Getal & Ruimte (12e editie) - vwo wiskunde C

'Breuken herleiden'.

1 vwo 6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

1p

a

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

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

a

\({7 \over 8 p} + {4 \over 8 p} = {11 \over 8 p}\)

1p

1p

b

\({2 \over x} - {4 \over 9 x}\)

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

b

\({2 \over x} - {4 \over 9 x} = {18 \over 9 x} - {4 \over 9 x} = {14 \over 9 x}\)

1p

1p

c

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

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

c

\({7 \over 9 x} + {5 \over 3 y} = {7 y \over 9 x y} + {15 x \over 9 x y} = {7 y + 15 x \over 9 x y}\)

1p

1p

d

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

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

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

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

○

\({2 a \over b} + {6 \over 5 b} = {10 a \over 5 b} + {6 \over 5 b} = {10 a + 6 \over 5 b}\)

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

\({p \over 6 p}\)

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

b

\({p \over 6 p} = {1 \over 6}\)

1p

1p

c

\({8 x \over 12 x}\)

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

c

\({8 x \over 12 x} = \frac{2}{3}\)

1p

1p

d

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

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

d

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

1p

opgave 4

Herleid.

1p

a

\({-15 a b \over 27 a c}\)

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

a

\({-15 a b \over 27 a c} = -{5 b \over 9 c}\)

1p

1p

b

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

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

b

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

1p

1p

c

\({24 x y z \over -4 y z}\)

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

c

\({24 x y z \over -4 y z} = -6 x\)

1p

1p

d

\({5 a b \over b} - {7 a c \over c}\)

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

d

\({5 a b \over b} - {7 a c \over c} = 5 a - 7 a = -2 a\)

1p

2 vwo 1.2 Herleiden van breuken

Breuken herleiden (10)

opgave 1

Herleid tot één breuk.

1p

a

\(2 x - {7 \over 4 x}\)

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

a

\(2 x - {7 \over 4 x} = {2 x \over 1} ⋅ {4 x \over 4 x} - {7 \over 4 x} = {8 x^{2} \over 4 x} - {7 \over 4 x} = {8 x^{2} - 7 \over 4 x}\)

1p

1p

b

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

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

b

\({3 b \over 4 a} - {2 a \over 9 b} = {27 b^{2} \over 36 a b} - {8 a^{2} \over 36 a b} = {-8 a^{2} + 27 b^{2} \over 36 a b}\)

1p

1p

c

\({9 \over a} ⋅ -{7 \over b}\)

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

c

\({9 \over a} ⋅ -{7 \over b} = -{63 \over a b}\)

1p

1p

d

\({p \over 3} ⋅ -{4 \over q}\)

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

a

\({2 \over 3} ⋅ x\)

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

a

\({2 \over 3} ⋅ x = {2 x \over 3}\)

1p

1p

b

\({8 y \over x} ⋅ {x + 5 \over 4}\)

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

b

\({8 y \over x} ⋅ {x + 5 \over 4} = {8 y (x + 5) \over 4 x} = {2 y (x + 5) \over x} = {2 x y + 10 y \over x}\)

1p

1p

c

\({6 \over a} : {4 \over b}\)

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

c

\({6 \over a} : {4 \over b} = {6 \over a} ⋅ {b \over 4} = {6 b \over 4 a} = {3 b \over 2 a}\)

1p

1p

d

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

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

d

\(-{4 \over 3} : x = -{4 \over 3} : {x \over 1} = -{4 \over 3} ⋅ {1 \over x} = -{4 \over 3 x}\)

1p

opgave 3

Herleid tot één breuk.

1p

a

\({2 \over 9} : {a - b \over b}\)

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

a

\({2 \over 9} : {a - b \over b} = {2 \over 9} ⋅ {b \over a - b} = {2 b \over 9 (a - b)} = {2 b \over 9 a - 9 b}\)

1p

1p

b

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

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

b

\({2 p \over 3} + {p - 6 \over 5} = {10 p \over 15} + {3 (p - 6) \over 15} = {10 p + 3 (p - 6) \over 15} = {13 p - 18 \over 15}\)

1p

3 vwo 5.3 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({-4 p + 5 \over 2 p + 3} - 7\)

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

○

\({-4 p + 5 \over 2 p + 3} - 7 = {-4 p + 5 \over 2 p + 3} - {7 (2 p + 3) \over 2 p + 3} = {-4 p + 5 - 7 (2 p + 3) \over 2 p + 3} = {-4 p + 5 - 14 p - 21 \over 2 p + 3} = {-18 p - 16 \over 2 p + 3}\)

1p

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