Getal & Ruimte (13e editie) - havo wiskunde A

'Breuken herleiden'.

2 havo/vwo 1.2 Breuken optellen

Breuken herleiden (15)

opgave 1

Herleid tot één breuk.

1p

a

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

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

a

\({8 \over 3 x} - {2 \over 3 x} = {6 \over 3 x} = {2 \over x}\)

1p

1p

b

\({9 \over a} - {7 \over 5 a}\)

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

b

\({9 \over a} - {7 \over 5 a} = {45 \over 5 a} - {7 \over 5 a} = {38 \over 5 a}\)

1p

1p

c

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

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

c

\({2 \over 3 x} - {9 \over 6 y} = {4 y \over 6 x y} - {9 x \over 6 x y} = {4 y - 9 x \over 6 x y}\)

1p

1p

d

\(6 - {4 \over 3 p}\)

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

d

\(6 - {4 \over 3 p} = {6 \over 1} - {4 \over 3 p} = {18 p \over 3 p} - {4 \over 3 p} = {18 p - 4 \over 3 p}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

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

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

a

\(6 a - {5 \over 4 a} = {6 a \over 1} ⋅ {4 a \over 4 a} - {5 \over 4 a} = {24 a^{2} \over 4 a} - {5 \over 4 a} = {24 a^{2} - 5 \over 4 a}\)

1p

1p

b

\({7 p \over q} + {3 \over 8 q}\)

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

b

\({7 p \over q} + {3 \over 8 q} = {56 p \over 8 q} + {3 \over 8 q} = {56 p + 3 \over 8 q}\)

1p

1p

c

\({9 y \over 5 x} + {3 x \over 8 y}\)

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

c

\({9 y \over 5 x} + {3 x \over 8 y} = {72 y^{2} \over 40 x y} + {15 x^{2} \over 40 x y} = {15 x^{2} + 72 y^{2} \over 40 x y}\)

1p

opgave 3

Herleid.

1p

a

\({6 x \over x}\)

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

a

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

1p

1p

b

\({a \over 6 a}\)

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

b

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

1p

1p

c

\({4 a \over -6 a}\)

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

c

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

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

\({16 p q \over 28 p r}\)

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

a

\({16 p q \over 28 p r} = {4 q \over 7 r}\)

1p

1p

b

\({-12 y \over 16 x y}\)

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

b

\({-12 y \over 16 x y} = -{3 \over 4 x}\)

1p

1p

c

\({-6 a b c \over -3 b c}\)

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

c

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

1p

1p

d

\({2 a b \over b} + {7 a c \over c}\)

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

d

\({2 a b \over b} + {7 a c \over c} = 2 a + 7 a = 9 a\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({2 \over a} ⋅ -{3 \over b}\)

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

a

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

1p

1p

b

\({p \over 6} ⋅ {2 \over q}\)

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

b

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

1p

1p

c

\(-{1 \over 7} ⋅ x\)

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

c

\(-{1 \over 7} ⋅ x = -{x \over 7}\)

1p

1p

d

\({9 \over x} : {2 \over y}\)

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

\(-{8 \over 7} : a\)

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

○

\(-{8 \over 7} : a = -{8 \over 7} : {a \over 1} = -{8 \over 7} ⋅ {1 \over a} = -{8 \over 7 a}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({5 a \over 2} + {a + 7 \over 9}\)

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

○

\({5 a \over 2} + {a + 7 \over 9} = {45 a \over 18} + {2 (a + 7) \over 18} = {45 a + 2 (a + 7) \over 18} = {47 a + 14 \over 18}\)

1p

havo wiskunde A 6.2 Formules met breuken

Breuken herleiden (2)

opgave 1

Herleid tot één breuk.

1p

a

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

Deling (3)
0097 - Breuken herleiden - basis - 0ms - dynamic variables

a

\({8 \over 7} : {a + 6 b \over b} = {8 \over 7} ⋅ {b \over a + 6 b} = {8 b \over 7 (a + 6 b)} = {8 b \over 7 a + 42 b}\)

1p

1p

b

\({-4 p + 7 \over -5 p - 3} + 2\)

Optellen (9)
00eh - Breuken herleiden - basis - 0ms - dynamic variables

b

\({-4 p + 7 \over -5 p - 3} + 2 = {-4 p + 7 \over -5 p - 3} - {-2 (-5 p - 3) \over -5 p - 3} = {-4 p + 7 + 2 (-5 p - 3) \over -5 p - 3} = {-4 p + 7 - 10 p - 6 \over -5 p - 3} = {-14 p + 1 \over -5 p - 3}\)

1p

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