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

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

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

a

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

1p

1p

b

\({6 \over a} + {9 \over 4 a}\)

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

b

\({6 \over a} + {9 \over 4 a} = {24 \over 4 a} + {9 \over 4 a} = {33 \over 4 a}\)

1p

1p

c

\({5 \over 4 a} + {3 \over 2 b}\)

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

c

\({5 \over 4 a} + {3 \over 2 b} = {5 b \over 4 a b} + {6 a \over 4 a b} = {5 b + 6 a \over 4 a b}\)

1p

1p

d

\(2 + {3 \over 5 x}\)

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

d

\(2 + {3 \over 5 x} = {2 \over 1} + {3 \over 5 x} = {10 x \over 5 x} + {3 \over 5 x} = {10 x + 3 \over 5 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(6 x + {5 \over 8 x}\)

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

a

\(6 x + {5 \over 8 x} = {6 x \over 1} ⋅ {8 x \over 8 x} + {5 \over 8 x} = {48 x^{2} \over 8 x} + {5 \over 8 x} = {48 x^{2} + 5 \over 8 x}\)

1p

1p

b

\({4 a \over b} - {5 \over 7 b}\)

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

b

\({4 a \over b} - {5 \over 7 b} = {28 a \over 7 b} - {5 \over 7 b} = {28 a - 5 \over 7 b}\)

1p

1p

c

\({3 y \over 6 x} - {8 x \over 2 y}\)

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

c

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

1p

opgave 3

Herleid.

1p

a

\({7 a \over a}\)

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

a

\({7 a \over a} = {7 \over 1} = 7\)

1p

1p

b

\({x \over 5 x}\)

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

b

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

1p

1p

c

\({10 p \over -45 p}\)

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

c

\({10 p \over -45 p} = -\frac{2}{9}\)

1p

1p

d

\({10 x \over 5 x}\)

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

d

\({10 x \over 5 x} = 2\)

1p

opgave 4

Herleid.

1p

a

\({12 a b \over 28 a c}\)

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

a

\({12 a b \over 28 a c} = {3 b \over 7 c}\)

1p

1p

b

\({15 q \over 40 p q}\)

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

b

\({15 q \over 40 p q} = {3 \over 8 p}\)

1p

1p

c

\({-24 a b c \over 4 b c}\)

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

c

\({-24 a b c \over 4 b c} = -6 a\)

1p

1p

d

\({2 x y \over y} - {6 x z \over z}\)

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

d

\({2 x y \over y} - {6 x z \over z} = 2 x - 6 x = -4 x\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({3 \over x} ⋅ {7 \over y}\)

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

a

\({3 \over x} ⋅ {7 \over y} = {21 \over x y}\)

1p

1p

b

\({a \over 2} ⋅ {9 \over b}\)

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

b

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

1p

1p

c

\(-{6 \over 7} ⋅ x\)

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

c

\(-{6 \over 7} ⋅ x = -{6 x \over 7}\)

1p

1p

d

\({2 \over a} : {8 \over b}\)

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

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

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

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

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({7 a \over 3} + {a - 9 \over 5}\)

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

\({7 a \over 3} + {a - 9 \over 5} = {35 a \over 15} + {3 (a - 9) \over 15} = {35 a + 3 (a - 9) \over 15} = {38 a - 27 \over 15}\)

1p

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