Getal & Ruimte (13e editie) - 2 havo/vwo

'Breuken herleiden'.

2 havo/vwo 1.2 Breuken optellen

Breuken herleiden (15)

opgave 1

Herleid tot één breuk.

1p

a

\({9 \over 8 x} + {7 \over 8 x}\)

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

a

\({9 \over 8 x} + {7 \over 8 x} = {16 \over 8 x} = {2 \over x}\)

1p

1p

b

\({9 \over x} - {3 \over 8 x}\)

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

b

\({9 \over x} - {3 \over 8 x} = {72 \over 8 x} - {3 \over 8 x} = {69 \over 8 x}\)

1p

1p

c

\({3 \over 6 p} + {8 \over 2 q}\)

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

c

\({3 \over 6 p} + {8 \over 2 q} = {3 q \over 6 p q} + {24 p \over 6 p q} = {3 q + 24 p \over 6 p q} = {q + 8 p \over 2 p q}\)

1p

1p

d

\(6 - {8 \over 3 a}\)

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

d

\(6 - {8 \over 3 a} = {6 \over 1} - {8 \over 3 a} = {18 a \over 3 a} - {8 \over 3 a} = {18 a - 8 \over 3 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(3 a - {9 \over 8 a}\)

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

a

\(3 a - {9 \over 8 a} = {3 a \over 1} ⋅ {8 a \over 8 a} - {9 \over 8 a} = {24 a^{2} \over 8 a} - {9 \over 8 a} = {24 a^{2} - 9 \over 8 a}\)

1p

1p

b

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

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

b

\({6 x \over y} - {4 \over 8 y} = {48 x \over 8 y} - {4 \over 8 y} = {48 x - 4 \over 8 y} = {12 x - 1 \over 2 y}\)

1p

1p

c

\({5 y \over 3 x} - {2 x \over 8 y}\)

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

c

\({5 y \over 3 x} - {2 x \over 8 y} = {40 y^{2} \over 24 x y} - {6 x^{2} \over 24 x y} = {-6 x^{2} + 40 y^{2} \over 24 x y} = {-3 x^{2} + 20 y^{2} \over 12 x y}\)

1p

opgave 3

Herleid.

1p

a

\({5 p \over p}\)

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

a

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

1p

1p

b

\({a \over 8 a}\)

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

b

\({a \over 8 a} = {1 \over 8}\)

1p

1p

c

\({-8 a \over 20 a}\)

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

c

\({-8 a \over 20 a} = -\frac{2}{5}\)

1p

1p

d

\({-16 a \over 2 a}\)

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

d

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

1p

opgave 4

Herleid.

1p

a

\({-25 x y \over -40 x z}\)

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

a

\({-25 x y \over -40 x z} = {5 y \over 8 z}\)

1p

1p

b

\({14 q \over 18 p q}\)

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

b

\({14 q \over 18 p q} = {7 \over 9 p}\)

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

\({6 x y \over y} + {4 x z \over z}\)

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

d

\({6 x y \over y} + {4 x z \over z} = 6 x + 4 x = 10 x\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({3 \over p} ⋅ -{8 \over q}\)

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

a

\({3 \over p} ⋅ -{8 \over q} = -{24 \over p q}\)

1p

1p

b

\({x \over 2} ⋅ -{3 \over y}\)

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

b

\({x \over 2} ⋅ -{3 \over y} = -{3 x \over 2 y}\)

1p

1p

c

\({7 \over 9} ⋅ a\)

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

c

\({7 \over 9} ⋅ a = {7 a \over 9}\)

1p

1p

d

\({4 \over a} : {8 \over b}\)

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

d

\({4 \over a} : {8 \over b} = {4 \over a} ⋅ {b \over 8} = {4 b \over 8 a} = {b \over 2 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

\(-{8 \over 7} : x\)

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

○

\(-{8 \over 7} : x = -{8 \over 7} : {x \over 1} = -{8 \over 7} ⋅ {1 \over x} = -{8 \over 7 x}\)

1p

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