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

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

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

a

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

1p

1p

b

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

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

b

\({4 \over x} + {8 \over 7 x} = {28 \over 7 x} + {8 \over 7 x} = {36 \over 7 x}\)

1p

1p

c

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

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

c

\({4 \over 6 a} - {3 \over 7 b} = {28 b \over 42 a b} - {18 a \over 42 a b} = {28 b - 18 a \over 42 a b} = {14 b - 9 a \over 21 a b}\)

1p

1p

d

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

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

d

\(6 - {5 \over 9 p} = {6 \over 1} - {5 \over 9 p} = {54 p \over 9 p} - {5 \over 9 p} = {54 p - 5 \over 9 p}\)

1p

opgave 2

Herleid tot één breuk.

1p

\({7 a \over b} + {4 \over 6 b}\)

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

\({7 a \over b} + {4 \over 6 b} = {42 a \over 6 b} + {4 \over 6 b} = {42 a + 4 \over 6 b} = {21 a + 2 \over 3 b}\)

1p

opgave 3

Herleid.

1p

a

\({9 p \over p}\)

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

a

\({9 p \over p} = {9 \over 1} = 9\)

1p

1p

b

\({a \over 3 a}\)

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

b

\({a \over 3 a} = {1 \over 3}\)

1p

1p

c

\({10 a \over -18 a}\)

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

c

\({10 a \over -18 a} = -\frac{5}{9}\)

1p

1p

d

\({-9 x \over -3 x}\)

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

d

\({-9 x \over -3 x} = 3\)

1p

opgave 4

Herleid.

1p

a

\({-16 x y \over 28 x z}\)

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

a

\({-16 x y \over 28 x z} = -{4 y \over 7 z}\)

1p

1p

b

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

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

b

\({6 b \over -9 a b} = -{2 \over 3 a}\)

1p

1p

c

\({12 p q r \over 2 q r}\)

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

c

\({12 p q r \over 2 q r} = 6 p\)

1p

1p

d

\({7 a b \over b} + {6 a c \over c}\)

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

d

\({7 a b \over b} + {6 a c \over c} = 7 a + 6 a = 13 a\)

1p

2 vwo 1.2 Herleiden van breuken

Breuken herleiden (10)

opgave 1

Herleid tot één breuk.

1p

a

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

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

a

\(6 a + {9 \over 5 a} = {6 a \over 1} ⋅ {5 a \over 5 a} + {9 \over 5 a} = {30 a^{2} \over 5 a} + {9 \over 5 a} = {30 a^{2} + 9 \over 5 a}\)

1p

1p

b

\({6 b \over 9 a} + {7 a \over 8 b}\)

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

b

\({6 b \over 9 a} + {7 a \over 8 b} = {48 b^{2} \over 72 a b} + {63 a^{2} \over 72 a b} = {63 a^{2} + 48 b^{2} \over 72 a b} = {21 a^{2} + 16 b^{2} \over 24 a b}\)

1p

1p

c

\({7 \over x} ⋅ {4 \over y}\)

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

c

\({7 \over x} ⋅ {4 \over y} = {28 \over x y}\)

1p

1p

d

\({x \over 7} ⋅ {9 \over y}\)

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

d

\({x \over 7} ⋅ {9 \over y} = {9 x \over 7 y}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\({8 \over 9} ⋅ p\)

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

a

\({8 \over 9} ⋅ p = {8 p \over 9}\)

1p

1p

b

\({5 y \over x} ⋅ {x - 6 \over 4}\)

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

b

\({5 y \over x} ⋅ {x - 6 \over 4} = {5 y (x - 6) \over 4 x} = {5 x y - 30 y \over 4 x}\)

1p

1p

c

\({4 \over p} : {9 \over q}\)

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

c

\({4 \over p} : {9 \over q} = {4 \over p} ⋅ {q \over 9} = {4 q \over 9 p}\)

1p

1p

d

\(-{9 \over 5} : a\)

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

d

\(-{9 \over 5} : a = -{9 \over 5} : {a \over 1} = -{9 \over 5} ⋅ {1 \over a} = -{9 \over 5 a}\)

1p

opgave 3

Herleid tot één breuk.

1p

a

\({1 \over 4} : {x - 6 y \over y}\)

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

a

\({1 \over 4} : {x - 6 y \over y} = {1 \over 4} ⋅ {y \over x - 6 y} = {y \over 4 (x - 6 y)} = {y \over 4 x - 24 y}\)

1p

1p

b

\({5 a \over 6} + {a + 1 \over 7}\)

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

b

\({5 a \over 6} + {a + 1 \over 7} = {35 a \over 42} + {6 (a + 1) \over 42} = {35 a + 6 (a + 1) \over 42} = {41 a + 6 \over 42}\)

1p

3 vwo 5.3 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({-7 p + 2 \over 4 p - 5} - 8\)

Optellen (9)
00eh - Breuken herleiden - basis - 1ms - dynamic variables

\({-7 p + 2 \over 4 p - 5} - 8 = {-7 p + 2 \over 4 p - 5} - {8 (4 p - 5) \over 4 p - 5} = {-7 p + 2 - 8 (4 p - 5) \over 4 p - 5} = {-7 p + 2 - 32 p + 40 \over 4 p - 5} = {-39 p + 42 \over 4 p - 5}\)

1p

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