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

\({6 \over 2 a} - {8 \over 2 a}\)

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

a

\({6 \over 2 a} - {8 \over 2 a} = -{2 \over 2 a} = -{1 \over a}\)

1p

1p

b

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

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

b

\({7 \over p} - {6 \over 4 p} = {28 \over 4 p} - {6 \over 4 p} = {22 \over 4 p} = {11 \over 2 p}\)

1p

1p

c

\({7 \over 5 x} - {8 \over 2 y}\)

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

c

\({7 \over 5 x} - {8 \over 2 y} = {14 y \over 10 x y} - {40 x \over 10 x y} = {14 y - 40 x \over 10 x y} = {7 y - 20 x \over 5 x y}\)

1p

1p

d

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

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

d

\(2 + {5 \over 8 x} = {2 \over 1} + {5 \over 8 x} = {16 x \over 8 x} + {5 \over 8 x} = {16 x + 5 \over 8 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

\({4 a \over b} + {3 \over 9 b}\)

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

○

\({4 a \over b} + {3 \over 9 b} = {36 a \over 9 b} + {3 \over 9 b} = {36 a + 3 \over 9 b} = {12 a + 1 \over 3 b}\)

1p

opgave 3

Herleid.

1p

a

\({8 p \over p}\)

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

a

\({8 p \over p} = {8 \over 1} = 8\)

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

\({12 x \over 16 x}\)

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

c

\({12 x \over 16 x} = \frac{3}{4}\)

1p

1p

d

\({-28 a \over 4 a}\)

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

d

\({-28 a \over 4 a} = -7\)

1p

opgave 4

Herleid.

1p

a

\({-8 x y \over 28 x z}\)

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

a

\({-8 x y \over 28 x z} = -{2 y \over 7 z}\)

1p

1p

b

\({6 y \over 15 x y}\)

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

b

\({6 y \over 15 x y} = {2 \over 5 x}\)

1p

1p

c

\({10 a b c \over 5 b c}\)

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

c

\({10 a b c \over 5 b c} = 2 a\)

1p

1p

d

\({3 x y \over y} + {5 x z \over z}\)

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

d

\({3 x y \over y} + {5 x z \over z} = 3 x + 5 x = 8 x\)

1p

2 vwo 1.2 Herleiden van breuken

Breuken herleiden (10)

opgave 1

Herleid tot één breuk.

1p

a

\(2 a + {5 \over 8 a}\)

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

a

\(2 a + {5 \over 8 a} = {2 a \over 1} ⋅ {8 a \over 8 a} + {5 \over 8 a} = {16 a^{2} \over 8 a} + {5 \over 8 a} = {16 a^{2} + 5 \over 8 a}\)

1p

1p

b

\({7 q \over 4 p} - {5 p \over 2 q}\)

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

b

\({7 q \over 4 p} - {5 p \over 2 q} = {7 q^{2} \over 4 p q} - {10 p^{2} \over 4 p q} = {-10 p^{2} + 7 q^{2} \over 4 p q}\)

1p

1p

c

\({7 \over x} ⋅ {3 \over y}\)

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

c

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

1p

1p

d

\({x \over 2} ⋅ -{7 \over y}\)

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

d

\({x \over 2} ⋅ -{7 \over y} = -{7 x \over 2 y}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\({8 \over 3} ⋅ a\)

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

a

\({8 \over 3} ⋅ a = {8 a \over 3}\)

1p

1p

b

\({6 b \over a} ⋅ {a - 3 \over 8}\)

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

b

\({6 b \over a} ⋅ {a - 3 \over 8} = {6 b (a - 3) \over 8 a} = {3 b (a - 3) \over 4 a} = {3 a b - 9 b \over 4 a}\)

1p

1p

c

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

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

c

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

1p

1p

d

\(-{2 \over 7} : a\)

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

d

\(-{2 \over 7} : a = -{2 \over 7} : {a \over 1} = -{2 \over 7} ⋅ {1 \over a} = -{2 \over 7 a}\)

1p

opgave 3

Herleid tot één breuk.

1p

a

\(-{4 \over 3} : {p - 6 q \over q}\)

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

a

\(-{4 \over 3} : {p - 6 q \over q} = -{4 \over 3} ⋅ {q \over p - 6 q} = -{4 q \over 3 (p - 6 q)} = -{4 q \over 3 p - 18 q}\)

1p

1p

b

\({3 x \over 7} + {x + 5 \over 9}\)

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

b

\({3 x \over 7} + {x + 5 \over 9} = {27 x \over 63} + {7 (x + 5) \over 63} = {27 x + 7 (x + 5) \over 63} = {34 x + 35 \over 63}\)

1p

3 vwo 5.3 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({-8 a + 9 \over -3 a + 4} - 2\)

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

○

\({-8 a + 9 \over -3 a + 4} - 2 = {-8 a + 9 \over -3 a + 4} + {-2 (-3 a + 4) \over -3 a + 4} = {-8 a + 9 - 2 (-3 a + 4) \over -3 a + 4} = {-8 a + 9 + 6 a - 8 \over -3 a + 4} = {-2 a + 1 \over -3 a + 4}\)

1p

vwo wiskunde A 3.1 Breuken en verhoudingen

Breuken herleiden (2)

opgave 1

Deel uit.

1p

a

\({3 p^{2} + 6 p + 90 \over 3 p}\)

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

a

\({3 p^{2} + 6 p + 90 \over 3 p} = {3 p^{2} \over 3 p} + {6 p \over 3 p} + {90 \over 3 p} = p + 2 + {30 \over p}\)

1p

1p

b

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

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

b

\({9 x^{2} - 7 x - 2 \over 6 x^{2}} = {9 x^{2} \over 6 x^{2}} - {7 x \over 6 x^{2}} - {2 \over 6 x^{2}} = 1\frac{1}{2} - {7 \over 6 x} - {1 \over 3 x^{2}}\)

1p

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