Getal & Ruimte (13e editie) - 3 havo
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({7 \over 4 x} - {5 \over 4 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({7 \over 4 x} - {5 \over 4 x} = {2 \over 4 x} = {1 \over 2 x}\) 1p 1p b \({8 \over a} - {4 \over 9 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({8 \over a} - {4 \over 9 a} = {72 \over 9 a} - {4 \over 9 a} = {68 \over 9 a}\) 1p 1p c \({7 \over 5 p} + {9 \over 6 q}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 5 p} + {9 \over 6 q} = {42 q \over 30 p q} + {45 p \over 30 p q} = {42 q + 45 p \over 30 p q} = {14 q + 15 p \over 10 p q}\) 1p 1p d \(3 - {8 \over 9 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(3 - {8 \over 9 x} = {3 \over 1} - {8 \over 9 x} = {27 x \over 9 x} - {8 \over 9 x} = {27 x - 8 \over 9 x}\) 1p opgave 2Herleid tot één breuk. 1p a \(6 a - {4 \over 9 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(6 a - {4 \over 9 a} = {6 a \over 1} ⋅ {9 a \over 9 a} - {4 \over 9 a} = {54 a^{2} \over 9 a} - {4 \over 9 a} = {54 a^{2} - 4 \over 9 a}\) 1p 1p b \({5 a \over b} + {7 \over 6 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({5 a \over b} + {7 \over 6 b} = {30 a \over 6 b} + {7 \over 6 b} = {30 a + 7 \over 6 b}\) 1p 1p c \({2 b \over 9 a} - {7 a \over 8 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({2 b \over 9 a} - {7 a \over 8 b} = {16 b^{2} \over 72 a b} - {63 a^{2} \over 72 a b} = {-63 a^{2} + 16 b^{2} \over 72 a b}\) 1p opgave 3Herleid. 1p a \({9 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 p \over p} = {9 \over 1} = 9\) 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 \({-12 x \over -28 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-12 x \over -28 x} = \frac{3}{7}\) 1p 1p d \({20 x \over -5 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({20 x \over -5 x} = -4\) 1p opgave 4Herleid. 1p a \({-20 x y \over -25 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-20 x y \over -25 x z} = {4 y \over 5 z}\) 1p 1p b \({-4 b \over -14 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-4 b \over -14 a b} = {2 \over 7 a}\) 1p 1p c \({-35 p q r \over -5 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-35 p q r \over -5 q r} = 7 p\) 1p 1p d \({6 a b \over b} - {5 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({6 a b \over b} - {5 a c \over c} = 6 a - 5 a = a\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({3 \over a} ⋅ -{5 \over b}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over a} ⋅ -{5 \over b} = -{15 \over a b}\) 1p 1p b \({x \over 8} ⋅ -{7 \over y}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 8} ⋅ -{7 \over y} = -{7 x \over 8 y}\) 1p 1p c \({1 \over 5} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({1 \over 5} ⋅ x = {x \over 5}\) 1p 1p d \({6 \over p} : {9 \over q}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({6 \over p} : {9 \over q} = {6 \over p} ⋅ {q \over 9} = {6 q \over 9 p} = {2 q \over 3 p}\) 1p opgave 2Herleid tot één breuk. 1p \({7 \over 4} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({7 \over 4} : a = {7 \over 4} : {a \over 1} = {7 \over 4} ⋅ {1 \over a} = {7 \over 4 a}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({7 p \over 3} + {p + 6 \over 5}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({7 p \over 3} + {p + 6 \over 5} = {35 p \over 15} + {3 (p + 6) \over 15} = {35 p + 3 (p + 6) \over 15} = {38 p + 18 \over 15}\) 1p |