Getal & Ruimte (13e editie) - 3 havo
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({9 \over 7 a} - {6 \over 7 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({9 \over 7 a} - {6 \over 7 a} = {3 \over 7 a}\) 1p 1p b \({6 \over p} - {4 \over 5 p}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over p} - {4 \over 5 p} = {30 \over 5 p} - {4 \over 5 p} = {26 \over 5 p}\) 1p 1p c \({9 \over 4 a} - {5 \over 8 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({9 \over 4 a} - {5 \over 8 b} = {18 b \over 8 a b} - {5 a \over 8 a b} = {18 b - 5 a \over 8 a b}\) 1p 1p d \(5 - {4 \over 3 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(5 - {4 \over 3 x} = {5 \over 1} - {4 \over 3 x} = {15 x \over 3 x} - {4 \over 3 x} = {15 x - 4 \over 3 x}\) 1p opgave 2Herleid tot één breuk. 1p a \(5 x - {7 \over 6 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(5 x - {7 \over 6 x} = {5 x \over 1} ⋅ {6 x \over 6 x} - {7 \over 6 x} = {30 x^{2} \over 6 x} - {7 \over 6 x} = {30 x^{2} - 7 \over 6 x}\) 1p 1p b \({4 a \over b} - {5 \over 7 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({4 a \over b} - {5 \over 7 b} = {28 a \over 7 b} - {5 \over 7 b} = {28 a - 5 \over 7 b}\) 1p 1p c \({9 b \over 3 a} - {7 a \over 2 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({9 b \over 3 a} - {7 a \over 2 b} = {18 b^{2} \over 6 a b} - {21 a^{2} \over 6 a b} = {-21 a^{2} + 18 b^{2} \over 6 a b} = {-7 a^{2} + 6 b^{2} \over 2 a b}\) 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 \({x \over 6 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 6 x} = {1 \over 6}\) 1p 1p c \({-25 x \over -40 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-25 x \over -40 x} = \frac{5}{8}\) 1p 1p d \({-30 x \over 5 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-30 x \over 5 x} = -6\) 1p opgave 4Herleid. 1p a \({-24 a b \over 28 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-24 a b \over 28 a c} = -{6 b \over 7 c}\) 1p 1p b \({6 y \over 14 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({6 y \over 14 x y} = {3 \over 7 x}\) 1p 1p c \({20 a b c \over -5 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({20 a b c \over -5 b c} = -4 a\) 1p 1p d \({6 p q \over q} - {2 p r \over r}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({6 p q \over q} - {2 p r \over r} = 6 p - 2 p = 4 p\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({2 \over x} ⋅ {4 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 \over x} ⋅ {4 \over y} = {8 \over x y}\) 1p 1p b \({a \over 4} ⋅ -{6 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 4} ⋅ -{6 \over b} = -{6 a \over 4 b} = -{3 a \over 2 b}\) 1p 1p c \(-{7 \over 4} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{7 \over 4} ⋅ a = -{7 a \over 4}\) 1p 1p d \({8 \over x} : {7 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({8 \over x} : {7 \over y} = {8 \over x} ⋅ {y \over 7} = {8 y \over 7 x}\) 1p opgave 2Herleid tot één breuk. 1p \({3 \over 2} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({3 \over 2} : p = {3 \over 2} : {p \over 1} = {3 \over 2} ⋅ {1 \over p} = {3 \over 2 p}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({5 x \over 8} + {x + 4 \over 7}\) Optellen (8) 0098 - Breuken herleiden - basis - 1ms - dynamic variables ○ \({5 x \over 8} + {x + 4 \over 7} = {35 x \over 56} + {8 (x + 4) \over 56} = {35 x + 8 (x + 4) \over 56} = {43 x + 32 \over 56}\) 1p |