Getal & Ruimte (13e editie) - havo wiskunde A

'Breuken herleiden'.

2 havo/vwo 1.2 Breuken optellen

Breuken herleiden (15)

opgave 1

Herleid tot één breuk.

1p

a

\({4 \over 7 x} - {2 \over 7 x}\)

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

a

\({4 \over 7 x} - {2 \over 7 x} = {2 \over 7 x}\)

1p

1p

b

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

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

b

\({7 \over a} + {9 \over 5 a} = {35 \over 5 a} + {9 \over 5 a} = {44 \over 5 a}\)

1p

1p

c

\({5 \over 7 a} + {3 \over 2 b}\)

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

c

\({5 \over 7 a} + {3 \over 2 b} = {10 b \over 14 a b} + {21 a \over 14 a b} = {10 b + 21 a \over 14 a b}\)

1p

1p

d

\(9 - {2 \over 3 p}\)

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

d

\(9 - {2 \over 3 p} = {9 \over 1} - {2 \over 3 p} = {27 p \over 3 p} - {2 \over 3 p} = {27 p - 2 \over 3 p}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(6 x - {7 \over 9 x}\)

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

a

\(6 x - {7 \over 9 x} = {6 x \over 1} ⋅ {9 x \over 9 x} - {7 \over 9 x} = {54 x^{2} \over 9 x} - {7 \over 9 x} = {54 x^{2} - 7 \over 9 x}\)

1p

1p

b

\({3 x \over y} + {8 \over 6 y}\)

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

b

\({3 x \over y} + {8 \over 6 y} = {18 x \over 6 y} + {8 \over 6 y} = {18 x + 8 \over 6 y} = {9 x + 4 \over 3 y}\)

1p

1p

c

\({6 b \over 9 a} - {2 a \over 5 b}\)

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

c

\({6 b \over 9 a} - {2 a \over 5 b} = {30 b^{2} \over 45 a b} - {18 a^{2} \over 45 a b} = {-18 a^{2} + 30 b^{2} \over 45 a b} = {-6 a^{2} + 10 b^{2} \over 15 a b}\)

1p

opgave 3

Herleid.

1p

a

\({4 a \over a}\)

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

a

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

1p

1p

b

\({p \over 3 p}\)

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

b

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

1p

1p

c

\({28 x \over -32 x}\)

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

c

\({28 x \over -32 x} = -\frac{7}{8}\)

1p

1p

d

\({12 a \over -4 a}\)

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

d

\({12 a \over -4 a} = -3\)

1p

opgave 4

Herleid.

1p

a

\({-16 p q \over -18 p r}\)

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

a

\({-16 p q \over -18 p r} = {8 q \over 9 r}\)

1p

1p

b

\({-16 y \over -18 x y}\)

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

b

\({-16 y \over -18 x y} = {8 \over 9 x}\)

1p

1p

c

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

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

c

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

1p

1p

d

\({5 x y \over y} + {6 x z \over z}\)

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

d

\({5 x y \over y} + {6 x z \over z} = 5 x + 6 x = 11 x\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({8 \over a} ⋅ -{7 \over b}\)

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

a

\({8 \over a} ⋅ -{7 \over b} = -{56 \over a b}\)

1p

1p

b

\({a \over 4} ⋅ {9 \over b}\)

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

b

\({a \over 4} ⋅ {9 \over b} = {9 a \over 4 b}\)

1p

1p

c

\({8 \over 9} ⋅ x\)

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

c

\({8 \over 9} ⋅ x = {8 x \over 9}\)

1p

1p

d

\({5 \over p} : {7 \over q}\)

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

d

\({5 \over p} : {7 \over q} = {5 \over p} ⋅ {q \over 7} = {5 q \over 7 p}\)

1p

opgave 2

Herleid tot één breuk.

1p

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

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

○

\({4 \over 9} : x = {4 \over 9} : {x \over 1} = {4 \over 9} ⋅ {1 \over x} = {4 \over 9 x}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({4 a \over 3} + {a + 9 \over 5}\)

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

○

\({4 a \over 3} + {a + 9 \over 5} = {20 a \over 15} + {3 (a + 9) \over 15} = {20 a + 3 (a + 9) \over 15} = {23 a + 27 \over 15}\)

1p

havo wiskunde A 6.2 Formules met breuken

Breuken herleiden (2)

opgave 1

Herleid tot één breuk.

1p

a

\(-{5 \over 6} : {a + 8 b \over b}\)

Deling (3)
0097 - Breuken herleiden - basis - 0ms - dynamic variables

a

\(-{5 \over 6} : {a + 8 b \over b} = -{5 \over 6} ⋅ {b \over a + 8 b} = -{5 b \over 6 (a + 8 b)} = -{5 b \over 6 a + 48 b}\)

1p

1p

b

\({-9 x - 4 \over -2 x - 6} - 8\)

Optellen (9)
00eh - Breuken herleiden - basis - 0ms - dynamic variables

b

\({-9 x - 4 \over -2 x - 6} - 8 = {-9 x - 4 \over -2 x - 6} + {-8 (-2 x - 6) \over -2 x - 6} = {-9 x - 4 - 8 (-2 x - 6) \over -2 x - 6} = {-9 x - 4 + 16 x + 48 \over -2 x - 6} = {7 x + 44 \over -2 x - 6}\)

1p

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