Getal & Ruimte (13e editie) - 2 vwo

'Breuken herleiden'.

1 vwo 6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

1p

a

\({9 \over 7 p} + {2 \over 7 p}\)

Optellen (1)
008u - Breuken herleiden - basis - 0ms - dynamic variables

a

\({9 \over 7 p} + {2 \over 7 p} = {11 \over 7 p}\)

1p

1p

b

\({5 \over a} - {4 \over 2 a}\)

Optellen (2)
008v - Breuken herleiden - basis - 0ms - dynamic variables

b

\({5 \over a} - {4 \over 2 a} = {10 \over 2 a} - {4 \over 2 a} = {6 \over 2 a} = {3 \over a}\)

1p

1p

c

\({6 \over 9 x} - {8 \over 4 y}\)

Optellen (3)
008w - Breuken herleiden - basis - 0ms - dynamic variables

c

\({6 \over 9 x} - {8 \over 4 y} = {24 y \over 36 x y} - {72 x \over 36 x y} = {24 y - 72 x \over 36 x y} = {2 y - 6 x \over 3 x y}\)

1p

1p

d

\(8 - {5 \over 2 a}\)

Optellen (4)
008x - Breuken herleiden - basis - 0ms - dynamic variables

d

\(8 - {5 \over 2 a} = {8 \over 1} - {5 \over 2 a} = {16 a \over 2 a} - {5 \over 2 a} = {16 a - 5 \over 2 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

\({9 x \over y} - {6 \over 4 y}\)

Optellen (6)
008z - Breuken herleiden - basis - 0ms - dynamic variables

\({9 x \over y} - {6 \over 4 y} = {36 x \over 4 y} - {6 \over 4 y} = {36 x - 6 \over 4 y} = {18 x - 3 \over 2 y}\)

1p

opgave 3

Herleid.

1p

a

\({6 a \over a}\)

Vereenvoudigen (1)
00h5 - Breuken herleiden - basis - 0ms - dynamic variables

a

\({6 a \over a} = {6 \over 1} = 6\)

1p

1p

b

\({a \over 5 a}\)

Vereenvoudigen (2)
00h6 - Breuken herleiden - basis - 0ms - dynamic variables

b

\({a \over 5 a} = {1 \over 5}\)

1p

1p

c

\({21 x \over 24 x}\)

Vereenvoudigen (3)
00h7 - Breuken herleiden - basis - 0ms - dynamic variables

c

\({21 x \over 24 x} = \frac{7}{8}\)

1p

1p

d

\({30 p \over -5 p}\)

Vereenvoudigen (4)
00h8 - Breuken herleiden - basis - 0ms - dynamic variables

d

\({30 p \over -5 p} = -6\)

1p

opgave 4

Herleid.

1p

a

\({14 x y \over 16 x z}\)

Vereenvoudigen (5)
00h9 - Breuken herleiden - basis - 0ms - dynamic variables

a

\({14 x y \over 16 x z} = {7 y \over 8 z}\)

1p

1p

b

\({12 y \over -28 x y}\)

Vereenvoudigen (6)
00ha - Breuken herleiden - basis - 0ms - dynamic variables

b

\({12 y \over -28 x y} = -{3 \over 7 x}\)

1p

1p

c

\({35 a b c \over 5 b c}\)

Vereenvoudigen (7)
00hb - Breuken herleiden - basis - 0ms - dynamic variables

c

\({35 a b c \over 5 b c} = 7 a\)

1p

1p

d

\({2 x y \over y} + {5 x z \over z}\)

Vereenvoudigen (8)
00hc - Breuken herleiden - basis - 0ms - dynamic variables

d

\({2 x y \over y} + {5 x z \over z} = 2 x + 5 x = 7 x\)

1p

2 vwo 1.2 Herleiden van breuken

Breuken herleiden (10)

opgave 1

Herleid tot één breuk.

1p

a

\(5 a + {8 \over 3 a}\)

Optellen (5)
008y - Breuken herleiden - basis - 0ms - dynamic variables

a

\(5 a + {8 \over 3 a} = {5 a \over 1} ⋅ {3 a \over 3 a} + {8 \over 3 a} = {15 a^{2} \over 3 a} + {8 \over 3 a} = {15 a^{2} + 8 \over 3 a}\)

1p

1p

b

\({9 b \over 5 a} - {4 a \over 6 b}\)

Optellen (7)
0090 - Breuken herleiden - basis - 0ms - dynamic variables

b

\({9 b \over 5 a} - {4 a \over 6 b} = {54 b^{2} \over 30 a b} - {20 a^{2} \over 30 a b} = {-20 a^{2} + 54 b^{2} \over 30 a b} = {-10 a^{2} + 27 b^{2} \over 15 a b}\)

1p

1p

c

\({6 \over x} ⋅ -{4 \over y}\)

Vermenigvuldiging (1)
0091 - Breuken herleiden - basis - 0ms - dynamic variables

c

\({6 \over x} ⋅ -{4 \over y} = -{24 \over x y}\)

1p

1p

d

\({x \over 8} ⋅ {7 \over y}\)

Vermenigvuldiging (2)
0092 - Breuken herleiden - basis - 0ms - dynamic variables

d

\({x \over 8} ⋅ {7 \over y} = {7 x \over 8 y}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\({3 \over 8} ⋅ p\)

Vermenigvuldiging (3)
0093 - Breuken herleiden - basis - 0ms - dynamic variables

a

\({3 \over 8} ⋅ p = {3 p \over 8}\)

1p

1p

b

\({4 b \over a} ⋅ {a - 7 \over 6}\)

Vermenigvuldiging (4)
0094 - Breuken herleiden - basis - 0ms - dynamic variables

b

\({4 b \over a} ⋅ {a - 7 \over 6} = {4 b (a - 7) \over 6 a} = {2 b (a - 7) \over 3 a} = {2 a b - 14 b \over 3 a}\)

1p

1p

c

\({3 \over a} : {8 \over b}\)

Deling (1)
0095 - Breuken herleiden - basis - 0ms - dynamic variables

c

\({3 \over a} : {8 \over b} = {3 \over a} ⋅ {b \over 8} = {3 b \over 8 a}\)

1p

1p

d

\(-{6 \over 5} : x\)

Deling (2)
0096 - Breuken herleiden - basis - 0ms - dynamic variables

d

\(-{6 \over 5} : x = -{6 \over 5} : {x \over 1} = -{6 \over 5} ⋅ {1 \over x} = -{6 \over 5 x}\)

1p

opgave 3

Herleid tot één breuk.

1p

a

\({5 \over 2} : {x - 6 y \over y}\)

Deling (3)
0097 - Breuken herleiden - basis - 0ms - dynamic variables

a

\({5 \over 2} : {x - 6 y \over y} = {5 \over 2} ⋅ {y \over x - 6 y} = {5 y \over 2 (x - 6 y)} = {5 y \over 2 x - 12 y}\)

1p

1p

b

\({7 p \over 6} + {p + 4 \over 5}\)

Optellen (8)
0098 - Breuken herleiden - basis - 0ms - dynamic variables

b

\({7 p \over 6} + {p + 4 \over 5} = {35 p \over 30} + {6 (p + 4) \over 30} = {35 p + 6 (p + 4) \over 30} = {41 p + 24 \over 30}\)

1p

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