Getal & Ruimte (12e editie) - havo wiskunde A

'Breuken herleiden'.

2 havo/vwo 1.2 Breuken optellen

Breuken herleiden (15)

opgave 1

Herleid tot één breuk.

1p

a

\({8 \over 2 x} + {9 \over 2 x}\)

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

a

\({8 \over 2 x} + {9 \over 2 x} = {17 \over 2 x}\)

1p

1p

b

\({9 \over x} - {5 \over 2 x}\)

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

b

\({9 \over x} - {5 \over 2 x} = {18 \over 2 x} - {5 \over 2 x} = {13 \over 2 x}\)

1p

1p

c

\({2 \over 7 a} - {5 \over 3 b}\)

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

c

\({2 \over 7 a} - {5 \over 3 b} = {6 b \over 21 a b} - {35 a \over 21 a b} = {6 b - 35 a \over 21 a b}\)

1p

1p

d

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

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

d

\(7 - {5 \over 6 p} = {7 \over 1} - {5 \over 6 p} = {42 p \over 6 p} - {5 \over 6 p} = {42 p - 5 \over 6 p}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(5 a + {7 \over 6 a}\)

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

a

\(5 a + {7 \over 6 a} = {5 a \over 1} ⋅ {6 a \over 6 a} + {7 \over 6 a} = {30 a^{2} \over 6 a} + {7 \over 6 a} = {30 a^{2} + 7 \over 6 a}\)

1p

1p

b

\({7 x \over y} - {9 \over 2 y}\)

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

b

\({7 x \over y} - {9 \over 2 y} = {14 x \over 2 y} - {9 \over 2 y} = {14 x - 9 \over 2 y}\)

1p

1p

c

\({7 b \over 2 a} - {5 a \over 3 b}\)

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

c

\({7 b \over 2 a} - {5 a \over 3 b} = {21 b^{2} \over 6 a b} - {10 a^{2} \over 6 a b} = {-10 a^{2} + 21 b^{2} \over 6 a b}\)

1p

opgave 3

Herleid.

1p

a

\({6 a \over a}\)

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

a

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

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

\({-8 p \over -20 p}\)

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

c

\({-8 p \over -20 p} = \frac{2}{5}\)

1p

1p

d

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

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

d

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

1p

opgave 4

Herleid.

1p

a

\({-8 a b \over -20 a c}\)

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

a

\({-8 a b \over -20 a c} = {2 b \over 5 c}\)

1p

1p

b

\({6 y \over -27 x y}\)

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

b

\({6 y \over -27 x y} = -{2 \over 9 x}\)

1p

1p

c

\({45 a b c \over 5 b c}\)

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

c

\({45 a b c \over 5 b c} = 9 a\)

1p

1p

d

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

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

d

\({3 x y \over y} + {2 x z \over z} = 3 x + 2 x = 5 x\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({8 \over a} ⋅ {2 \over b}\)

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

a

\({8 \over a} ⋅ {2 \over b} = {16 \over a b}\)

1p

1p

b

\({p \over 4} ⋅ -{5 \over q}\)

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

b

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

1p

1p

c

\({4 \over 9} ⋅ a\)

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

c

\({4 \over 9} ⋅ a = {4 a \over 9}\)

1p

1p

d

\({8 \over x} : {5 \over y}\)

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

\({5 \over 3} : x\)

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

\({5 \over 3} : x = {5 \over 3} : {x \over 1} = {5 \over 3} ⋅ {1 \over x} = {5 \over 3 x}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({7 x \over 3} + {x + 5 \over 4}\)

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

\({7 x \over 3} + {x + 5 \over 4} = {28 x \over 12} + {3 (x + 5) \over 12} = {28 x + 3 (x + 5) \over 12} = {31 x + 15 \over 12}\)

1p

havo wiskunde A 6.3 Formules met breuken

Breuken herleiden (2)

opgave 1

Herleid tot één breuk.

1p

a

\({9 q \over p} ⋅ {p - 5 \over 8}\)

Vermenigvuldiging (4)
0094 - Breuken herleiden - basis - 0ms - dynamic variables

a

\({9 q \over p} ⋅ {p - 5 \over 8} = {9 q (p - 5) \over 8 p} = {9 p q - 45 q \over 8 p}\)

1p

1p

b

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

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

b

\(-{6 \over 5} : {a + 2 b \over b} = -{6 \over 5} ⋅ {b \over a + 2 b} = -{6 b \over 5 (a + 2 b)} = -{6 b \over 5 a + 10 b}\)

1p

havo wiskunde A 11.2 Herleiden en combineren van formules

Breuken herleiden (2)

opgave 1

Deel uit.

1p

a

\({6 a^{2} + 9 a + 30 \over 3 a}\)

Uitdelen (1)
00ei - Breuken herleiden - basis - 0ms - dynamic variables

a

\({6 a^{2} + 9 a + 30 \over 3 a} = {6 a^{2} \over 3 a} + {9 a \over 3 a} + {30 \over 3 a} = 2 a + 3 + {10 \over a}\)

1p

1p

b

\({7 x^{2} + 5 x + 9 \over 4 x^{2}}\)

Uitdelen (2)
00ej - Breuken herleiden - basis - 0ms - dynamic variables

b

\({7 x^{2} + 5 x + 9 \over 4 x^{2}} = {7 x^{2} \over 4 x^{2}} + {5 x \over 4 x^{2}} + {9 \over 4 x^{2}} = 1\frac{3}{4} + {5 \over 4 x} + {9 \over 4 x^{2}}\)

1p

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