over y} + {4 \over 2 y} = {16 x \over 2 y} + {4 \over 2 y} = {16 x + 4 \over 2 y} = {8 x + 2 \over y}\) 1p 1p c \({2 q \over 3 p} + {7 p \over 4 q}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({2 q \over 3 p} + {7 p \over 4 q} = {8 q^{2} \over 12 p q} + {21 p^{2} \over 12 p q} = {21 p^{2} + 8 q^{2} \over 12 p q}\) 1p opgave 3Herleid. 1p a \({9 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 a \over a} = {9 \over 1} = 9\) 1p 1p b \({x \over 6 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 6 x} = {1 \over 6}\) 1p 1p c \({8 a \over -12 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 a \over -12 a} = -\frac{2}{3}\) 1p 1p d \({-14 x \over 2 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-14 x \over 2 x} = -7\) 1p opgave 4Herleid. 1p a \({40 a b \over -45 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({40 a b \over -45 a c} = -{8 b \over 9 c}\) 1p 1p b \({28 b \over -32 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({28 b \over -32 a b} = -{7 \over 8 a}\) 1p 1p c \({-27 p q r \over 3 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-27 p q r \over 3 q r} = -9 p\) 1p 1p d \({7 x y \over y} - {6 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 x y \over y} - {6 x z \over z} = 7 x - 6 x = x\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({2 \over p} ⋅ {8 \over q}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 \over p} ⋅ {8 \over q} = {16 \over p q}\) 1p 1p b \({x \over 4} ⋅ {9 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 4} ⋅ {9 \over y} = {9 x \over 4 y}\) 1p 1p c \(-{7 \over 4} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{7 \over 4} ⋅ x = -{7 x \over 4}\) 1p 1p d \({9 \over a} : {4 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({9 \over a} : {4 \over b} = {9 \over a} ⋅ {b \over 4} = {9 b \over 4 a}\) 1p opgave 2Herleid tot één breuk. 1p \(-{1 \over 9} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{1 \over 9} : a = -{1 \over 9} : {a \over 1} = -{1 \over 9} ⋅ {1 \over a} = -{1 \over 9 a}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({9 p \over 7} + {p + 6 \over 4}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({9 p \over 7} + {p + 6 \over 4} = {36 p \over 28} + {7 (p + 6) \over 28} = {36 p + 7 (p + 6) \over 28} = {43 p + 42 \over 28}\) 1p |
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| havo wiskunde A | 6.3 Formules met breuken |
opgave 1Herleid tot één breuk. 1p a \({6 b \over a} ⋅ {a + 4 \over 8}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables a \({6 b \over a} ⋅ {a + 4 \over 8} = {6 b (a + 4) \over 8 a} = {3 b (a + 4) \over 4 a} = {3 a b + 12 b \over 4 a}\) 1p 1p b \(-{3 \over 2} : {x - y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables b \(-{3 \over 2} : {x - y \over y} = -{3 \over 2} ⋅ {y \over x - y} = -{3 y \over 2 (x - y)} = -{3 y \over 2 x - 2 y}\) 1p |
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| havo wiskunde A | 11.2 Herleiden en combineren van formules |
opgave 1Deel uit. 1p a \({2 x^{2} + 3 x - 10 \over x}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({2 x^{2} + 3 x - 10 \over x} = {2 x^{2} \over x} + {3 x \over x} - {10 \over x} = 2 x + 3 - {10 \over x}\) 1p 1p b \({2 a^{2} - 9 a + 7 \over 6 a^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({2 a^{2} - 9 a + 7 \over 6 a^{2}} = {2 a^{2} \over 6 a^{2}} - {9 a \over 6 a^{2}} + {7 \over 6 a^{2}} = \frac{1}{3} - {3 \over 2 a} + {7 \over 6 a^{2}}\) 1p |