Getal & Ruimte (13e editie) - 3 vwo
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({8 \over 9 x} - {2 \over 9 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over 9 x} - {2 \over 9 x} = {6 \over 9 x} = {2 \over 3 x}\) 1p 1p b \({3 \over p} + {2 \over 6 p}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({3 \over p} + {2 \over 6 p} = {18 \over 6 p} + {2 \over 6 p} = {20 \over 6 p} = {10 \over 3 p}\) 1p 1p c \({6 \over 3 x} + {2 \over 4 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 3 x} + {2 \over 4 y} = {24 y \over 12 x y} + {6 x \over 12 x y} = {24 y + 6 x \over 12 x y} = {4 y + x \over 2 x y}\) 1p 1p d \(9 + {3 \over 4 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(9 + {3 \over 4 a} = {9 \over 1} + {3 \over 4 a} = {36 a \over 4 a} + {3 \over 4 a} = {36 a + 3 \over 4 a}\) 1p opgave 2Herleid tot één breuk. 1p \({7 a \over b} + {9 \over 8 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({7 a \over b} + {9 \over 8 b} = {56 a \over 8 b} + {9 \over 8 b} = {56 a + 9 \over 8 b}\) 1p opgave 3Herleid. 1p a \({3 x \over x}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 x \over x} = {3 \over 1} = 3\) 1p 1p b \({x \over 9 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 9 x} = {1 \over 9}\) 1p 1p c \({-32 a \over -36 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-32 a \over -36 a} = \frac{8}{9}\) 1p 1p d \({-28 p \over 4 p}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-28 p \over 4 p} = -7\) 1p opgave 4Herleid. 1p a \({-15 a b \over 18 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-15 a b \over 18 a c} = -{5 b \over 6 c}\) 1p 1p b \({4 y \over 14 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({4 y \over 14 x y} = {2 \over 7 x}\) 1p 1p c \({4 a b c \over -2 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({4 a b c \over -2 b c} = -2 a\) 1p 1p d \({5 p q \over q} + {2 p r \over r}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({5 p q \over q} + {2 p r \over r} = 5 p + 2 p = 7 p\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(4 a - {7 \over 6 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(4 a - {7 \over 6 a} = {4 a \over 1} ⋅ {6 a \over 6 a} - {7 \over 6 a} = {24 a^{2} \over 6 a} - {7 \over 6 a} = {24 a^{2} - 7 \over 6 a}\) 1p 1p b \({7 b \over 3 a} - {4 a \over 2 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({7 b \over 3 a} - {4 a \over 2 b} = {14 b^{2} \over 6 a b} - {12 a^{2} \over 6 a b} = {-12 a^{2} + 14 b^{2} \over 6 a b} = {-6 a^{2} + 7 b^{2} \over 3 a b}\) 1p 1p c \({8 \over x} ⋅ {7 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over x} ⋅ {7 \over y} = {56 \over x y}\) 1p 1p d \({x \over 3} ⋅ -{5 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({x \over 3} ⋅ -{5 \over y} = -{5 x \over 3 y}\) 1p opgave 2Herleid tot één breuk. 1p a \(-{7 \over 4} ⋅ p\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{7 \over 4} ⋅ p = -{7 p \over 4}\) 1p 1p b \({7 b \over a} ⋅ {a - 2 \over 9}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({7 b \over a} ⋅ {a - 2 \over 9} = {7 b (a - 2) \over 9 a} = {7 a b - 14 b \over 9 a}\) 1p 1p c \({3 \over x} : {9 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({3 \over x} : {9 \over y} = {3 \over x} ⋅ {y \over 9} = {3 y \over 9 x} = {y \over 3 x}\) 1p 1p d \(-{5 \over 6} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{5 \over 6} : p = -{5 \over 6} : {p \over 1} = -{5 \over 6} ⋅ {1 \over p} = -{5 \over 6 p}\) 1p opgave 3Herleid tot één breuk. 1p a \({8 \over 5} : {x - 4 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 \over 5} : {x - 4 y \over y} = {8 \over 5} ⋅ {y \over x - 4 y} = {8 y \over 5 (x - 4 y)} = {8 y \over 5 x - 20 y}\) 1p 1p b \({a \over 8} + {a - 6 \over 9}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 8} + {a - 6 \over 9} = {9 a \over 72} + {8 (a - 6) \over 72} = {9 a + 8 (a - 6) \over 72} = {17 a - 48 \over 72}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-9 p - 3 \over -7 p - 1} - 4\) Optellen (9) 00eh - Breuken herleiden - basis - 0ms - dynamic variables ○ \({-9 p - 3 \over -7 p - 1} - 4 = {-9 p - 3 \over -7 p - 1} + {-4 (-7 p - 1) \over -7 p - 1} = {-9 p - 3 - 4 (-7 p - 1) \over -7 p - 1} = {-9 p - 3 + 28 p + 4 \over -7 p - 1} = {19 p + 1 \over -7 p - 1}\) 1p |