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

\({3 \over 4 p} + {5 \over 4 p}\)

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

a

\({3 \over 4 p} + {5 \over 4 p} = {8 \over 4 p} = {2 \over p}\)

1p

1p

b

\({6 \over x} - {5 \over 8 x}\)

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

b

\({6 \over x} - {5 \over 8 x} = {48 \over 8 x} - {5 \over 8 x} = {43 \over 8 x}\)

1p

1p

c

\({5 \over 7 x} + {8 \over 6 y}\)

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

c

\({5 \over 7 x} + {8 \over 6 y} = {30 y \over 42 x y} + {56 x \over 42 x y} = {30 y + 56 x \over 42 x y} = {15 y + 28 x \over 21 x y}\)

1p

1p

d

\(9 - {6 \over 5 a}\)

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

d

\(9 - {6 \over 5 a} = {9 \over 1} - {6 \over 5 a} = {45 a \over 5 a} - {6 \over 5 a} = {45 a - 6 \over 5 a}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

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

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

a

\(7 a - {9 \over 4 a} = {7 a \over 1} ⋅ {4 a \over 4 a} - {9 \over 4 a} = {28 a^{2} \over 4 a} - {9 \over 4 a} = {28 a^{2} - 9 \over 4 a}\)

1p

1p

b

\({3 p \over q} - {9 \over 7 q}\)

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

b

\({3 p \over q} - {9 \over 7 q} = {21 p \over 7 q} - {9 \over 7 q} = {21 p - 9 \over 7 q}\)

1p

1p

c

\({4 b \over 3 a} + {9 a \over 2 b}\)

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

c

\({4 b \over 3 a} + {9 a \over 2 b} = {8 b^{2} \over 6 a b} + {27 a^{2} \over 6 a b} = {27 a^{2} + 8 b^{2} \over 6 a b}\)

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

\({a \over 4 a}\)

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

b

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

1p

1p

c

\({-4 x \over 14 x}\)

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

c

\({-4 x \over 14 x} = -\frac{2}{7}\)

1p

1p

d

\({15 x \over -5 x}\)

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

d

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

1p

opgave 4

Herleid.

1p

a

\({-28 a b \over 32 a c}\)

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

a

\({-28 a b \over 32 a c} = -{7 b \over 8 c}\)

1p

1p

b

\({32 y \over -36 x y}\)

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

b

\({32 y \over -36 x y} = -{8 \over 9 x}\)

1p

1p

c

\({16 a b c \over -4 b c}\)

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

c

\({16 a b c \over -4 b c} = -4 a\)

1p

1p

d

\({7 p q \over q} - {4 p r \over r}\)

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

d

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

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({5 \over x} ⋅ -{3 \over y}\)

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

a

\({5 \over x} ⋅ -{3 \over y} = -{15 \over x y}\)

1p

1p

b

\({a \over 9} ⋅ {6 \over b}\)

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

b

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

1p

1p

c

\({8 \over 3} ⋅ x\)

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

c

\({8 \over 3} ⋅ x = {8 x \over 3}\)

1p

1p

d

\({9 \over p} : {6 \over q}\)

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

d

\({9 \over p} : {6 \over q} = {9 \over p} ⋅ {q \over 6} = {9 q \over 6 p} = {3 q \over 2 p}\)

1p

opgave 2

Herleid tot één breuk.

1p

\({7 \over 5} : a\)

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

○

\({7 \over 5} : a = {7 \over 5} : {a \over 1} = {7 \over 5} ⋅ {1 \over a} = {7 \over 5 a}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({p \over 7} + {p - 5 \over 3}\)

Optellen (8)
0098 - Breuken herleiden - basis - 0ms - dynamic variables

○

\({p \over 7} + {p - 5 \over 3} = {3 p \over 21} + {7 (p - 5) \over 21} = {3 p + 7 (p - 5) \over 21} = {10 p - 35 \over 21}\)

1p

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