Getal & Ruimte (13e editie) - vwo wiskunde A
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({4 \over 6 a} - {8 \over 6 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 6 a} - {8 \over 6 a} = -{4 \over 6 a} = -{2 \over 3 a}\) 1p 1p b \({2 \over a} - {3 \over 7 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({2 \over a} - {3 \over 7 a} = {14 \over 7 a} - {3 \over 7 a} = {11 \over 7 a}\) 1p 1p c \({2 \over 3 p} + {5 \over 8 q}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({2 \over 3 p} + {5 \over 8 q} = {16 q \over 24 p q} + {15 p \over 24 p q} = {16 q + 15 p \over 24 p q}\) 1p 1p d \(6 - {3 \over 4 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(6 - {3 \over 4 x} = {6 \over 1} - {3 \over 4 x} = {24 x \over 4 x} - {3 \over 4 x} = {24 x - 3 \over 4 x}\) 1p opgave 2Herleid tot één breuk. 1p \({7 x \over y} - {4 \over 3 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({7 x \over y} - {4 \over 3 y} = {21 x \over 3 y} - {4 \over 3 y} = {21 x - 4 \over 3 y}\) 1p opgave 3Herleid. 1p a \({7 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({7 p \over p} = {7 \over 1} = 7\) 1p 1p b \({a \over 4 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 4 a} = {1 \over 4}\) 1p 1p c \({-16 x \over -36 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-16 x \over -36 x} = \frac{4}{9}\) 1p 1p d \({6 x \over -3 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({6 x \over -3 x} = -2\) 1p opgave 4Herleid. 1p a \({8 a b \over -10 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 a b \over -10 a c} = -{4 b \over 5 c}\) 1p 1p b \({-8 y \over 10 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-8 y \over 10 x y} = -{4 \over 5 x}\) 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 \({6 x y \over y} + {3 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({6 x y \over y} + {3 x z \over z} = 6 x + 3 x = 9 x\) 1p |
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| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(4 x - {8 \over 5 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(4 x - {8 \over 5 x} = {4 x \over 1} ⋅ {5 x \over 5 x} - {8 \over 5 x} = {20 x^{2} \over 5 x} - {8 \over 5 x} = {20 x^{2} - 8 \over 5 x}\) 1p 1p b \({8 b \over 6 a} + {7 a \over 5 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({8 b \over 6 a} + {7 a \over 5 b} = {40 b^{2} \over 30 a b} + {42 a^{2} \over 30 a b} = {42 a^{2} + 40 b^{2} \over 30 a b} = {21 a^{2} + 20 b^{2} \over 15 a b}\) 1p 1p c \({4 \over a} ⋅ -{5 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({4 \over a} ⋅ -{5 \over b} = -{20 \over a b}\) 1p 1p d \({p \over 9} ⋅ {6 \over q}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({p \over 9} ⋅ {6 \over q} = {6 p \over 9 q} = {2 p \over 3 q}\) 1p opgave 2Herleid tot één breuk. 1p a \({1 \over 3} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \({1 \over 3} ⋅ x = {x \over 3}\) 1p 1p b \({5 b \over a} ⋅ {a - 6 \over 2}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({5 b \over a} ⋅ {a - 6 \over 2} = {5 b (a - 6) \over 2 a} = {5 a b - 30 b \over 2 a}\) 1p 1p c \({8 \over p} : {7 \over q}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over p} : {7 \over q} = {8 \over p} ⋅ {q \over 7} = {8 q \over 7 p}\) 1p 1p d \(-{1 \over 6} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \(-{1 \over 6} : a = -{1 \over 6} : {a \over 1} = -{1 \over 6} ⋅ {1 \over a} = -{1 \over 6 a}\) 1p opgave 3Herleid tot één breuk. 1p a \(-{6 \over 5} : {x + 9 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{6 \over 5} : {x + 9 y \over y} = -{6 \over 5} ⋅ {y \over x + 9 y} = -{6 y \over 5 (x + 9 y)} = -{6 y \over 5 x + 45 y}\) 1p 1p b \({2 x \over 5} + {x - 1 \over 6}\) Optellen (8) 0098 - Breuken herleiden - basis - 1ms - dynamic variables b \({2 x \over 5} + {x - 1 \over 6} = {12 x \over 30} + {5 (x - 1) \over 30} = {12 x + 5 (x - 1) \over 30} = {17 x - 5 \over 30}\) 1p |
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| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({4 x - 7 \over 2 x - 1} + 6\) Optellen (9) 00eh - Breuken herleiden - basis - 1ms - dynamic variables ○ \({4 x - 7 \over 2 x - 1} + 6 = {4 x - 7 \over 2 x - 1} + {6 (2 x - 1) \over 2 x - 1} = {4 x - 7 + 6 (2 x - 1) \over 2 x - 1} = {4 x - 7 + 12 x - 6 \over 2 x - 1} = {16 x - 13 \over 2 x - 1}\) 1p |
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| vwo wiskunde A | 3.1 Breuken en verhoudingen |
opgave 1Deel uit. 1p a \({3 p^{2} + 9 p - 60 \over 3 p}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({3 p^{2} + 9 p - 60 \over 3 p} = {3 p^{2} \over 3 p} + {9 p \over 3 p} - {60 \over 3 p} = p + 3 - {20 \over p}\) 1p 1p b \({8 a^{2} + 3 a - 6 \over 4 a^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({8 a^{2} + 3 a - 6 \over 4 a^{2}} = {8 a^{2} \over 4 a^{2}} + {3 a \over 4 a^{2}} - {6 \over 4 a^{2}} = 2 + {3 \over 4 a} - {3 \over 2 a^{2}}\) 1p |