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

\({5 \over 8 a} + {7 \over 8 a}\)

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

a

\({5 \over 8 a} + {7 \over 8 a} = {12 \over 8 a} = {3 \over 2 a}\)

1p

1p

b

\({2 \over x} - {4 \over 6 x}\)

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

b

\({2 \over x} - {4 \over 6 x} = {12 \over 6 x} - {4 \over 6 x} = {8 \over 6 x} = {4 \over 3 x}\)

1p

1p

c

\({2 \over 5 p} - {9 \over 8 q}\)

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

c

\({2 \over 5 p} - {9 \over 8 q} = {16 q \over 40 p q} - {45 p \over 40 p q} = {16 q - 45 p \over 40 p q}\)

1p

1p

d

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

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

d

\(9 - {8 \over 3 a} = {9 \over 1} - {8 \over 3 a} = {27 a \over 3 a} - {8 \over 3 a} = {27 a - 8 \over 3 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(2 x - {9 \over 7 x}\)

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

a

\(2 x - {9 \over 7 x} = {2 x \over 1} ⋅ {7 x \over 7 x} - {9 \over 7 x} = {14 x^{2} \over 7 x} - {9 \over 7 x} = {14 x^{2} - 9 \over 7 x}\)

1p

1p

b

\({6 p \over q} - {8 \over 7 q}\)

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

b

\({6 p \over q} - {8 \over 7 q} = {42 p \over 7 q} - {8 \over 7 q} = {42 p - 8 \over 7 q}\)

1p

1p

c

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

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

c

\({6 b \over 4 a} - {5 a \over 9 b} = {54 b^{2} \over 36 a b} - {20 a^{2} \over 36 a b} = {-20 a^{2} + 54 b^{2} \over 36 a b} = {-10 a^{2} + 27 b^{2} \over 18 a b}\)

1p

opgave 3

Herleid.

1p

a

\({4 x \over x}\)

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

a

\({4 x \over x} = {4 \over 1} = 4\)

1p

1p

b

\({x \over 3 x}\)

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

b

\({x \over 3 x} = {1 \over 3}\)

1p

1p

c

\({21 a \over -24 a}\)

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

c

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

1p

1p

d

\({18 a \over 2 a}\)

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

d

\({18 a \over 2 a} = 9\)

1p

opgave 4

Herleid.

1p

a

\({-6 x y \over 10 x z}\)

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

a

\({-6 x y \over 10 x z} = -{3 y \over 5 z}\)

1p

1p

b

\({-28 b \over 32 a b}\)

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

b

\({-28 b \over 32 a b} = -{7 \over 8 a}\)

1p

1p

c

\({-9 p q r \over 3 q r}\)

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

c

\({-9 p q r \over 3 q r} = -3 p\)

1p

1p

d

\({7 x y \over y} + {6 x z \over z}\)

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

d

\({7 x y \over y} + {6 x z \over z} = 7 x + 6 x = 13 x\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({3 \over a} ⋅ -{9 \over b}\)

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

a

\({3 \over a} ⋅ -{9 \over b} = -{27 \over a b}\)

1p

1p

b

\({x \over 7} ⋅ -{6 \over y}\)

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

b

\({x \over 7} ⋅ -{6 \over y} = -{6 x \over 7 y}\)

1p

1p

c

\({6 \over 5} ⋅ a\)

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

c

\({6 \over 5} ⋅ a = {6 a \over 5}\)

1p

1p

d

\({4 \over x} : {9 \over y}\)

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

d

\({4 \over x} : {9 \over y} = {4 \over x} ⋅ {y \over 9} = {4 y \over 9 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

\(-{4 \over 3} : p\)

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

\(-{4 \over 3} : p = -{4 \over 3} : {p \over 1} = -{4 \over 3} ⋅ {1 \over p} = -{4 \over 3 p}\)

1p

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