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

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

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

a

\({8 \over 5 a} - {7 \over 5 a} = {1 \over 5 a}\)

1p

1p

b

\({4 \over x} - {6 \over 5 x}\)

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

b

\({4 \over x} - {6 \over 5 x} = {20 \over 5 x} - {6 \over 5 x} = {14 \over 5 x}\)

1p

1p

c

\({5 \over 3 a} - {4 \over 8 b}\)

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

c

\({5 \over 3 a} - {4 \over 8 b} = {40 b \over 24 a b} - {12 a \over 24 a b} = {40 b - 12 a \over 24 a b} = {10 b - 3 a \over 6 a b}\)

1p

1p

d

\(8 + {4 \over 3 x}\)

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

d

\(8 + {4 \over 3 x} = {8 \over 1} + {4 \over 3 x} = {24 x \over 3 x} + {4 \over 3 x} = {24 x + 4 \over 3 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(2 p + {5 \over 9 p}\)

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

a

\(2 p + {5 \over 9 p} = {2 p \over 1} ⋅ {9 p \over 9 p} + {5 \over 9 p} = {18 p^{2} \over 9 p} + {5 \over 9 p} = {18 p^{2} + 5 \over 9 p}\)

1p

1p

b

\({7 x \over y} + {9 \over 3 y}\)

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

b

\({7 x \over y} + {9 \over 3 y} = {21 x \over 3 y} + {9 \over 3 y} = {21 x + 9 \over 3 y} = {7 x + 3 \over y}\)

1p

1p

c

\({9 b \over 2 a} + {7 a \over 3 b}\)

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

c

\({9 b \over 2 a} + {7 a \over 3 b} = {27 b^{2} \over 6 a b} + {14 a^{2} \over 6 a b} = {14 a^{2} + 27 b^{2} \over 6 a b}\)

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

\({p \over 4 p}\)

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

b

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

1p

1p

c

\({-4 a \over 18 a}\)

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

c

\({-4 a \over 18 a} = -\frac{2}{9}\)

1p

1p

d

\({12 x \over 2 x}\)

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

d

\({12 x \over 2 x} = 6\)

1p

opgave 4

Herleid.

1p

a

\({12 a b \over 20 a c}\)

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

a

\({12 a b \over 20 a c} = {3 b \over 5 c}\)

1p

1p

b

\({32 b \over -36 a b}\)

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

b

\({32 b \over -36 a b} = -{8 \over 9 a}\)

1p

1p

c

\({-6 x y z \over -3 y z}\)

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

c

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

1p

1p

d

\({5 p q \over q} - {2 p r \over r}\)

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

d

\({5 p q \over q} - {2 p r \over r} = 5 p - 2 p = 3 p\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({9 \over p} ⋅ {2 \over q}\)

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

a

\({9 \over p} ⋅ {2 \over q} = {18 \over p q}\)

1p

1p

b

\({x \over 7} ⋅ {9 \over y}\)

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

b

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

1p

1p

c

\(-{6 \over 7} ⋅ a\)

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

c

\(-{6 \over 7} ⋅ a = -{6 a \over 7}\)

1p

1p

d

\({8 \over a} : {4 \over b}\)

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

\(-{2 \over 3} : x\)

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

\(-{2 \over 3} : x = -{2 \over 3} : {x \over 1} = -{2 \over 3} ⋅ {1 \over x} = -{2 \over 3 x}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({9 a \over 5} + {a + 6 \over 2}\)

Optellen (8)
0098 - Breuken herleiden - basis - 1ms - dynamic variables

\({9 a \over 5} + {a + 6 \over 2} = {18 a \over 10} + {5 (a + 6) \over 10} = {18 a + 5 (a + 6) \over 10} = {23 a + 30 \over 10}\)

1p

havo wiskunde A 6.2 Formules met breuken

Breuken herleiden (2)

opgave 1

Herleid tot één breuk.

1p

a

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

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

a

\({3 \over 2} : {x - 8 y \over y} = {3 \over 2} ⋅ {y \over x - 8 y} = {3 y \over 2 (x - 8 y)} = {3 y \over 2 x - 16 y}\)

1p

1p

b

\({-2 p - 6 \over 3 p - 5} - 8\)

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

b

\({-2 p - 6 \over 3 p - 5} - 8 = {-2 p - 6 \over 3 p - 5} - {8 (3 p - 5) \over 3 p - 5} = {-2 p - 6 - 8 (3 p - 5) \over 3 p - 5} = {-2 p - 6 - 24 p + 40 \over 3 p - 5} = {-26 p + 34 \over 3 p - 5}\)

1p

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