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

\({9 \over 7 p} + {4 \over 7 p}\)

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

a

\({9 \over 7 p} + {4 \over 7 p} = {13 \over 7 p}\)

1p

1p

b

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

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

b

\({4 \over a} - {7 \over 6 a} = {24 \over 6 a} - {7 \over 6 a} = {17 \over 6 a}\)

1p

1p

c

\({9 \over 2 x} + {6 \over 8 y}\)

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

c

\({9 \over 2 x} + {6 \over 8 y} = {36 y \over 8 x y} + {6 x \over 8 x y} = {36 y + 6 x \over 8 x y} = {18 y + 3 x \over 4 x y}\)

1p

1p

d

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

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

d

\(7 - {5 \over 6 x} = {7 \over 1} - {5 \over 6 x} = {42 x \over 6 x} - {5 \over 6 x} = {42 x - 5 \over 6 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

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

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

a

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

1p

1p

b

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

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

b

\({3 a \over b} + {9 \over 5 b} = {15 a \over 5 b} + {9 \over 5 b} = {15 a + 9 \over 5 b}\)

1p

1p

c

\({5 y \over 6 x} - {7 x \over 3 y}\)

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

c

\({5 y \over 6 x} - {7 x \over 3 y} = {5 y^{2} \over 6 x y} - {14 x^{2} \over 6 x y} = {-14 x^{2} + 5 y^{2} \over 6 x y}\)

1p

opgave 3

Herleid.

1p

a

\({2 a \over a}\)

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

a

\({2 a \over a} = {2 \over 1} = 2\)

1p

1p

b

\({x \over 9 x}\)

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

b

\({x \over 9 x} = {1 \over 9}\)

1p

1p

c

\({8 p \over -20 p}\)

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

c

\({8 p \over -20 p} = -\frac{2}{5}\)

1p

1p

d

\({25 a \over -5 a}\)

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

d

\({25 a \over -5 a} = -5\)

1p

opgave 4

Herleid.

1p

a

\({12 x y \over -20 x z}\)

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

a

\({12 x y \over -20 x z} = -{3 y \over 5 z}\)

1p

1p

b

\({-15 b \over 25 a b}\)

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

b

\({-15 b \over 25 a b} = -{3 \over 5 a}\)

1p

1p

c

\({14 x y z \over 2 y z}\)

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

c

\({14 x y z \over 2 y z} = 7 x\)

1p

1p

d

\({4 p q \over q} + {5 p r \over r}\)

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

d

\({4 p q \over q} + {5 p r \over r} = 4 p + 5 p = 9 p\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({7 \over a} ⋅ {2 \over b}\)

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

a

\({7 \over a} ⋅ {2 \over b} = {14 \over a b}\)

1p

1p

b

\({p \over 4} ⋅ {3 \over q}\)

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

b

\({p \over 4} ⋅ {3 \over q} = {3 p \over 4 q}\)

1p

1p

c

\({4 \over 7} ⋅ a\)

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

c

\({4 \over 7} ⋅ a = {4 a \over 7}\)

1p

1p

d

\({6 \over x} : {7 \over y}\)

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

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

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

\(-{6 \over 5} : x = -{6 \over 5} : {x \over 1} = -{6 \over 5} ⋅ {1 \over x} = -{6 \over 5 x}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({8 a \over 5} + {a + 1 \over 7}\)

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

\({8 a \over 5} + {a + 1 \over 7} = {56 a \over 35} + {5 (a + 1) \over 35} = {56 a + 5 (a + 1) \over 35} = {61 a + 5 \over 35}\)

1p

havo wiskunde A 6.2 Formules met breuken

Breuken herleiden (2)

opgave 1

Herleid tot één breuk.

1p

a

\({5 \over 4} : {x - 8 y \over y}\)

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

a

\({5 \over 4} : {x - 8 y \over y} = {5 \over 4} ⋅ {y \over x - 8 y} = {5 y \over 4 (x - 8 y)} = {5 y \over 4 x - 32 y}\)

1p

1p

b

\({-4 a + 1 \over -7 a + 6} - 3\)

Optellen (9)
00eh - Breuken herleiden - basis - 1ms - dynamic variables

b

\({-4 a + 1 \over -7 a + 6} - 3 = {-4 a + 1 \over -7 a + 6} + {-3 (-7 a + 6) \over -7 a + 6} = {-4 a + 1 - 3 (-7 a + 6) \over -7 a + 6} = {-4 a + 1 + 21 a - 18 \over -7 a + 6} = {17 a - 17 \over -7 a + 6}\)

1p

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