Getal & Ruimte (13e editie) - vwo wiskunde B
'Breuken herleiden'.
| 1 vwo | 6.6 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \({3 \over 8 x} - {5 \over 8 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 8 x} - {5 \over 8 x} = -{2 \over 8 x} = -{1 \over 4 x}\) 1p 1p b \({5 \over a} - {2 \over 7 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({5 \over a} - {2 \over 7 a} = {35 \over 7 a} - {2 \over 7 a} = {33 \over 7 a}\) 1p 1p c \({6 \over 3 a} - {5 \over 4 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 3 a} - {5 \over 4 b} = {24 b \over 12 a b} - {15 a \over 12 a b} = {24 b - 15 a \over 12 a b} = {8 b - 5 a \over 4 a b}\) 1p 1p d \(2 - {5 \over 3 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(2 - {5 \over 3 p} = {2 \over 1} - {5 \over 3 p} = {6 p \over 3 p} - {5 \over 3 p} = {6 p - 5 \over 3 p}\) 1p opgave 2Herleid tot één breuk. 1p \({8 x \over y} + {4 \over 9 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 x \over y} + {4 \over 9 y} = {72 x \over 9 y} + {4 \over 9 y} = {72 x + 4 \over 9 y}\) 1p opgave 3Herleid. 1p a \({9 x \over x}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 x \over x} = {9 \over 1} = 9\) 1p 1p b \({a \over 3 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 3 a} = {1 \over 3}\) 1p 1p c \({6 p \over 9 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 p \over 9 p} = \frac{2}{3}\) 1p 1p d \({20 x \over 4 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({20 x \over 4 x} = 5\) 1p opgave 4Herleid. 1p a \({-20 a b \over -35 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-20 a b \over -35 a c} = {4 b \over 7 c}\) 1p 1p b \({15 q \over 35 p q}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({15 q \over 35 p q} = {3 \over 7 p}\) 1p 1p c \({16 a b c \over 4 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({16 a b c \over 4 b c} = 4 a\) 1p 1p d \({4 a b \over b} - {7 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({4 a b \over b} - {7 a c \over c} = 4 a - 7 a = -3 a\) 1p |
|
| 2 vwo | 1.2 Herleiden van breuken |
opgave 1Herleid tot één breuk. 1p a \(8 x - {7 \over 6 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(8 x - {7 \over 6 x} = {8 x \over 1} ⋅ {6 x \over 6 x} - {7 \over 6 x} = {48 x^{2} \over 6 x} - {7 \over 6 x} = {48 x^{2} - 7 \over 6 x}\) 1p 1p b \({4 y \over 2 x} + {8 x \over 5 y}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables b \({4 y \over 2 x} + {8 x \over 5 y} = {20 y^{2} \over 10 x y} + {16 x^{2} \over 10 x y} = {16 x^{2} + 20 y^{2} \over 10 x y} = {8 x^{2} + 10 y^{2} \over 5 x y}\) 1p 1p c \({9 \over a} ⋅ -{6 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over a} ⋅ -{6 \over b} = -{54 \over a b}\) 1p 1p d \({a \over 9} ⋅ -{2 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables d \({a \over 9} ⋅ -{2 \over b} = -{2 a \over 9 b}\) 1p opgave 2Herleid tot één breuk. 1p a \(-{5 \over 4} ⋅ p\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{5 \over 4} ⋅ p = -{5 p \over 4}\) 1p 1p b \({9 y \over x} ⋅ {x + 5 \over 4}\) Vermenigvuldiging (4) 0094 - Breuken herleiden - basis - 0ms - dynamic variables b \({9 y \over x} ⋅ {x + 5 \over 4} = {9 y (x + 5) \over 4 x} = {9 x y + 45 y \over 4 x}\) 1p 1p c \({8 \over a} : {5 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over a} : {5 \over b} = {8 \over a} ⋅ {b \over 5} = {8 b \over 5 a}\) 1p 1p d \({6 \over 5} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables d \({6 \over 5} : a = {6 \over 5} : {a \over 1} = {6 \over 5} ⋅ {1 \over a} = {6 \over 5 a}\) 1p opgave 3Herleid tot één breuk. 1p a \(-{6 \over 5} : {x + 3 y \over y}\) Deling (3) 0097 - Breuken herleiden - basis - 0ms - dynamic variables a \(-{6 \over 5} : {x + 3 y \over y} = -{6 \over 5} ⋅ {y \over x + 3 y} = -{6 y \over 5 (x + 3 y)} = -{6 y \over 5 x + 15 y}\) 1p 1p b \({5 p \over 6} + {p - 9 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 1ms - dynamic variables b \({5 p \over 6} + {p - 9 \over 7} = {35 p \over 42} + {6 (p - 9) \over 42} = {35 p + 6 (p - 9) \over 42} = {41 p - 54 \over 42}\) 1p |
|
| 3 vwo | 5.3 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({-9 p + 3 \over 5 p + 4} + 8\) Optellen (9) 00eh - Breuken herleiden - basis - 1ms - dynamic variables ○ \({-9 p + 3 \over 5 p + 4} + 8 = {-9 p + 3 \over 5 p + 4} + {8 (5 p + 4) \over 5 p + 4} = {-9 p + 3 + 8 (5 p + 4) \over 5 p + 4} = {-9 p + 3 + 40 p + 32 \over 5 p + 4} = {31 p + 35 \over 5 p + 4}\) 1p |
|
| vwo wiskunde B | 4.4 Formules met breuken herleiden |
opgave 1Deel uit. 1p a \({2 a^{2} - 4 a - 60 \over 2 a}\) Uitdelen (1) 00ei - Breuken herleiden - basis - 0ms - dynamic variables a \({2 a^{2} - 4 a - 60 \over 2 a} = {2 a^{2} \over 2 a} - {4 a \over 2 a} - {60 \over 2 a} = a - 2 - {30 \over a}\) 1p 1p b \({9 x^{2} + 4 x + 3 \over 2 x^{2}}\) Uitdelen (2) 00ej - Breuken herleiden - basis - 0ms - dynamic variables b \({9 x^{2} + 4 x + 3 \over 2 x^{2}} = {9 x^{2} \over 2 x^{2}} + {4 x \over 2 x^{2}} + {3 \over 2 x^{2}} = 4\frac{1}{2} + {2 \over x} + {3 \over 2 x^{2}}\) 1p |