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

'Breuken herleiden'.

1 vwo 6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

1p

a

\({6 \over 7 p} - {2 \over 7 p}\)

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

a

\({6 \over 7 p} - {2 \over 7 p} = {4 \over 7 p}\)

1p

1p

b

\({6 \over x} + {3 \over 5 x}\)

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

b

\({6 \over x} + {3 \over 5 x} = {30 \over 5 x} + {3 \over 5 x} = {33 \over 5 x}\)

1p

1p

c

\({9 \over 3 a} + {6 \over 5 b}\)

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

c

\({9 \over 3 a} + {6 \over 5 b} = {45 b \over 15 a b} + {18 a \over 15 a b} = {45 b + 18 a \over 15 a b} = {15 b + 6 a \over 5 a b}\)

1p

1p

d

\(4 + {7 \over 5 a}\)

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

d

\(4 + {7 \over 5 a} = {4 \over 1} + {7 \over 5 a} = {20 a \over 5 a} + {7 \over 5 a} = {20 a + 7 \over 5 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

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

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

○

\({8 x \over y} + {3 \over 4 y} = {32 x \over 4 y} + {3 \over 4 y} = {32 x + 3 \over 4 y}\)

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

\({x \over 5 x}\)

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

b

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

1p

1p

c

\({-8 p \over -18 p}\)

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

c

\({-8 p \over -18 p} = \frac{4}{9}\)

1p

1p

d

\({10 a \over -5 a}\)

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

d

\({10 a \over -5 a} = -2\)

1p

opgave 4

Herleid.

1p

a

\({-20 x y \over 36 x z}\)

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

a

\({-20 x y \over 36 x z} = -{5 y \over 9 z}\)

1p

1p

b

\({-8 b \over -12 a b}\)

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

b

\({-8 b \over -12 a b} = {2 \over 3 a}\)

1p

1p

c

\({15 a b c \over -3 b c}\)

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

c

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

1p

1p

d

\({7 x y \over y} + {2 x z \over z}\)

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

d

\({7 x y \over y} + {2 x z \over z} = 7 x + 2 x = 9 x\)

1p

2 vwo 1.2 Herleiden van breuken

Breuken herleiden (10)

opgave 1

Herleid tot één breuk.

1p

a

\(7 p + {4 \over 3 p}\)

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

a

\(7 p + {4 \over 3 p} = {7 p \over 1} ⋅ {3 p \over 3 p} + {4 \over 3 p} = {21 p^{2} \over 3 p} + {4 \over 3 p} = {21 p^{2} + 4 \over 3 p}\)

1p

1p

b

\({2 b \over 9 a} + {4 a \over 5 b}\)

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

b

\({2 b \over 9 a} + {4 a \over 5 b} = {10 b^{2} \over 45 a b} + {36 a^{2} \over 45 a b} = {36 a^{2} + 10 b^{2} \over 45 a b}\)

1p

1p

c

\({9 \over x} ⋅ {5 \over y}\)

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

c

\({9 \over x} ⋅ {5 \over y} = {45 \over x y}\)

1p

1p

d

\({x \over 8} ⋅ -{2 \over y}\)

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

d

\({x \over 8} ⋅ -{2 \over y} = -{2 x \over 8 y} = -{x \over 4 y}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\({1 \over 3} ⋅ a\)

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

a

\({1 \over 3} ⋅ a = {a \over 3}\)

1p

1p

b

\({3 b \over a} ⋅ {a + 9 \over 8}\)

Vermenigvuldiging (4)
0094 - Breuken herleiden - basis - 0ms - dynamic variables

b

\({3 b \over a} ⋅ {a + 9 \over 8} = {3 b (a + 9) \over 8 a} = {3 a b + 27 b \over 8 a}\)

1p

1p

c

\({8 \over x} : {6 \over y}\)

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

c

\({8 \over x} : {6 \over y} = {8 \over x} ⋅ {y \over 6} = {8 y \over 6 x} = {4 y \over 3 x}\)

1p

1p

d

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

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

d

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

1p

opgave 3

Herleid tot één breuk.

1p

a

\({6 \over 7} : {x + 2 y \over y}\)

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

a

\({6 \over 7} : {x + 2 y \over y} = {6 \over 7} ⋅ {y \over x + 2 y} = {6 y \over 7 (x + 2 y)} = {6 y \over 7 x + 14 y}\)

1p

1p

b

\({7 p \over 9} + {p + 8 \over 4}\)

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

b

\({7 p \over 9} + {p + 8 \over 4} = {28 p \over 36} + {9 (p + 8) \over 36} = {28 p + 9 (p + 8) \over 36} = {37 p + 72 \over 36}\)

1p

3 vwo 5.3 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({-5 x + 8 \over 9 x - 3} - 1\)

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

○

\({-5 x + 8 \over 9 x - 3} - 1 = {-5 x + 8 \over 9 x - 3} - {1 (9 x - 3) \over 9 x - 3} = {-5 x + 8 - 1 (9 x - 3) \over 9 x - 3} = {-5 x + 8 - 9 x + 3 \over 9 x - 3} = {-14 x + 11 \over 9 x - 3}\)

1p

vwo wiskunde A 3.1 Breuken en verhoudingen

Breuken herleiden (2)

opgave 1

Deel uit.

1p

a

\({2 a^{2} - 4 a - 60 \over 2 a}\)

Uitdelen (1)
00ei - Breuken herleiden - basis - 0ms - dynamic variables

a

\({2 a^{2} - 4 a - 60 \over 2 a} = {2 a^{2} \over 2 a} - {4 a \over 2 a} - {60 \over 2 a} = a - 2 - {30 \over a}\)

1p

1p

b

\({6 x^{2} - 7 x - 4 \over 8 x^{2}}\)

Uitdelen (2)
00ej - Breuken herleiden - basis - 0ms - dynamic variables

b

\({6 x^{2} - 7 x - 4 \over 8 x^{2}} = {6 x^{2} \over 8 x^{2}} - {7 x \over 8 x^{2}} - {4 \over 8 x^{2}} = \frac{3}{4} - {7 \over 8 x} - {1 \over 2 x^{2}}\)

1p

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