Getal & Ruimte (13e editie) - 2 vwo

'Breuken herleiden'.

1 vwo 6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

1p

a

\({3 \over 9 p} - {2 \over 9 p}\)

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

a

\({3 \over 9 p} - {2 \over 9 p} = {1 \over 9 p}\)

1p

1p

b

\({6 \over a} - {9 \over 4 a}\)

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

b

\({6 \over a} - {9 \over 4 a} = {24 \over 4 a} - {9 \over 4 a} = {15 \over 4 a}\)

1p

1p

c

\({2 \over 4 x} + {7 \over 8 y}\)

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

c

\({2 \over 4 x} + {7 \over 8 y} = {4 y \over 8 x y} + {7 x \over 8 x y} = {4 y + 7 x \over 8 x y}\)

1p

1p

d

\(6 - {8 \over 5 a}\)

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

d

\(6 - {8 \over 5 a} = {6 \over 1} - {8 \over 5 a} = {30 a \over 5 a} - {8 \over 5 a} = {30 a - 8 \over 5 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

\({4 x \over y} + {2 \over 3 y}\)

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

○

\({4 x \over y} + {2 \over 3 y} = {12 x \over 3 y} + {2 \over 3 y} = {12 x + 2 \over 3 y}\)

1p

opgave 3

Herleid.

1p

a

\({2 a \over a}\)

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

a

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

1p

1p

b

\({p \over 7 p}\)

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

b

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

1p

1p

c

\({9 a \over -12 a}\)

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

c

\({9 a \over -12 a} = -\frac{3}{4}\)

1p

1p

d

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

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

d

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

1p

opgave 4

Herleid.

1p

a

\({-9 x y \over 21 x z}\)

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

a

\({-9 x y \over 21 x z} = -{3 y \over 7 z}\)

1p

1p

b

\({35 y \over -45 x y}\)

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

b

\({35 y \over -45 x y} = -{7 \over 9 x}\)

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

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

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

d

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

1p

2 vwo 1.2 Herleiden van breuken

Breuken herleiden (10)

opgave 1

Herleid tot één breuk.

1p

a

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

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

a

\(9 p + {8 \over 5 p} = {9 p \over 1} ⋅ {5 p \over 5 p} + {8 \over 5 p} = {45 p^{2} \over 5 p} + {8 \over 5 p} = {45 p^{2} + 8 \over 5 p}\)

1p

1p

b

\({3 b \over 6 a} + {9 a \over 7 b}\)

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

b

\({3 b \over 6 a} + {9 a \over 7 b} = {21 b^{2} \over 42 a b} + {54 a^{2} \over 42 a b} = {54 a^{2} + 21 b^{2} \over 42 a b} = {18 a^{2} + 7 b^{2} \over 14 a b}\)

1p

1p

c

\({7 \over x} ⋅ {2 \over y}\)

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

c

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

1p

1p

d

\({a \over 8} ⋅ -{4 \over b}\)

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

d

\({a \over 8} ⋅ -{4 \over b} = -{4 a \over 8 b} = -{a \over 2 b}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\({8 \over 5} ⋅ x\)

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

a

\({8 \over 5} ⋅ x = {8 x \over 5}\)

1p

1p

b

\({3 b \over a} ⋅ {a - 8 \over 9}\)

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

b

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

1p

1p

c

\({8 \over a} : {4 \over b}\)

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

c

\({8 \over a} : {4 \over b} = {8 \over a} ⋅ {b \over 4} = {8 b \over 4 a} = {2 b \over a}\)

1p

1p

d

\({2 \over 3} : p\)

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

d

\({2 \over 3} : p = {2 \over 3} : {p \over 1} = {2 \over 3} ⋅ {1 \over p} = {2 \over 3 p}\)

1p

opgave 3

Herleid tot één breuk.

1p

a

\({1 \over 6} : {x - 8 y \over y}\)

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

a

\({1 \over 6} : {x - 8 y \over y} = {1 \over 6} ⋅ {y \over x - 8 y} = {y \over 6 (x - 8 y)} = {y \over 6 x - 48 y}\)

1p

1p

b

\({x \over 4} + {x + 5 \over 9}\)

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

b

\({x \over 4} + {x + 5 \over 9} = {9 x \over 36} + {4 (x + 5) \over 36} = {9 x + 4 (x + 5) \over 36} = {13 x + 20 \over 36}\)

1p

"