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

\({6 \over 8 x} + {2 \over 8 x}\)

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

a

\({6 \over 8 x} + {2 \over 8 x} = {8 \over 8 x} = {1 \over x}\)

1p

1p

b

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

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

b

\({8 \over a} + {9 \over 5 a} = {40 \over 5 a} + {9 \over 5 a} = {49 \over 5 a}\)

1p

1p

c

\({5 \over 9 x} - {7 \over 8 y}\)

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

c

\({5 \over 9 x} - {7 \over 8 y} = {40 y \over 72 x y} - {63 x \over 72 x y} = {40 y - 63 x \over 72 x y}\)

1p

1p

d

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

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

d

\(7 + {4 \over 9 a} = {7 \over 1} + {4 \over 9 a} = {63 a \over 9 a} + {4 \over 9 a} = {63 a + 4 \over 9 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

\({3 p \over q} - {2 \over 8 q}\)

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

○

\({3 p \over q} - {2 \over 8 q} = {24 p \over 8 q} - {2 \over 8 q} = {24 p - 2 \over 8 q} = {12 p - 1 \over 4 q}\)

1p

opgave 3

Herleid.

1p

a

\({7 a \over a}\)

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

a

\({7 a \over a} = {7 \over 1} = 7\)

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

\({20 p \over -25 p}\)

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

c

\({20 p \over -25 p} = -\frac{4}{5}\)

1p

1p

d

\({25 x \over -5 x}\)

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

d

\({25 x \over -5 x} = -5\)

1p

opgave 4

Herleid.

1p

a

\({20 x y \over -32 x z}\)

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

a

\({20 x y \over -32 x z} = -{5 y \over 8 z}\)

1p

1p

b

\({-16 y \over 20 x y}\)

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

b

\({-16 y \over 20 x y} = -{4 \over 5 x}\)

1p

1p

c

\({-25 a b c \over 5 b c}\)

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

c

\({-25 a b c \over 5 b c} = -5 a\)

1p

1p

d

\({2 p q \over q} + {7 p r \over r}\)

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

d

\({2 p q \over q} + {7 p r \over r} = 2 p + 7 p = 9 p\)

1p

2 vwo 1.2 Herleiden van breuken

Breuken herleiden (10)

opgave 1

Herleid tot één breuk.

1p

a

\(4 x - {3 \over 7 x}\)

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

a

\(4 x - {3 \over 7 x} = {4 x \over 1} ⋅ {7 x \over 7 x} - {3 \over 7 x} = {28 x^{2} \over 7 x} - {3 \over 7 x} = {28 x^{2} - 3 \over 7 x}\)

1p

1p

b

\({3 b \over 2 a} - {4 a \over 7 b}\)

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

b

\({3 b \over 2 a} - {4 a \over 7 b} = {21 b^{2} \over 14 a b} - {8 a^{2} \over 14 a b} = {-8 a^{2} + 21 b^{2} \over 14 a b}\)

1p

1p

c

\({2 \over p} ⋅ -{5 \over q}\)

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

c

\({2 \over p} ⋅ -{5 \over q} = -{10 \over p q}\)

1p

1p

d

\({a \over 7} ⋅ {4 \over b}\)

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

d

\({a \over 7} ⋅ {4 \over b} = {4 a \over 7 b}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\({3 \over 5} ⋅ x\)

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

a

\({3 \over 5} ⋅ x = {3 x \over 5}\)

1p

1p

b

\({9 y \over x} ⋅ {x + 2 \over 8}\)

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

b

\({9 y \over x} ⋅ {x + 2 \over 8} = {9 y (x + 2) \over 8 x} = {9 x y + 18 y \over 8 x}\)

1p

1p

c

\({9 \over p} : {5 \over q}\)

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

c

\({9 \over p} : {5 \over q} = {9 \over p} ⋅ {q \over 5} = {9 q \over 5 p}\)

1p

1p

d

\({9 \over 2} : x\)

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

d

\({9 \over 2} : x = {9 \over 2} : {x \over 1} = {9 \over 2} ⋅ {1 \over x} = {9 \over 2 x}\)

1p

opgave 3

Herleid tot één breuk.

1p

a

\({6 \over 5} : {a - 7 b \over b}\)

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

a

\({6 \over 5} : {a - 7 b \over b} = {6 \over 5} ⋅ {b \over a - 7 b} = {6 b \over 5 (a - 7 b)} = {6 b \over 5 a - 35 b}\)

1p

1p

b

\({3 a \over 4} + {a - 2 \over 7}\)

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

b

\({3 a \over 4} + {a - 2 \over 7} = {21 a \over 28} + {4 (a - 2) \over 28} = {21 a + 4 (a - 2) \over 28} = {25 a - 8 \over 28}\)

1p

3 vwo 5.3 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({4 a + 7 \over 2 a - 3} + 6\)

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

○

\({4 a + 7 \over 2 a - 3} + 6 = {4 a + 7 \over 2 a - 3} + {6 (2 a - 3) \over 2 a - 3} = {4 a + 7 + 6 (2 a - 3) \over 2 a - 3} = {4 a + 7 + 12 a - 18 \over 2 a - 3} = {16 a - 11 \over 2 a - 3}\)

1p

vwo wiskunde A 3.1 Breuken en verhoudingen

Breuken herleiden (2)

opgave 1

Deel uit.

1p

a

\({3 a^{2} - a + 20 \over a}\)

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

a

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

1p

1p

b

\({4 x^{2} - 9 x + 3 \over 5 x^{2}}\)

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

b

\({4 x^{2} - 9 x + 3 \over 5 x^{2}} = {4 x^{2} \over 5 x^{2}} - {9 x \over 5 x^{2}} + {3 \over 5 x^{2}} = \frac{4}{5} - {9 \over 5 x} + {3 \over 5 x^{2}}\)

1p

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