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

\({3 \over 8 a} - {2 \over 8 a}\)

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

a

\({3 \over 8 a} - {2 \over 8 a} = {1 \over 8 a}\)

1p

1p

b

\({3 \over x} - {9 \over 6 x}\)

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

b

\({3 \over x} - {9 \over 6 x} = {18 \over 6 x} - {9 \over 6 x} = {9 \over 6 x} = {3 \over 2 x}\)

1p

1p

c

\({6 \over 7 x} - {2 \over 5 y}\)

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

c

\({6 \over 7 x} - {2 \over 5 y} = {30 y \over 35 x y} - {14 x \over 35 x y} = {30 y - 14 x \over 35 x y}\)

1p

1p

d

\(7 + {8 \over 9 p}\)

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

d

\(7 + {8 \over 9 p} = {7 \over 1} + {8 \over 9 p} = {63 p \over 9 p} + {8 \over 9 p} = {63 p + 8 \over 9 p}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(4 a - {7 \over 2 a}\)

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

a

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

1p

1p

b

\({4 p \over q} + {2 \over 3 q}\)

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

b

\({4 p \over q} + {2 \over 3 q} = {12 p \over 3 q} + {2 \over 3 q} = {12 p + 2 \over 3 q}\)

1p

1p

c

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

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

c

\({9 b \over 6 a} + {5 a \over 2 b} = {9 b^{2} \over 6 a b} + {15 a^{2} \over 6 a b} = {15 a^{2} + 9 b^{2} \over 6 a b} = {5 a^{2} + 3 b^{2} \over 2 a b}\)

1p

opgave 3

Herleid.

1p

a

\({3 x \over x}\)

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

a

\({3 x \over x} = {3 \over 1} = 3\)

1p

1p

b

\({a \over 3 a}\)

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

b

\({a \over 3 a} = {1 \over 3}\)

1p

1p

c

\({10 x \over -45 x}\)

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

c

\({10 x \over -45 x} = -\frac{2}{9}\)

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

\({-12 x y \over 15 x z}\)

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

a

\({-12 x y \over 15 x z} = -{4 y \over 5 z}\)

1p

1p

b

\({-20 q \over 25 p q}\)

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

b

\({-20 q \over 25 p q} = -{4 \over 5 p}\)

1p

1p

c

\({12 a b c \over 3 b c}\)

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

c

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

1p

1p

d

\({2 x y \over y} - {3 x z \over z}\)

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

d

\({2 x y \over y} - {3 x z \over z} = 2 x - 3 x = -x\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({3 \over x} ⋅ -{7 \over y}\)

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

a

\({3 \over x} ⋅ -{7 \over y} = -{21 \over x y}\)

1p

1p

b

\({x \over 8} ⋅ {5 \over y}\)

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

b

\({x \over 8} ⋅ {5 \over y} = {5 x \over 8 y}\)

1p

1p

c

\({1 \over 8} ⋅ a\)

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

c

\({1 \over 8} ⋅ a = {a \over 8}\)

1p

1p

d

\({3 \over p} : {2 \over q}\)

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

d

\({3 \over p} : {2 \over q} = {3 \over p} ⋅ {q \over 2} = {3 q \over 2 p}\)

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

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