Getal & Ruimte (13e editie) - 3 havo
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({7 \over 4 x} - {8 \over 4 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({7 \over 4 x} - {8 \over 4 x} = -{1 \over 4 x}\) 1p 1p b \({5 \over p} + {9 \over 3 p}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({5 \over p} + {9 \over 3 p} = {15 \over 3 p} + {9 \over 3 p} = {24 \over 3 p} = {8 \over p}\) 1p 1p c \({7 \over 3 a} + {8 \over 6 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 3 a} + {8 \over 6 b} = {14 b \over 6 a b} + {8 a \over 6 a b} = {14 b + 8 a \over 6 a b} = {7 b + 4 a \over 3 a b}\) 1p 1p d \(5 + {3 \over 8 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(5 + {3 \over 8 a} = {5 \over 1} + {3 \over 8 a} = {40 a \over 8 a} + {3 \over 8 a} = {40 a + 3 \over 8 a}\) 1p opgave 2Herleid tot één breuk. 1p a \(5 x + {3 \over 2 x}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(5 x + {3 \over 2 x} = {5 x \over 1} ⋅ {2 x \over 2 x} + {3 \over 2 x} = {10 x^{2} \over 2 x} + {3 \over 2 x} = {10 x^{2} + 3 \over 2 x}\) 1p 1p b \({8 x \over y} + {9 \over 4 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({8 x \over y} + {9 \over 4 y} = {32 x \over 4 y} + {9 \over 4 y} = {32 x + 9 \over 4 y}\) 1p 1p c \({4 b \over 9 a} - {7 a \over 8 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({4 b \over 9 a} - {7 a \over 8 b} = {32 b^{2} \over 72 a b} - {63 a^{2} \over 72 a b} = {-63 a^{2} + 32 b^{2} \over 72 a b}\) 1p opgave 3Herleid. 1p a \({2 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({2 a \over a} = {2 \over 1} = 2\) 1p 1p b \({p \over 9 p}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 9 p} = {1 \over 9}\) 1p 1p c \({-15 x \over -21 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-15 x \over -21 x} = \frac{5}{7}\) 1p 1p d \({-9 x \over 3 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-9 x \over 3 x} = -3\) 1p opgave 4Herleid. 1p a \({12 a b \over -28 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({12 a b \over -28 a c} = -{3 b \over 7 c}\) 1p 1p b \({15 b \over 24 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({15 b \over 24 a b} = {5 \over 8 a}\) 1p 1p c \({-35 x y z \over 5 y z}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-35 x y z \over 5 y z} = -7 x\) 1p 1p d \({4 p q \over q} + {3 p r \over r}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({4 p q \over q} + {3 p r \over r} = 4 p + 3 p = 7 p\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({4 \over a} ⋅ {3 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over a} ⋅ {3 \over b} = {12 \over a b}\) 1p 1p b \({x \over 6} ⋅ {9 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 6} ⋅ {9 \over y} = {9 x \over 6 y} = {3 x \over 2 y}\) 1p 1p c \(-{6 \over 7} ⋅ a\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \(-{6 \over 7} ⋅ a = -{6 a \over 7}\) 1p 1p d \({7 \over x} : {8 \over y}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({7 \over x} : {8 \over y} = {7 \over x} ⋅ {y \over 8} = {7 y \over 8 x}\) 1p opgave 2Herleid tot één breuk. 1p \(-{8 \over 9} : p\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \(-{8 \over 9} : p = -{8 \over 9} : {p \over 1} = -{8 \over 9} ⋅ {1 \over p} = -{8 \over 9 p}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({x \over 7} + {x - 2 \over 3}\) Optellen (8) 0098 - Breuken herleiden - basis - 1ms - dynamic variables ○ \({x \over 7} + {x - 2 \over 3} = {3 x \over 21} + {7 (x - 2) \over 21} = {3 x + 7 (x - 2) \over 21} = {10 x - 14 \over 21}\) 1p |