Getal & Ruimte (13e editie) - 3 havo

'Breuken herleiden'.

2 havo/vwo 1.2 Breuken optellen

Breuken herleiden (15)

opgave 1

Herleid tot één breuk.

1p

a

\({4 \over 2 x} - {8 \over 2 x}\)

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

a

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

1p

1p

b

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

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

b

\({4 \over x} - {9 \over 8 x} = {32 \over 8 x} - {9 \over 8 x} = {23 \over 8 x}\)

1p

1p

c

\({6 \over 9 a} - {7 \over 4 b}\)

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

c

\({6 \over 9 a} - {7 \over 4 b} = {24 b \over 36 a b} - {63 a \over 36 a b} = {24 b - 63 a \over 36 a b} = {8 b - 21 a \over 12 a b}\)

1p

1p

d

\(4 - {6 \over 7 p}\)

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

d

\(4 - {6 \over 7 p} = {4 \over 1} - {6 \over 7 p} = {28 p \over 7 p} - {6 \over 7 p} = {28 p - 6 \over 7 p}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(9 a + {3 \over 2 a}\)

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

a

\(9 a + {3 \over 2 a} = {9 a \over 1} ⋅ {2 a \over 2 a} + {3 \over 2 a} = {18 a^{2} \over 2 a} + {3 \over 2 a} = {18 a^{2} + 3 \over 2 a}\)

1p

1p

b

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

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

b

\({9 x \over y} - {4 \over 6 y} = {54 x \over 6 y} - {4 \over 6 y} = {54 x - 4 \over 6 y} = {27 x - 2 \over 3 y}\)

1p

1p

c

\({8 b \over 2 a} - {7 a \over 4 b}\)

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

c

\({8 b \over 2 a} - {7 a \over 4 b} = {16 b^{2} \over 4 a b} - {7 a^{2} \over 4 a b} = {-7 a^{2} + 16 b^{2} \over 4 a b}\)

1p

opgave 3

Herleid.

1p

a

\({6 x \over x}\)

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

a

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

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

\({40 p \over -45 p}\)

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

c

\({40 p \over -45 p} = -\frac{8}{9}\)

1p

1p

d

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

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

d

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

1p

opgave 4

Herleid.

1p

a

\({-9 x y \over -24 x z}\)

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

a

\({-9 x y \over -24 x z} = {3 y \over 8 z}\)

1p

1p

b

\({35 b \over -45 a b}\)

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

b

\({35 b \over -45 a b} = -{7 \over 9 a}\)

1p

1p

c

\({-24 p q r \over 3 q r}\)

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

c

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

1p

1p

d

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

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

d

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

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({4 \over x} ⋅ {6 \over y}\)

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

a

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

1p

1p

b

\({a \over 9} ⋅ {2 \over b}\)

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

b

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

1p

1p

c

\(-{1 \over 5} ⋅ a\)

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

c

\(-{1 \over 5} ⋅ a = -{a \over 5}\)

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 2

Herleid tot één breuk.

1p

\({5 \over 3} : x\)

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

○

\({5 \over 3} : x = {5 \over 3} : {x \over 1} = {5 \over 3} ⋅ {1 \over x} = {5 \over 3 x}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

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

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

○

\({5 p \over 4} + {p - 7 \over 3} = {15 p \over 12} + {4 (p - 7) \over 12} = {15 p + 4 (p - 7) \over 12} = {19 p - 28 \over 12}\)

1p

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