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

'Breuken herleiden'.

1 vwo 6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

1p

a

\({4 \over 7 p} - {8 \over 7 p}\)

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

a

\({4 \over 7 p} - {8 \over 7 p} = -{4 \over 7 p}\)

1p

1p

b

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

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

b

\({8 \over a} - {4 \over 5 a} = {40 \over 5 a} - {4 \over 5 a} = {36 \over 5 a}\)

1p

1p

c

\({5 \over 3 x} - {7 \over 2 y}\)

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

c

\({5 \over 3 x} - {7 \over 2 y} = {10 y \over 6 x y} - {21 x \over 6 x y} = {10 y - 21 x \over 6 x y}\)

1p

1p

d

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

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

d

\(9 + {5 \over 3 a} = {9 \over 1} + {5 \over 3 a} = {27 a \over 3 a} + {5 \over 3 a} = {27 a + 5 \over 3 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

\({8 x \over y} + {5 \over 2 y}\)

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

○

\({8 x \over y} + {5 \over 2 y} = {16 x \over 2 y} + {5 \over 2 y} = {16 x + 5 \over 2 y}\)

1p

opgave 3

Herleid.

1p

a

\({9 x \over x}\)

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

a

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

1p

1p

b

\({a \over 2 a}\)

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

b

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

1p

1p

c

\({20 a \over 36 a}\)

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

c

\({20 a \over 36 a} = \frac{5}{9}\)

1p

1p

d

\({30 p \over 5 p}\)

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

d

\({30 p \over 5 p} = 6\)

1p

opgave 4

Herleid.

1p

a

\({-16 x y \over -36 x z}\)

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

a

\({-16 x y \over -36 x z} = {4 y \over 9 z}\)

1p

1p

b

\({4 q \over 14 p q}\)

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

b

\({4 q \over 14 p q} = {2 \over 7 p}\)

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

\({7 a b \over b} - {3 a c \over c}\)

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

d

\({7 a b \over b} - {3 a c \over c} = 7 a - 3 a = 4 a\)

1p

2 vwo 1.2 Herleiden van breuken

Breuken herleiden (10)

opgave 1

Herleid tot één breuk.

1p

a

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

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

a

\(7 x + {4 \over 9 x} = {7 x \over 1} ⋅ {9 x \over 9 x} + {4 \over 9 x} = {63 x^{2} \over 9 x} + {4 \over 9 x} = {63 x^{2} + 4 \over 9 x}\)

1p

1p

b

\({9 b \over 4 a} - {3 a \over 7 b}\)

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

b

\({9 b \over 4 a} - {3 a \over 7 b} = {63 b^{2} \over 28 a b} - {12 a^{2} \over 28 a b} = {-12 a^{2} + 63 b^{2} \over 28 a b}\)

1p

1p

c

\({5 \over p} ⋅ {6 \over q}\)

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

c

\({5 \over p} ⋅ {6 \over q} = {30 \over p q}\)

1p

1p

d

\({x \over 9} ⋅ {6 \over y}\)

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

d

\({x \over 9} ⋅ {6 \over y} = {6 x \over 9 y} = {2 x \over 3 y}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\({1 \over 5} ⋅ a\)

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

a

\({1 \over 5} ⋅ a = {a \over 5}\)

1p

1p

b

\({4 y \over x} ⋅ {x - 9 \over 3}\)

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

b

\({4 y \over x} ⋅ {x - 9 \over 3} = {4 y (x - 9) \over 3 x} = {4 x y - 36 y \over 3 x}\)

1p

1p

c

\({7 \over p} : {4 \over q}\)

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

c

\({7 \over p} : {4 \over q} = {7 \over p} ⋅ {q \over 4} = {7 q \over 4 p}\)

1p

1p

d

\(-{5 \over 3} : x\)

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

d

\(-{5 \over 3} : x = -{5 \over 3} : {x \over 1} = -{5 \over 3} ⋅ {1 \over x} = -{5 \over 3 x}\)

1p

opgave 3

Herleid tot één breuk.

1p

a

\(-{8 \over 5} : {a - 9 b \over b}\)

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

a

\(-{8 \over 5} : {a - 9 b \over b} = -{8 \over 5} ⋅ {b \over a - 9 b} = -{8 b \over 5 (a - 9 b)} = -{8 b \over 5 a - 45 b}\)

1p

1p

b

\({5 a \over 9} + {a + 8 \over 7}\)

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

b

\({5 a \over 9} + {a + 8 \over 7} = {35 a \over 63} + {9 (a + 8) \over 63} = {35 a + 9 (a + 8) \over 63} = {44 a + 72 \over 63}\)

1p

3 vwo 5.3 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({-7 x + 3 \over 9 x + 4} - 8\)

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

○

\({-7 x + 3 \over 9 x + 4} - 8 = {-7 x + 3 \over 9 x + 4} - {8 (9 x + 4) \over 9 x + 4} = {-7 x + 3 - 8 (9 x + 4) \over 9 x + 4} = {-7 x + 3 - 72 x - 32 \over 9 x + 4} = {-79 x - 29 \over 9 x + 4}\)

1p

vwo wiskunde A 3.1 Breuken en verhoudingen

Breuken herleiden (2)

opgave 1

Deel uit.

1p

a

\({6 a^{2} + 2 a - 40 \over 2 a}\)

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

a

\({6 a^{2} + 2 a - 40 \over 2 a} = {6 a^{2} \over 2 a} + {2 a \over 2 a} - {40 \over 2 a} = 3 a + 1 - {20 \over a}\)

1p

1p

b

\({6 a^{2} - 9 a - 7 \over 5 a^{2}}\)

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

b

\({6 a^{2} - 9 a - 7 \over 5 a^{2}} = {6 a^{2} \over 5 a^{2}} - {9 a \over 5 a^{2}} - {7 \over 5 a^{2}} = 1\frac{1}{5} - {9 \over 5 a} - {7 \over 5 a^{2}}\)

1p

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