Getal & Ruimte (13e editie) - 2 havo/vwo

'Breuken herleiden'.

2 havo/vwo 1.2 Breuken optellen

Breuken herleiden (15)

opgave 1

Herleid tot één breuk.

1p

a

\({3 \over 9 x} - {8 \over 9 x}\)

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

a

\({3 \over 9 x} - {8 \over 9 x} = -{5 \over 9 x}\)

1p

1p

b

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

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

b

\({2 \over x} + {9 \over 3 x} = {6 \over 3 x} + {9 \over 3 x} = {15 \over 3 x} = {5 \over x}\)

1p

1p

c

\({5 \over 4 a} - {8 \over 2 b}\)

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

c

\({5 \over 4 a} - {8 \over 2 b} = {5 b \over 4 a b} - {16 a \over 4 a b} = {5 b - 16 a \over 4 a b}\)

1p

1p

d

\(4 - {9 \over 8 p}\)

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

d

\(4 - {9 \over 8 p} = {4 \over 1} - {9 \over 8 p} = {32 p \over 8 p} - {9 \over 8 p} = {32 p - 9 \over 8 p}\)

1p

opgave 2

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

\({5 p \over q} + {4 \over 7 q}\)

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

b

\({5 p \over q} + {4 \over 7 q} = {35 p \over 7 q} + {4 \over 7 q} = {35 p + 4 \over 7 q}\)

1p

1p

c

\({4 y \over 7 x} + {5 x \over 6 y}\)

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

c

\({4 y \over 7 x} + {5 x \over 6 y} = {24 y^{2} \over 42 x y} + {35 x^{2} \over 42 x y} = {35 x^{2} + 24 y^{2} \over 42 x y}\)

1p

opgave 3

Herleid.

1p

a

\({5 a \over a}\)

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

a

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

1p

1p

b

\({x \over 7 x}\)

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

b

\({x \over 7 x} = {1 \over 7}\)

1p

1p

c

\({-12 a \over 16 a}\)

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

c

\({-12 a \over 16 a} = -\frac{3}{4}\)

1p

1p

d

\({15 a \over 3 a}\)

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

d

\({15 a \over 3 a} = 5\)

1p

opgave 4

Herleid.

1p

a

\({40 p q \over 45 p r}\)

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

a

\({40 p q \over 45 p r} = {8 q \over 9 r}\)

1p

1p

b

\({15 y \over -35 x y}\)

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

b

\({15 y \over -35 x y} = -{3 \over 7 x}\)

1p

1p

c

\({12 x y z \over 4 y z}\)

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

c

\({12 x y z \over 4 y z} = 3 x\)

1p

1p

d

\({5 a b \over b} + {6 a c \over c}\)

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

d

\({5 a b \over b} + {6 a c \over c} = 5 a + 6 a = 11 a\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({2 \over x} ⋅ -{9 \over y}\)

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

a

\({2 \over x} ⋅ -{9 \over y} = -{18 \over x y}\)

1p

1p

b

\({a \over 7} ⋅ -{5 \over b}\)

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

b

\({a \over 7} ⋅ -{5 \over b} = -{5 a \over 7 b}\)

1p

1p

c

\(-{5 \over 2} ⋅ x\)

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

c

\(-{5 \over 2} ⋅ x = -{5 x \over 2}\)

1p

1p

d

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

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

\(-{4 \over 3} : a\)

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

○

\(-{4 \over 3} : a = -{4 \over 3} : {a \over 1} = -{4 \over 3} ⋅ {1 \over a} = -{4 \over 3 a}\)

1p

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