Getal & Ruimte (13e editie) - 3 havo

'Breuken herleiden'.

2 havo/vwo 1.2 Breuken optellen

Breuken herleiden (15)

opgave 1

Herleid tot één breuk.

1p

a

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

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

a

\({7 \over 4 x} - {8 \over 4 x} = -{1 \over 4 x}\)

1p

1p

b

\({5 \over p} + {9 \over 3 p}\)

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

b

\({5 \over p} + {9 \over 3 p} = {15 \over 3 p} + {9 \over 3 p} = {24 \over 3 p} = {8 \over p}\)

1p

1p

c

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

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

c

\({7 \over 3 a} + {8 \over 6 b} = {14 b \over 6 a b} + {8 a \over 6 a b} = {14 b + 8 a \over 6 a b} = {7 b + 4 a \over 3 a b}\)

1p

1p

d

\(5 + {3 \over 8 a}\)

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

d

\(5 + {3 \over 8 a} = {5 \over 1} + {3 \over 8 a} = {40 a \over 8 a} + {3 \over 8 a} = {40 a + 3 \over 8 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(5 x + {3 \over 2 x}\)

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

a

\(5 x + {3 \over 2 x} = {5 x \over 1} ⋅ {2 x \over 2 x} + {3 \over 2 x} = {10 x^{2} \over 2 x} + {3 \over 2 x} = {10 x^{2} + 3 \over 2 x}\)

1p

1p

b

\({8 x \over y} + {9 \over 4 y}\)

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

b

\({8 x \over y} + {9 \over 4 y} = {32 x \over 4 y} + {9 \over 4 y} = {32 x + 9 \over 4 y}\)

1p

1p

c

\({4 b \over 9 a} - {7 a \over 8 b}\)

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

c

\({4 b \over 9 a} - {7 a \over 8 b} = {32 b^{2} \over 72 a b} - {63 a^{2} \over 72 a b} = {-63 a^{2} + 32 b^{2} \over 72 a b}\)

1p

opgave 3

Herleid.

1p

a

\({2 a \over a}\)

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

a

\({2 a \over a} = {2 \over 1} = 2\)

1p

1p

b

\({p \over 9 p}\)

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

b

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

1p

1p

c

\({-15 x \over -21 x}\)

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

c

\({-15 x \over -21 x} = \frac{5}{7}\)

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

\({12 a b \over -28 a c}\)

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

a

\({12 a b \over -28 a c} = -{3 b \over 7 c}\)

1p

1p

b

\({15 b \over 24 a b}\)

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

b

\({15 b \over 24 a b} = {5 \over 8 a}\)

1p

1p

c

\({-35 x y z \over 5 y z}\)

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

c

\({-35 x y z \over 5 y z} = -7 x\)

1p

1p

d

\({4 p q \over q} + {3 p r \over r}\)

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

d

\({4 p q \over q} + {3 p r \over r} = 4 p + 3 p = 7 p\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({4 \over a} ⋅ {3 \over b}\)

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

a

\({4 \over a} ⋅ {3 \over b} = {12 \over a b}\)

1p

1p

b

\({x \over 6} ⋅ {9 \over y}\)

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

b

\({x \over 6} ⋅ {9 \over y} = {9 x \over 6 y} = {3 x \over 2 y}\)

1p

1p

c

\(-{6 \over 7} ⋅ a\)

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

c

\(-{6 \over 7} ⋅ a = -{6 a \over 7}\)

1p

1p

d

\({7 \over x} : {8 \over y}\)

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

\(-{8 \over 9} : p\)

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

\(-{8 \over 9} : p = -{8 \over 9} : {p \over 1} = -{8 \over 9} ⋅ {1 \over p} = -{8 \over 9 p}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({x \over 7} + {x - 2 \over 3}\)

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

\({x \over 7} + {x - 2 \over 3} = {3 x \over 21} + {7 (x - 2) \over 21} = {3 x + 7 (x - 2) \over 21} = {10 x - 14 \over 21}\)

1p

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