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

\({8 \over 9 x} - {2 \over 9 x}\)

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

a

\({8 \over 9 x} - {2 \over 9 x} = {6 \over 9 x} = {2 \over 3 x}\)

1p

1p

b

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

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

b

\({3 \over p} + {2 \over 6 p} = {18 \over 6 p} + {2 \over 6 p} = {20 \over 6 p} = {10 \over 3 p}\)

1p

1p

c

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

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

c

\({6 \over 3 x} + {2 \over 4 y} = {24 y \over 12 x y} + {6 x \over 12 x y} = {24 y + 6 x \over 12 x y} = {4 y + x \over 2 x y}\)

1p

1p

d

\(9 + {3 \over 4 a}\)

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

d

\(9 + {3 \over 4 a} = {9 \over 1} + {3 \over 4 a} = {36 a \over 4 a} + {3 \over 4 a} = {36 a + 3 \over 4 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

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

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

○

\({7 a \over b} + {9 \over 8 b} = {56 a \over 8 b} + {9 \over 8 b} = {56 a + 9 \over 8 b}\)

1p

opgave 3

Herleid.

1p

a

\({3 x \over x}\)

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

a

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

1p

1p

b

\({x \over 9 x}\)

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

b

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

1p

1p

c

\({-32 a \over -36 a}\)

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

c

\({-32 a \over -36 a} = \frac{8}{9}\)

1p

1p

d

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

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

d

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

1p

opgave 4

Herleid.

1p

a

\({-15 a b \over 18 a c}\)

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

a

\({-15 a b \over 18 a c} = -{5 b \over 6 c}\)

1p

1p

b

\({4 y \over 14 x y}\)

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

b

\({4 y \over 14 x y} = {2 \over 7 x}\)

1p

1p

c

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

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

c

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

1p

1p

d

\({5 p q \over q} + {2 p r \over r}\)

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

d

\({5 p q \over q} + {2 p r \over r} = 5 p + 2 p = 7 p\)

1p

2 vwo 1.2 Herleiden van breuken

Breuken herleiden (10)

opgave 1

Herleid tot één breuk.

1p

a

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

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

a

\(4 a - {7 \over 6 a} = {4 a \over 1} ⋅ {6 a \over 6 a} - {7 \over 6 a} = {24 a^{2} \over 6 a} - {7 \over 6 a} = {24 a^{2} - 7 \over 6 a}\)

1p

1p

b

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

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

b

\({7 b \over 3 a} - {4 a \over 2 b} = {14 b^{2} \over 6 a b} - {12 a^{2} \over 6 a b} = {-12 a^{2} + 14 b^{2} \over 6 a b} = {-6 a^{2} + 7 b^{2} \over 3 a b}\)

1p

1p

c

\({8 \over x} ⋅ {7 \over y}\)

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

c

\({8 \over x} ⋅ {7 \over y} = {56 \over x y}\)

1p

1p

d

\({x \over 3} ⋅ -{5 \over y}\)

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

d

\({x \over 3} ⋅ -{5 \over y} = -{5 x \over 3 y}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(-{7 \over 4} ⋅ p\)

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

a

\(-{7 \over 4} ⋅ p = -{7 p \over 4}\)

1p

1p

b

\({7 b \over a} ⋅ {a - 2 \over 9}\)

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

b

\({7 b \over a} ⋅ {a - 2 \over 9} = {7 b (a - 2) \over 9 a} = {7 a b - 14 b \over 9 a}\)

1p

1p

c

\({3 \over x} : {9 \over y}\)

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

c

\({3 \over x} : {9 \over y} = {3 \over x} ⋅ {y \over 9} = {3 y \over 9 x} = {y \over 3 x}\)

1p

1p

d

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

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

d

\(-{5 \over 6} : p = -{5 \over 6} : {p \over 1} = -{5 \over 6} ⋅ {1 \over p} = -{5 \over 6 p}\)

1p

opgave 3

Herleid tot één breuk.

1p

a

\({8 \over 5} : {x - 4 y \over y}\)

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

a

\({8 \over 5} : {x - 4 y \over y} = {8 \over 5} ⋅ {y \over x - 4 y} = {8 y \over 5 (x - 4 y)} = {8 y \over 5 x - 20 y}\)

1p

1p

b

\({a \over 8} + {a - 6 \over 9}\)

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

b

\({a \over 8} + {a - 6 \over 9} = {9 a \over 72} + {8 (a - 6) \over 72} = {9 a + 8 (a - 6) \over 72} = {17 a - 48 \over 72}\)

1p

3 vwo 5.3 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({-9 p - 3 \over -7 p - 1} - 4\)

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

○

\({-9 p - 3 \over -7 p - 1} - 4 = {-9 p - 3 \over -7 p - 1} + {-4 (-7 p - 1) \over -7 p - 1} = {-9 p - 3 - 4 (-7 p - 1) \over -7 p - 1} = {-9 p - 3 + 28 p + 4 \over -7 p - 1} = {19 p + 1 \over -7 p - 1}\)

1p

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