Getal & Ruimte (13e editie) - 2 havo/vwo
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({6 \over 7 a} + {8 \over 7 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({6 \over 7 a} + {8 \over 7 a} = {14 \over 7 a} = {2 \over a}\) 1p 1p b \({3 \over x} + {9 \over 4 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({3 \over x} + {9 \over 4 x} = {12 \over 4 x} + {9 \over 4 x} = {21 \over 4 x}\) 1p 1p c \({4 \over 5 x} - {8 \over 7 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({4 \over 5 x} - {8 \over 7 y} = {28 y \over 35 x y} - {40 x \over 35 x y} = {28 y - 40 x \over 35 x y}\) 1p 1p d \(5 - {2 \over 7 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(5 - {2 \over 7 p} = {5 \over 1} - {2 \over 7 p} = {35 p \over 7 p} - {2 \over 7 p} = {35 p - 2 \over 7 p}\) 1p opgave 2Herleid tot één breuk. 1p a \(3 a + {7 \over 4 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(3 a + {7 \over 4 a} = {3 a \over 1} ⋅ {4 a \over 4 a} + {7 \over 4 a} = {12 a^{2} \over 4 a} + {7 \over 4 a} = {12 a^{2} + 7 \over 4 a}\) 1p 1p b \({2 a \over b} - {5 \over 9 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({2 a \over b} - {5 \over 9 b} = {18 a \over 9 b} - {5 \over 9 b} = {18 a - 5 \over 9 b}\) 1p 1p c \({9 y \over 3 x} - {2 x \over 8 y}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 y \over 3 x} - {2 x \over 8 y} = {72 y^{2} \over 24 x y} - {6 x^{2} \over 24 x y} = {-6 x^{2} + 72 y^{2} \over 24 x y} = {-x^{2} + 12 y^{2} \over 4 x y}\) 1p opgave 3Herleid. 1p a \({9 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 a \over a} = {9 \over 1} = 9\) 1p 1p b \({x \over 8 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 8 x} = {1 \over 8}\) 1p 1p c \({10 p \over -16 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({10 p \over -16 p} = -\frac{5}{8}\) 1p 1p d \({32 a \over -4 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({32 a \over -4 a} = -8\) 1p opgave 4Herleid. 1p a \({20 p q \over 36 p r}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({20 p q \over 36 p r} = {5 q \over 9 r}\) 1p 1p b \({8 y \over 36 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({8 y \over 36 x y} = {2 \over 9 x}\) 1p 1p c \({15 a b c \over -3 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({15 a b c \over -3 b c} = -5 a\) 1p 1p d \({5 x y \over y} - {6 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({5 x y \over y} - {6 x z \over z} = 5 x - 6 x = -x\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({6 \over a} ⋅ {5 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({6 \over a} ⋅ {5 \over b} = {30 \over a b}\) 1p 1p b \({x \over 9} ⋅ -{6 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 9} ⋅ -{6 \over y} = -{6 x \over 9 y} = -{2 x \over 3 y}\) 1p 1p c \({7 \over 2} ⋅ p\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 2} ⋅ p = {7 p \over 2}\) 1p 1p d \({2 \over a} : {8 \over b}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({2 \over a} : {8 \over b} = {2 \over a} ⋅ {b \over 8} = {2 b \over 8 a} = {b \over 4 a}\) 1p opgave 2Herleid tot één breuk. 1p \({1 \over 8} : x\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({1 \over 8} : x = {1 \over 8} : {x \over 1} = {1 \over 8} ⋅ {1 \over x} = {1 \over 8 x}\) 1p |