Getal & Ruimte (13e editie) - vwo wiskunde A

'Breuken herleiden'.

1 vwo 6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

1p

a

\({4 \over 9 x} - {7 \over 9 x}\)

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

a

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

1p

1p

b

\({7 \over p} + {8 \over 3 p}\)

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

b

\({7 \over p} + {8 \over 3 p} = {21 \over 3 p} + {8 \over 3 p} = {29 \over 3 p}\)

1p

1p

c

\({3 \over 8 a} + {6 \over 7 b}\)

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

c

\({3 \over 8 a} + {6 \over 7 b} = {21 b \over 56 a b} + {48 a \over 56 a b} = {21 b + 48 a \over 56 a b}\)

1p

1p

d

\(7 + {8 \over 5 a}\)

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

d

\(7 + {8 \over 5 a} = {7 \over 1} + {8 \over 5 a} = {35 a \over 5 a} + {8 \over 5 a} = {35 a + 8 \over 5 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

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

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

\({8 x \over y} - {5 \over 4 y} = {32 x \over 4 y} - {5 \over 4 y} = {32 x - 5 \over 4 y}\)

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

\({a \over 8 a}\)

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

b

\({a \over 8 a} = {1 \over 8}\)

1p

1p

c

\({-4 x \over 18 x}\)

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

c

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

1p

1p

d

\({20 x \over -4 x}\)

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

d

\({20 x \over -4 x} = -5\)

1p

opgave 4

Herleid.

1p

a

\({-20 a b \over -36 a c}\)

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

a

\({-20 a b \over -36 a c} = {5 b \over 9 c}\)

1p

1p

b

\({-20 y \over 36 x y}\)

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

b

\({-20 y \over 36 x y} = -{5 \over 9 x}\)

1p

1p

c

\({-45 a b c \over -5 b c}\)

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

c

\({-45 a b c \over -5 b c} = 9 a\)

1p

1p

d

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

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

d

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

1p

2 vwo 1.2 Herleiden van breuken

Breuken herleiden (10)

opgave 1

Herleid tot één breuk.

1p

a

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

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

a

\(9 a + {7 \over 2 a} = {9 a \over 1} ⋅ {2 a \over 2 a} + {7 \over 2 a} = {18 a^{2} \over 2 a} + {7 \over 2 a} = {18 a^{2} + 7 \over 2 a}\)

1p

1p

b

\({3 b \over 7 a} + {2 a \over 8 b}\)

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

b

\({3 b \over 7 a} + {2 a \over 8 b} = {24 b^{2} \over 56 a b} + {14 a^{2} \over 56 a b} = {14 a^{2} + 24 b^{2} \over 56 a b} = {7 a^{2} + 12 b^{2} \over 28 a b}\)

1p

1p

c

\({9 \over p} ⋅ {7 \over q}\)

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

c

\({9 \over p} ⋅ {7 \over q} = {63 \over p q}\)

1p

1p

d

\({x \over 5} ⋅ -{3 \over y}\)

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

a

\(-{4 \over 9} ⋅ x\)

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

a

\(-{4 \over 9} ⋅ x = -{4 x \over 9}\)

1p

1p

b

\({5 y \over x} ⋅ {x - 4 \over 3}\)

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

b

\({5 y \over x} ⋅ {x - 4 \over 3} = {5 y (x - 4) \over 3 x} = {5 x y - 20 y \over 3 x}\)

1p

1p

c

\({8 \over a} : {3 \over b}\)

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

c

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

1p

1p

d

\(-{4 \over 7} : p\)

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

d

\(-{4 \over 7} : p = -{4 \over 7} : {p \over 1} = -{4 \over 7} ⋅ {1 \over p} = -{4 \over 7 p}\)

1p

opgave 3

Herleid tot één breuk.

1p

a

\({7 \over 4} : {a + 2 b \over b}\)

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

a

\({7 \over 4} : {a + 2 b \over b} = {7 \over 4} ⋅ {b \over a + 2 b} = {7 b \over 4 (a + 2 b)} = {7 b \over 4 a + 8 b}\)

1p

1p

b

\({9 x \over 5} + {x - 4 \over 7}\)

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

b

\({9 x \over 5} + {x - 4 \over 7} = {63 x \over 35} + {5 (x - 4) \over 35} = {63 x + 5 (x - 4) \over 35} = {68 x - 20 \over 35}\)

1p

3 vwo 5.3 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({-4 x - 2 \over -9 x + 6} - 3\)

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

\({-4 x - 2 \over -9 x + 6} - 3 = {-4 x - 2 \over -9 x + 6} + {-3 (-9 x + 6) \over -9 x + 6} = {-4 x - 2 - 3 (-9 x + 6) \over -9 x + 6} = {-4 x - 2 + 27 x - 18 \over -9 x + 6} = {23 x - 20 \over -9 x + 6}\)

1p

vwo wiskunde A 3.1 Breuken en verhoudingen

Breuken herleiden (2)

opgave 1

Deel uit.

1p

a

\({2 a^{2} + 4 a - 60 \over 2 a}\)

Uitdelen (1)
00ei - Breuken herleiden - basis - 0ms - dynamic variables

a

\({2 a^{2} + 4 a - 60 \over 2 a} = {2 a^{2} \over 2 a} + {4 a \over 2 a} - {60 \over 2 a} = a + 2 - {30 \over a}\)

1p

1p

b

\({9 x^{2} + 7 x + 1 \over 2 x^{2}}\)

Uitdelen (2)
00ej - Breuken herleiden - basis - 0ms - dynamic variables

b

\({9 x^{2} + 7 x + 1 \over 2 x^{2}} = {9 x^{2} \over 2 x^{2}} + {7 x \over 2 x^{2}} + {1 \over 2 x^{2}} = 4\frac{1}{2} + {7 \over 2 x} + {1 \over 2 x^{2}}\)

1p

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