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

'Breuken herleiden'.

2 havo/vwo 1.2 Breuken optellen

Breuken herleiden (15)

opgave 1

Herleid tot één breuk.

1p

a

\({3 \over 5 a} - {2 \over 5 a}\)

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

a

\({3 \over 5 a} - {2 \over 5 a} = {1 \over 5 a}\)

1p

1p

b

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

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

b

\({9 \over a} + {3 \over 4 a} = {36 \over 4 a} + {3 \over 4 a} = {39 \over 4 a}\)

1p

1p

c

\({4 \over 7 x} + {2 \over 6 y}\)

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

c

\({4 \over 7 x} + {2 \over 6 y} = {24 y \over 42 x y} + {14 x \over 42 x y} = {24 y + 14 x \over 42 x y} = {12 y + 7 x \over 21 x y}\)

1p

1p

d

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

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

d

\(9 - {4 \over 7 x} = {9 \over 1} - {4 \over 7 x} = {63 x \over 7 x} - {4 \over 7 x} = {63 x - 4 \over 7 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

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

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

a

\(3 p - {7 \over 8 p} = {3 p \over 1} ⋅ {8 p \over 8 p} - {7 \over 8 p} = {24 p^{2} \over 8 p} - {7 \over 8 p} = {24 p^{2} - 7 \over 8 p}\)

1p

1p

b

\({3 p \over q} + {7 \over 5 q}\)

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

b

\({3 p \over q} + {7 \over 5 q} = {15 p \over 5 q} + {7 \over 5 q} = {15 p + 7 \over 5 q}\)

1p

1p

c

\({3 b \over 9 a} - {5 a \over 4 b}\)

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

c

\({3 b \over 9 a} - {5 a \over 4 b} = {12 b^{2} \over 36 a b} - {45 a^{2} \over 36 a b} = {-45 a^{2} + 12 b^{2} \over 36 a b} = {-15 a^{2} + 4 b^{2} \over 12 a b}\)

1p

opgave 3

Herleid.

1p

a

\({5 x \over x}\)

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

a

\({5 x \over x} = {5 \over 1} = 5\)

1p

1p

b

\({a \over 6 a}\)

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

b

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

1p

1p

c

\({-8 x \over 28 x}\)

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

c

\({-8 x \over 28 x} = -\frac{2}{7}\)

1p

1p

d

\({-16 a \over 2 a}\)

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

d

\({-16 a \over 2 a} = -8\)

1p

opgave 4

Herleid.

1p

a

\({18 x y \over 21 x z}\)

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

a

\({18 x y \over 21 x z} = {6 y \over 7 z}\)

1p

1p

b

\({-18 q \over 21 p q}\)

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

b

\({-18 q \over 21 p q} = -{6 \over 7 p}\)

1p

1p

c

\({8 x y z \over 4 y z}\)

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

c

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

1p

1p

d

\({3 a b \over b} + {2 a c \over c}\)

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

d

\({3 a b \over b} + {2 a c \over c} = 3 a + 2 a = 5 a\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({9 \over x} ⋅ {4 \over y}\)

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

a

\({9 \over x} ⋅ {4 \over y} = {36 \over x y}\)

1p

1p

b

\({x \over 9} ⋅ -{7 \over y}\)

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

b

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

1p

1p

c

\(-{2 \over 9} ⋅ p\)

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

c

\(-{2 \over 9} ⋅ p = -{2 p \over 9}\)

1p

1p

d

\({3 \over a} : {9 \over b}\)

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

\({6 \over 7} : a\)

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

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

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({8 a \over 9} + {a + 6 \over 2}\)

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

\({8 a \over 9} + {a + 6 \over 2} = {16 a \over 18} + {9 (a + 6) \over 18} = {16 a + 9 (a + 6) \over 18} = {25 a + 54 \over 18}\)

1p

havo wiskunde A 6.2 Formules met breuken

Breuken herleiden (2)

opgave 1

Herleid tot één breuk.

1p

a

\(-{2 \over 9} : {p + 3 q \over q}\)

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

a

\(-{2 \over 9} : {p + 3 q \over q} = -{2 \over 9} ⋅ {q \over p + 3 q} = -{2 q \over 9 (p + 3 q)} = -{2 q \over 9 p + 27 q}\)

1p

1p

b

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

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

b

\({2 a - 4 \over -3 a - 9} + 6 = {2 a - 4 \over -3 a - 9} - {-6 (-3 a - 9) \over -3 a - 9} = {2 a - 4 + 6 (-3 a - 9) \over -3 a - 9} = {2 a - 4 - 18 a - 54 \over -3 a - 9} = {-16 a - 58 \over -3 a - 9}\)

1p

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