Getal & Ruimte (13e editie) - havo wiskunde A
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({8 \over 3 x} - {2 \over 3 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over 3 x} - {2 \over 3 x} = {6 \over 3 x} = {2 \over x}\) 1p 1p b \({9 \over a} - {7 \over 5 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({9 \over a} - {7 \over 5 a} = {45 \over 5 a} - {7 \over 5 a} = {38 \over 5 a}\) 1p 1p c \({2 \over 3 x} - {9 \over 6 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({2 \over 3 x} - {9 \over 6 y} = {4 y \over 6 x y} - {9 x \over 6 x y} = {4 y - 9 x \over 6 x y}\) 1p 1p d \(6 - {4 \over 3 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(6 - {4 \over 3 p} = {6 \over 1} - {4 \over 3 p} = {18 p \over 3 p} - {4 \over 3 p} = {18 p - 4 \over 3 p}\) 1p opgave 2Herleid tot één breuk. 1p a \(6 a - {5 \over 4 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(6 a - {5 \over 4 a} = {6 a \over 1} ⋅ {4 a \over 4 a} - {5 \over 4 a} = {24 a^{2} \over 4 a} - {5 \over 4 a} = {24 a^{2} - 5 \over 4 a}\) 1p 1p b \({7 p \over q} + {3 \over 8 q}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({7 p \over q} + {3 \over 8 q} = {56 p \over 8 q} + {3 \over 8 q} = {56 p + 3 \over 8 q}\) 1p 1p c \({9 y \over 5 x} + {3 x \over 8 y}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 y \over 5 x} + {3 x \over 8 y} = {72 y^{2} \over 40 x y} + {15 x^{2} \over 40 x y} = {15 x^{2} + 72 y^{2} \over 40 x y}\) 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 \({a \over 6 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 6 a} = {1 \over 6}\) 1p 1p c \({4 a \over -6 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({4 a \over -6 a} = -\frac{2}{3}\) 1p 1p d \({-9 x \over 3 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-9 x \over 3 x} = -3\) 1p opgave 4Herleid. 1p a \({16 p q \over 28 p r}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({16 p q \over 28 p r} = {4 q \over 7 r}\) 1p 1p b \({-12 y \over 16 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-12 y \over 16 x y} = -{3 \over 4 x}\) 1p 1p c \({-6 a b c \over -3 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-6 a b c \over -3 b c} = 2 a\) 1p 1p d \({2 a b \over b} + {7 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({2 a b \over b} + {7 a c \over c} = 2 a + 7 a = 9 a\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({2 \over a} ⋅ -{3 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 \over a} ⋅ -{3 \over b} = -{6 \over a b}\) 1p 1p b \({p \over 6} ⋅ {2 \over q}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 6} ⋅ {2 \over q} = {2 p \over 6 q} = {p \over 3 q}\) 1p 1p c \(-{1 \over 7} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{1 \over 7} ⋅ x = -{x \over 7}\) 1p 1p d \({9 \over x} : {2 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({9 \over x} : {2 \over y} = {9 \over x} ⋅ {y \over 2} = {9 y \over 2 x}\) 1p opgave 2Herleid tot één breuk. 1p \(-{8 \over 7} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{8 \over 7} : a = -{8 \over 7} : {a \over 1} = -{8 \over 7} ⋅ {1 \over a} = -{8 \over 7 a}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({5 a \over 2} + {a + 7 \over 9}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({5 a \over 2} + {a + 7 \over 9} = {45 a \over 18} + {2 (a + 7) \over 18} = {45 a + 2 (a + 7) \over 18} = {47 a + 14 \over 18}\) 1p |
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| havo wiskunde A | 6.2 Formules met breuken |
opgave 1Herleid tot één breuk. 1p a \({8 \over 7} : {a + 6 b \over b}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over 7} : {a + 6 b \over b} = {8 \over 7} ⋅ {b \over a + 6 b} = {8 b \over 7 (a + 6 b)} = {8 b \over 7 a + 42 b}\) 1p 1p b \({-4 p + 7 \over -5 p - 3} + 2\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables b \({-4 p + 7 \over -5 p - 3} + 2 = {-4 p + 7 \over -5 p - 3} - {-2 (-5 p - 3) \over -5 p - 3} = {-4 p + 7 + 2 (-5 p - 3) \over -5 p - 3} = {-4 p + 7 - 10 p - 6 \over -5 p - 3} = {-14 p + 1 \over -5 p - 3}\) 1p |