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

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

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

a

\({9 \over 4 a} - {6 \over 4 a} = {3 \over 4 a}\)

1p

1p

b

\({2 \over p} + {8 \over 9 p}\)

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

b

\({2 \over p} + {8 \over 9 p} = {18 \over 9 p} + {8 \over 9 p} = {26 \over 9 p}\)

1p

1p

c

\({6 \over 8 x} - {7 \over 4 y}\)

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

c

\({6 \over 8 x} - {7 \over 4 y} = {6 y \over 8 x y} - {14 x \over 8 x y} = {6 y - 14 x \over 8 x y} = {3 y - 7 x \over 4 x y}\)

1p

1p

d

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

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

d

\(4 - {5 \over 8 x} = {4 \over 1} - {5 \over 8 x} = {32 x \over 8 x} - {5 \over 8 x} = {32 x - 5 \over 8 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

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

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

a

\(4 a + {6 \over 7 a} = {4 a \over 1} ⋅ {7 a \over 7 a} + {6 \over 7 a} = {28 a^{2} \over 7 a} + {6 \over 7 a} = {28 a^{2} + 6 \over 7 a}\)

1p

1p

b

\({3 x \over y} + {4 \over 2 y}\)

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

b

\({3 x \over y} + {4 \over 2 y} = {6 x \over 2 y} + {4 \over 2 y} = {6 x + 4 \over 2 y} = {3 x + 2 \over y}\)

1p

1p

c

\({7 b \over 5 a} - {8 a \over 4 b}\)

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

c

\({7 b \over 5 a} - {8 a \over 4 b} = {28 b^{2} \over 20 a b} - {40 a^{2} \over 20 a b} = {-40 a^{2} + 28 b^{2} \over 20 a b} = {-10 a^{2} + 7 b^{2} \over 5 a b}\)

1p

opgave 3

Herleid.

1p

a

\({6 p \over p}\)

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

a

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

1p

1p

b

\({a \over 6 a}\)

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

b

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

1p

1p

c

\({-32 x \over -36 x}\)

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

c

\({-32 x \over -36 x} = \frac{8}{9}\)

1p

1p

d

\({24 p \over 3 p}\)

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

d

\({24 p \over 3 p} = 8\)

1p

opgave 4

Herleid.

1p

a

\({-10 x y \over -45 x z}\)

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

a

\({-10 x y \over -45 x z} = {2 y \over 9 z}\)

1p

1p

b

\({6 b \over 16 a b}\)

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

b

\({6 b \over 16 a b} = {3 \over 8 a}\)

1p

1p

c

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

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

c

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

1p

1p

d

\({7 a b \over b} - {6 a c \over c}\)

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

d

\({7 a b \over b} - {6 a c \over c} = 7 a - 6 a = a\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({7 \over a} ⋅ {3 \over b}\)

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

a

\({7 \over a} ⋅ {3 \over b} = {21 \over a b}\)

1p

1p

b

\({p \over 8} ⋅ -{3 \over q}\)

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

b

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

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

\({9 \over x} : {7 \over y}\)

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

d

\({9 \over x} : {7 \over y} = {9 \over x} ⋅ {y \over 7} = {9 y \over 7 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

\({8 \over 9} : a\)

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

○

\({8 \over 9} : a = {8 \over 9} : {a \over 1} = {8 \over 9} ⋅ {1 \over a} = {8 \over 9 a}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({5 x \over 9} + {x - 3 \over 8}\)

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

○

\({5 x \over 9} + {x - 3 \over 8} = {40 x \over 72} + {9 (x - 3) \over 72} = {40 x + 9 (x - 3) \over 72} = {49 x - 27 \over 72}\)

1p

havo wiskunde A 6.2 Formules met breuken

Breuken herleiden (2)

opgave 1

Herleid tot één breuk.

1p

a

\({8 \over 3} : {a - b \over b}\)

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

a

\({8 \over 3} : {a - b \over b} = {8 \over 3} ⋅ {b \over a - b} = {8 b \over 3 (a - b)} = {8 b \over 3 a - 3 b}\)

1p

1p

b

\({4 x + 8 \over 7 x - 2} - 9\)

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

b

\({4 x + 8 \over 7 x - 2} - 9 = {4 x + 8 \over 7 x - 2} - {9 (7 x - 2) \over 7 x - 2} = {4 x + 8 - 9 (7 x - 2) \over 7 x - 2} = {4 x + 8 - 63 x + 18 \over 7 x - 2} = {-59 x + 26 \over 7 x - 2}\)

1p

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