Getal & Ruimte (13e editie) - 3 vwo

'Breuken herleiden'.

1 vwo 6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

1p

a

\({9 \over 8 a} - {3 \over 8 a}\)

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

a

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

1p

1p

b

\({6 \over p} + {5 \over 9 p}\)

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

b

\({6 \over p} + {5 \over 9 p} = {54 \over 9 p} + {5 \over 9 p} = {59 \over 9 p}\)

1p

1p

c

\({7 \over 4 x} - {6 \over 5 y}\)

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

c

\({7 \over 4 x} - {6 \over 5 y} = {35 y \over 20 x y} - {24 x \over 20 x y} = {35 y - 24 x \over 20 x y}\)

1p

1p

d

\(2 - {7 \over 6 a}\)

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

d

\(2 - {7 \over 6 a} = {2 \over 1} - {7 \over 6 a} = {12 a \over 6 a} - {7 \over 6 a} = {12 a - 7 \over 6 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

\({6 x \over y} - {2 \over 4 y}\)

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

○

\({6 x \over y} - {2 \over 4 y} = {24 x \over 4 y} - {2 \over 4 y} = {24 x - 2 \over 4 y} = {12 x - 1 \over 2 y}\)

1p

opgave 3

Herleid.

1p

a

\({6 a \over a}\)

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

a

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

1p

1p

b

\({x \over 6 x}\)

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

b

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

1p

1p

c

\({6 p \over -14 p}\)

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

c

\({6 p \over -14 p} = -\frac{3}{7}\)

1p

1p

d

\({25 a \over 5 a}\)

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

d

\({25 a \over 5 a} = 5\)

1p

opgave 4

Herleid.

1p

a

\({20 x y \over -35 x z}\)

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

a

\({20 x y \over -35 x z} = -{4 y \over 7 z}\)

1p

1p

b

\({-6 b \over -21 a b}\)

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

b

\({-6 b \over -21 a b} = {2 \over 7 a}\)

1p

1p

c

\({-18 x y z \over 3 y z}\)

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

c

\({-18 x y z \over 3 y z} = -6 x\)

1p

1p

d

\({4 a b \over b} + {2 a c \over c}\)

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

d

\({4 a b \over b} + {2 a c \over c} = 4 a + 2 a = 6 a\)

1p

2 vwo 1.2 Herleiden van breuken

Breuken herleiden (10)

opgave 1

Herleid tot één breuk.

1p

a

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

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

a

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

1p

1p

b

\({5 b \over 8 a} - {3 a \over 6 b}\)

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

b

\({5 b \over 8 a} - {3 a \over 6 b} = {15 b^{2} \over 24 a b} - {12 a^{2} \over 24 a b} = {-12 a^{2} + 15 b^{2} \over 24 a b} = {-4 a^{2} + 5 b^{2} \over 8 a b}\)

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

\({a \over 5} ⋅ {3 \over b}\)

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

d

\({a \over 5} ⋅ {3 \over b} = {3 a \over 5 b}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(-{9 \over 7} ⋅ x\)

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

a

\(-{9 \over 7} ⋅ x = -{9 x \over 7}\)

1p

1p

b

\({6 y \over x} ⋅ {x + 2 \over 9}\)

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

b

\({6 y \over x} ⋅ {x + 2 \over 9} = {6 y (x + 2) \over 9 x} = {2 y (x + 2) \over 3 x} = {2 x y + 4 y \over 3 x}\)

1p

1p

c

\({9 \over a} : {4 \over b}\)

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

c

\({9 \over a} : {4 \over b} = {9 \over a} ⋅ {b \over 4} = {9 b \over 4 a}\)

1p

1p

d

\(-{7 \over 6} : x\)

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

d

\(-{7 \over 6} : x = -{7 \over 6} : {x \over 1} = -{7 \over 6} ⋅ {1 \over x} = -{7 \over 6 x}\)

1p

opgave 3

Herleid tot één breuk.

1p

a

\(-{5 \over 8} : {p - 3 q \over q}\)

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

a

\(-{5 \over 8} : {p - 3 q \over q} = -{5 \over 8} ⋅ {q \over p - 3 q} = -{5 q \over 8 (p - 3 q)} = -{5 q \over 8 p - 24 q}\)

1p

1p

b

\({a \over 2} + {a + 9 \over 7}\)

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

b

\({a \over 2} + {a + 9 \over 7} = {7 a \over 14} + {2 (a + 9) \over 14} = {7 a + 2 (a + 9) \over 14} = {9 a + 18 \over 14}\)

1p

3 vwo 5.3 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({8 x + 3 \over 5 x + 7} - 1\)

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

○

\({8 x + 3 \over 5 x + 7} - 1 = {8 x + 3 \over 5 x + 7} - {1 (5 x + 7) \over 5 x + 7} = {8 x + 3 - 1 (5 x + 7) \over 5 x + 7} = {8 x + 3 - 5 x - 7 \over 5 x + 7} = {3 x - 4 \over 5 x + 7}\)

1p

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