Getal & Ruimte (12e editie) - havo wiskunde A
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({4 \over 3 p} - {8 \over 3 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 3 p} - {8 \over 3 p} = -{4 \over 3 p}\) 1p 1p b \({2 \over x} - {9 \over 8 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({2 \over x} - {9 \over 8 x} = {16 \over 8 x} - {9 \over 8 x} = {7 \over 8 x}\) 1p 1p c \({9 \over 2 x} + {5 \over 4 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over 2 x} + {5 \over 4 y} = {18 y \over 4 x y} + {5 x \over 4 x y} = {18 y + 5 x \over 4 x y}\) 1p 1p d \(7 - {9 \over 8 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(7 - {9 \over 8 a} = {7 \over 1} - {9 \over 8 a} = {56 a \over 8 a} - {9 \over 8 a} = {56 a - 9 \over 8 a}\) 1p opgave 2Herleid tot één breuk. 1p a \(4 a + {5 \over 3 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(4 a + {5 \over 3 a} = {4 a \over 1} ⋅ {3 a \over 3 a} + {5 \over 3 a} = {12 a^{2} \over 3 a} + {5 \over 3 a} = {12 a^{2} + 5 \over 3 a}\) 1p 1p b \({3 x \over y} + {2 \over 6 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({3 x \over y} + {2 \over 6 y} = {18 x \over 6 y} + {2 \over 6 y} = {18 x + 2 \over 6 y} = {9 x + 1 \over 3 y}\) 1p 1p c \({2 y \over 6 x} - {5 x \over 3 y}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({2 y \over 6 x} - {5 x \over 3 y} = {2 y^{2} \over 6 x y} - {10 x^{2} \over 6 x y} = {-10 x^{2} + 2 y^{2} \over 6 x y} = {-5 x^{2} + y^{2} \over 3 x y}\) 1p opgave 3Herleid. 1p a \({4 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 p \over p} = {4 \over 1} = 4\) 1p 1p b \({a \over 5 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 5 a} = {1 \over 5}\) 1p 1p c \({16 a \over 28 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({16 a \over 28 a} = \frac{4}{7}\) 1p 1p d \({-6 x \over 2 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-6 x \over 2 x} = -3\) 1p opgave 4Herleid. 1p a \({16 x y \over 36 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({16 x y \over 36 x z} = {4 y \over 9 z}\) 1p 1p b \({-12 q \over 28 p q}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-12 q \over 28 p q} = -{3 \over 7 p}\) 1p 1p c \({15 a b c \over -5 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({15 a b c \over -5 b c} = -3 a\) 1p 1p d \({6 a b \over b} + {4 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({6 a b \over b} + {4 a c \over c} = 6 a + 4 a = 10 a\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({9 \over x} ⋅ {2 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 \over x} ⋅ {2 \over y} = {18 \over x y}\) 1p 1p b \({x \over 9} ⋅ {5 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 9} ⋅ {5 \over y} = {5 x \over 9 y}\) 1p 1p c \({8 \over 3} ⋅ p\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over 3} ⋅ p = {8 p \over 3}\) 1p 1p d \({5 \over a} : {9 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({5 \over a} : {9 \over b} = {5 \over a} ⋅ {b \over 9} = {5 b \over 9 a}\) 1p opgave 2Herleid tot één breuk. 1p \({4 \over 5} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({4 \over 5} : a = {4 \over 5} : {a \over 1} = {4 \over 5} ⋅ {1 \over a} = {4 \over 5 a}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({6 a \over 5} + {a - 2 \over 8}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({6 a \over 5} + {a - 2 \over 8} = {48 a \over 40} + {5 (a - 2) \over 40} = {48 a + 5 (a - 2) \over 40} = {53 a - 10 \over 40}\) 1p |
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| havo wiskunde A | 6.3 Formules met breuken |
opgave 1Herleid tot één breuk. 1p a \({4 y \over x} ⋅ {x + 9 \over 7}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 y \over x} ⋅ {x + 9 \over 7} = {4 y (x + 9) \over 7 x} = {4 x y + 36 y \over 7 x}\) 1p 1p b \(-{3 \over 7} : {p - 2 q \over q}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables b \(-{3 \over 7} : {p - 2 q \over q} = -{3 \over 7} ⋅ {q \over p - 2 q} = -{3 q \over 7 (p - 2 q)} = -{3 q \over 7 p - 14 q}\) 1p |
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| havo wiskunde A | 11.2 Herleiden en combineren van formules |
opgave 1Deel uit. 1p a \({3 x^{2} + 9 x + 60 \over 3 x}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({3 x^{2} + 9 x + 60 \over 3 x} = {3 x^{2} \over 3 x} + {9 x \over 3 x} + {60 \over 3 x} = x + 3 + {20 \over x}\) 1p 1p b \({9 p^{2} + 8 p + 1 \over 4 p^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({9 p^{2} + 8 p + 1 \over 4 p^{2}} = {9 p^{2} \over 4 p^{2}} + {8 p \over 4 p^{2}} + {1 \over 4 p^{2}} = 2\frac{1}{4} + {2 \over p} + {1 \over 4 p^{2}}\) 1p |