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

\({9 \over 7 a} - {6 \over 7 a}\)

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

a

\({9 \over 7 a} - {6 \over 7 a} = {3 \over 7 a}\)

1p

1p

b

\({6 \over p} - {4 \over 5 p}\)

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

b

\({6 \over p} - {4 \over 5 p} = {30 \over 5 p} - {4 \over 5 p} = {26 \over 5 p}\)

1p

1p

c

\({9 \over 4 a} - {5 \over 8 b}\)

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

c

\({9 \over 4 a} - {5 \over 8 b} = {18 b \over 8 a b} - {5 a \over 8 a b} = {18 b - 5 a \over 8 a b}\)

1p

1p

d

\(5 - {4 \over 3 x}\)

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

d

\(5 - {4 \over 3 x} = {5 \over 1} - {4 \over 3 x} = {15 x \over 3 x} - {4 \over 3 x} = {15 x - 4 \over 3 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

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

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

a

\(5 x - {7 \over 6 x} = {5 x \over 1} ⋅ {6 x \over 6 x} - {7 \over 6 x} = {30 x^{2} \over 6 x} - {7 \over 6 x} = {30 x^{2} - 7 \over 6 x}\)

1p

1p

b

\({4 a \over b} - {5 \over 7 b}\)

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

b

\({4 a \over b} - {5 \over 7 b} = {28 a \over 7 b} - {5 \over 7 b} = {28 a - 5 \over 7 b}\)

1p

1p

c

\({9 b \over 3 a} - {7 a \over 2 b}\)

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

c

\({9 b \over 3 a} - {7 a \over 2 b} = {18 b^{2} \over 6 a b} - {21 a^{2} \over 6 a b} = {-21 a^{2} + 18 b^{2} \over 6 a b} = {-7 a^{2} + 6 b^{2} \over 2 a b}\)

1p

opgave 3

Herleid.

1p

a

\({4 p \over p}\)

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

a

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

1p

1p

b

\({x \over 6 x}\)

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

b

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

1p

1p

c

\({-25 x \over -40 x}\)

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

c

\({-25 x \over -40 x} = \frac{5}{8}\)

1p

1p

d

\({-30 x \over 5 x}\)

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

d

\({-30 x \over 5 x} = -6\)

1p

opgave 4

Herleid.

1p

a

\({-24 a b \over 28 a c}\)

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

a

\({-24 a b \over 28 a c} = -{6 b \over 7 c}\)

1p

1p

b

\({6 y \over 14 x y}\)

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

b

\({6 y \over 14 x y} = {3 \over 7 x}\)

1p

1p

c

\({20 a b c \over -5 b c}\)

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

c

\({20 a b c \over -5 b c} = -4 a\)

1p

1p

d

\({6 p q \over q} - {2 p r \over r}\)

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

d

\({6 p q \over q} - {2 p r \over r} = 6 p - 2 p = 4 p\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({2 \over x} ⋅ {4 \over y}\)

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

a

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

1p

1p

b

\({a \over 4} ⋅ -{6 \over b}\)

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

b

\({a \over 4} ⋅ -{6 \over b} = -{6 a \over 4 b} = -{3 a \over 2 b}\)

1p

1p

c

\(-{7 \over 4} ⋅ a\)

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

c

\(-{7 \over 4} ⋅ a = -{7 a \over 4}\)

1p

1p

d

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

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

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

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

\({3 \over 2} : p = {3 \over 2} : {p \over 1} = {3 \over 2} ⋅ {1 \over p} = {3 \over 2 p}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({5 x \over 8} + {x + 4 \over 7}\)

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

\({5 x \over 8} + {x + 4 \over 7} = {35 x \over 56} + {8 (x + 4) \over 56} = {35 x + 8 (x + 4) \over 56} = {43 x + 32 \over 56}\)

1p

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