Getal & Ruimte (13e editie) - 3 havo
'Breuken herleiden'.
| 2 havo/vwo | 1.2 Breuken optellen |
opgave 1Herleid tot één breuk. 1p a \({3 \over 4 p} + {5 \over 4 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 4 p} + {5 \over 4 p} = {8 \over 4 p} = {2 \over p}\) 1p 1p b \({6 \over x} - {5 \over 8 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over x} - {5 \over 8 x} = {48 \over 8 x} - {5 \over 8 x} = {43 \over 8 x}\) 1p 1p c \({5 \over 7 x} + {8 \over 6 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over 7 x} + {8 \over 6 y} = {30 y \over 42 x y} + {56 x \over 42 x y} = {30 y + 56 x \over 42 x y} = {15 y + 28 x \over 21 x y}\) 1p 1p d \(9 - {6 \over 5 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(9 - {6 \over 5 a} = {9 \over 1} - {6 \over 5 a} = {45 a \over 5 a} - {6 \over 5 a} = {45 a - 6 \over 5 a}\) 1p opgave 2Herleid tot één breuk. 1p a \(7 a - {9 \over 4 a}\) Optellen (5) 008y - Breuken herleiden - basis - 0ms - dynamic variables a \(7 a - {9 \over 4 a} = {7 a \over 1} ⋅ {4 a \over 4 a} - {9 \over 4 a} = {28 a^{2} \over 4 a} - {9 \over 4 a} = {28 a^{2} - 9 \over 4 a}\) 1p 1p b \({3 p \over q} - {9 \over 7 q}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables b \({3 p \over q} - {9 \over 7 q} = {21 p \over 7 q} - {9 \over 7 q} = {21 p - 9 \over 7 q}\) 1p 1p c \({4 b \over 3 a} + {9 a \over 2 b}\) Optellen (7) 0090 - Breuken herleiden - basis - 0ms - dynamic variables c \({4 b \over 3 a} + {9 a \over 2 b} = {8 b^{2} \over 6 a b} + {27 a^{2} \over 6 a b} = {27 a^{2} + 8 b^{2} \over 6 a b}\) 1p opgave 3Herleid. 1p a \({3 x \over x}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({3 x \over x} = {3 \over 1} = 3\) 1p 1p b \({a \over 4 a}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 4 a} = {1 \over 4}\) 1p 1p c \({-4 x \over 14 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-4 x \over 14 x} = -\frac{2}{7}\) 1p 1p d \({15 x \over -5 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({15 x \over -5 x} = -3\) 1p opgave 4Herleid. 1p a \({-28 a b \over 32 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-28 a b \over 32 a c} = -{7 b \over 8 c}\) 1p 1p b \({32 y \over -36 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({32 y \over -36 x y} = -{8 \over 9 x}\) 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 \({7 p q \over q} - {4 p r \over r}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 p q \over q} - {4 p r \over r} = 7 p - 4 p = 3 p\) 1p |
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| 2 havo/vwo | 1.3 Breuken vermenigvuldigen en delen |
opgave 1Herleid tot één breuk. 1p a \({5 \over x} ⋅ -{3 \over y}\) Vermenigvuldiging (1) 0091 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 \over x} ⋅ -{3 \over y} = -{15 \over x y}\) 1p 1p b \({a \over 9} ⋅ {6 \over b}\) Vermenigvuldiging (2) 0092 - Breuken herleiden - basis - 0ms - dynamic variables b \({a \over 9} ⋅ {6 \over b} = {6 a \over 9 b} = {2 a \over 3 b}\) 1p 1p c \({8 \over 3} ⋅ x\) Vermenigvuldiging (3) 0093 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 \over 3} ⋅ x = {8 x \over 3}\) 1p 1p d \({9 \over p} : {6 \over q}\) Deling (1) 0095 - Breuken herleiden - basis - 0ms - dynamic variables d \({9 \over p} : {6 \over q} = {9 \over p} ⋅ {q \over 6} = {9 q \over 6 p} = {3 q \over 2 p}\) 1p opgave 2Herleid tot één breuk. 1p \({7 \over 5} : a\) Deling (2) 0096 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({7 \over 5} : a = {7 \over 5} : {a \over 1} = {7 \over 5} ⋅ {1 \over a} = {7 \over 5 a}\) 1p |
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| 3 havo | 5.2 Breuken met letters herleiden |
opgave 1Herleid tot één breuk. 1p \({p \over 7} + {p - 5 \over 3}\) Optellen (8) 0098 - Breuken herleiden - basis - 0ms - dynamic variables ○ \({p \over 7} + {p - 5 \over 3} = {3 p \over 21} + {7 (p - 5) \over 21} = {3 p + 7 (p - 5) \over 21} = {10 p - 35 \over 21}\) 1p |