Getal & Ruimte (12e editie) - havo wiskunde B

'Breuken herleiden'.

2 havo/vwo 1.2 Breuken optellen

Breuken herleiden (15)

opgave 1

Herleid tot één breuk.

1p

a

\({7 \over 8 a} - {9 \over 8 a}\)

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

a

\({7 \over 8 a} - {9 \over 8 a} = -{2 \over 8 a} = -{1 \over 4 a}\)

1p

1p

b

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

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

b

\({7 \over x} + {6 \over 4 x} = {28 \over 4 x} + {6 \over 4 x} = {34 \over 4 x} = {17 \over 2 x}\)

1p

1p

c

\({6 \over 7 p} - {5 \over 3 q}\)

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

c

\({6 \over 7 p} - {5 \over 3 q} = {18 q \over 21 p q} - {35 p \over 21 p q} = {18 q - 35 p \over 21 p q}\)

1p

1p

d

\(3 - {9 \over 2 x}\)

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

d

\(3 - {9 \over 2 x} = {3 \over 1} - {9 \over 2 x} = {6 x \over 2 x} - {9 \over 2 x} = {6 x - 9 \over 2 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

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

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

a

\(6 a - {8 \over 9 a} = {6 a \over 1} ⋅ {9 a \over 9 a} - {8 \over 9 a} = {54 a^{2} \over 9 a} - {8 \over 9 a} = {54 a^{2} - 8 \over 9 a}\)

1p

1p

b

\({3 x \over y} + {4 \over 7 y}\)

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

b

\({3 x \over y} + {4 \over 7 y} = {21 x \over 7 y} + {4 \over 7 y} = {21 x + 4 \over 7 y}\)

1p

1p

c

\({6 b \over 8 a} + {3 a \over 2 b}\)

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

c

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

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

\({p \over 4 p}\)

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

b

\({p \over 4 p} = {1 \over 4}\)

1p

1p

c

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

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

c

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

1p

1p

d

\({4 a \over 2 a}\)

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

d

\({4 a \over 2 a} = 2\)

1p

opgave 4

Herleid.

1p

a

\({-16 a b \over -18 a c}\)

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

a

\({-16 a b \over -18 a c} = {8 b \over 9 c}\)

1p

1p

b

\({25 y \over 45 x y}\)

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

b

\({25 y \over 45 x y} = {5 \over 9 x}\)

1p

1p

c

\({16 p q r \over 2 q r}\)

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

c

\({16 p q r \over 2 q r} = 8 p\)

1p

1p

d

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

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

d

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

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({5 \over x} ⋅ {6 \over y}\)

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

a

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

1p

1p

b

\({p \over 3} ⋅ {7 \over q}\)

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

b

\({p \over 3} ⋅ {7 \over q} = {7 p \over 3 q}\)

1p

1p

c

\({4 \over 3} ⋅ a\)

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

c

\({4 \over 3} ⋅ a = {4 a \over 3}\)

1p

1p

d

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

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

\({8 \over 3} : x\)

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

\({8 \over 3} : x = {8 \over 3} : {x \over 1} = {8 \over 3} ⋅ {1 \over x} = {8 \over 3 x}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({4 a \over 7} + {a - 6 \over 5}\)

Optellen (8)
0098 - Breuken herleiden - basis - 1ms - dynamic variables

\({4 a \over 7} + {a - 6 \over 5} = {20 a \over 35} + {7 (a - 6) \over 35} = {20 a + 7 (a - 6) \over 35} = {27 a - 42 \over 35}\)

1p

havo wiskunde B 11.5 Gebroken functies

Breuken herleiden (3)

opgave 1

Herleid tot één breuk.

1p

\({5 a + 6 \over -2 a + 8} - 9\)

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

\({5 a + 6 \over -2 a + 8} - 9 = {5 a + 6 \over -2 a + 8} + {-9 (-2 a + 8) \over -2 a + 8} = {5 a + 6 - 9 (-2 a + 8) \over -2 a + 8} = {5 a + 6 + 18 a - 72 \over -2 a + 8} = {23 a - 66 \over -2 a + 8}\)

1p

opgave 2

Deel uit.

1p

a

\({9 p^{2} - 3 p + 60 \over 3 p}\)

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

a

\({9 p^{2} - 3 p + 60 \over 3 p} = {9 p^{2} \over 3 p} - {3 p \over 3 p} + {60 \over 3 p} = 3 p - 1 + {20 \over p}\)

1p

1p

b

\({6 x^{2} - 5 x + 9 \over x^{2}}\)

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

b

\({6 x^{2} - 5 x + 9 \over x^{2}} = {6 x^{2} \over x^{2}} - {5 x \over x^{2}} + {9 \over x^{2}} = 6 - {5 \over x} + {9 \over x^{2}}\)

1p

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