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

\({4 \over 8 a} + {6 \over 8 a}\)

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

a

\({4 \over 8 a} + {6 \over 8 a} = {10 \over 8 a} = {5 \over 4 a}\)

1p

1p

b

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

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

b

\({9 \over x} - {2 \over 7 x} = {63 \over 7 x} - {2 \over 7 x} = {61 \over 7 x}\)

1p

1p

c

\({5 \over 3 p} + {4 \over 7 q}\)

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

c

\({5 \over 3 p} + {4 \over 7 q} = {35 q \over 21 p q} + {12 p \over 21 p q} = {35 q + 12 p \over 21 p q}\)

1p

1p

d

\(5 - {7 \over 6 x}\)

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

d

\(5 - {7 \over 6 x} = {5 \over 1} - {7 \over 6 x} = {30 x \over 6 x} - {7 \over 6 x} = {30 x - 7 \over 6 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(5 a - {2 \over 9 a}\)

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

a

\(5 a - {2 \over 9 a} = {5 a \over 1} ⋅ {9 a \over 9 a} - {2 \over 9 a} = {45 a^{2} \over 9 a} - {2 \over 9 a} = {45 a^{2} - 2 \over 9 a}\)

1p

1p

b

\({9 p \over q} + {3 \over 4 q}\)

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

b

\({9 p \over q} + {3 \over 4 q} = {36 p \over 4 q} + {3 \over 4 q} = {36 p + 3 \over 4 q}\)

1p

1p

c

\({4 b \over 8 a} - {2 a \over 6 b}\)

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

c

\({4 b \over 8 a} - {2 a \over 6 b} = {12 b^{2} \over 24 a b} - {8 a^{2} \over 24 a b} = {-8 a^{2} + 12 b^{2} \over 24 a b} = {-2 a^{2} + 3 b^{2} \over 6 a b}\)

1p

opgave 3

Herleid.

1p

a

\({5 a \over a}\)

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

a

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

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

\({20 x \over 24 x}\)

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

c

\({20 x \over 24 x} = \frac{5}{6}\)

1p

1p

d

\({-6 a \over 2 a}\)

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

d

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

1p

opgave 4

Herleid.

1p

a

\({10 x y \over 18 x z}\)

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

a

\({10 x y \over 18 x z} = {5 y \over 9 z}\)

1p

1p

b

\({-9 q \over 15 p q}\)

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

b

\({-9 q \over 15 p q} = -{3 \over 5 p}\)

1p

1p

c

\({-8 a b c \over 2 b c}\)

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

c

\({-8 a b c \over 2 b c} = -4 a\)

1p

1p

d

\({4 x y \over y} - {5 x z \over z}\)

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

d

\({4 x y \over y} - {5 x z \over z} = 4 x - 5 x = -x\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({2 \over a} ⋅ {9 \over b}\)

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

a

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

1p

1p

b

\({a \over 6} ⋅ -{3 \over b}\)

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

b

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

1p

1p

c

\(-{9 \over 5} ⋅ x\)

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

c

\(-{9 \over 5} ⋅ x = -{9 x \over 5}\)

1p

1p

d

\({3 \over x} : {4 \over y}\)

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

d

\({3 \over x} : {4 \over y} = {3 \over x} ⋅ {y \over 4} = {3 y \over 4 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

\(-{2 \over 5} : p\)

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

○

\(-{2 \over 5} : p = -{2 \over 5} : {p \over 1} = -{2 \over 5} ⋅ {1 \over p} = -{2 \over 5 p}\)

1p

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