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

\({7 \over 4 x} - {5 \over 4 x}\)

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

a

\({7 \over 4 x} - {5 \over 4 x} = {2 \over 4 x} = {1 \over 2 x}\)

1p

1p

b

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

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

b

\({8 \over a} - {4 \over 9 a} = {72 \over 9 a} - {4 \over 9 a} = {68 \over 9 a}\)

1p

1p

c

\({7 \over 5 p} + {9 \over 6 q}\)

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

c

\({7 \over 5 p} + {9 \over 6 q} = {42 q \over 30 p q} + {45 p \over 30 p q} = {42 q + 45 p \over 30 p q} = {14 q + 15 p \over 10 p q}\)

1p

1p

d

\(3 - {8 \over 9 x}\)

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

d

\(3 - {8 \over 9 x} = {3 \over 1} - {8 \over 9 x} = {27 x \over 9 x} - {8 \over 9 x} = {27 x - 8 \over 9 x}\)

1p

opgave 2

Herleid tot één breuk.

1p

a

\(6 a - {4 \over 9 a}\)

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

a

\(6 a - {4 \over 9 a} = {6 a \over 1} ⋅ {9 a \over 9 a} - {4 \over 9 a} = {54 a^{2} \over 9 a} - {4 \over 9 a} = {54 a^{2} - 4 \over 9 a}\)

1p

1p

b

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

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

b

\({5 a \over b} + {7 \over 6 b} = {30 a \over 6 b} + {7 \over 6 b} = {30 a + 7 \over 6 b}\)

1p

1p

c

\({2 b \over 9 a} - {7 a \over 8 b}\)

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

c

\({2 b \over 9 a} - {7 a \over 8 b} = {16 b^{2} \over 72 a b} - {63 a^{2} \over 72 a b} = {-63 a^{2} + 16 b^{2} \over 72 a b}\)

1p

opgave 3

Herleid.

1p

a

\({9 p \over p}\)

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

a

\({9 p \over p} = {9 \over 1} = 9\)

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

\({-12 x \over -28 x}\)

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

c

\({-12 x \over -28 x} = \frac{3}{7}\)

1p

1p

d

\({20 x \over -5 x}\)

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

d

\({20 x \over -5 x} = -4\)

1p

opgave 4

Herleid.

1p

a

\({-20 x y \over -25 x z}\)

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

a

\({-20 x y \over -25 x z} = {4 y \over 5 z}\)

1p

1p

b

\({-4 b \over -14 a b}\)

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

b

\({-4 b \over -14 a b} = {2 \over 7 a}\)

1p

1p

c

\({-35 p q r \over -5 q r}\)

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

c

\({-35 p q r \over -5 q r} = 7 p\)

1p

1p

d

\({6 a b \over b} - {5 a c \over c}\)

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

d

\({6 a b \over b} - {5 a c \over c} = 6 a - 5 a = a\)

1p

2 havo/vwo 1.3 Breuken vermenigvuldigen en delen

Breuken herleiden (5)

opgave 1

Herleid tot één breuk.

1p

a

\({3 \over a} ⋅ -{5 \over b}\)

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

a

\({3 \over a} ⋅ -{5 \over b} = -{15 \over a b}\)

1p

1p

b

\({x \over 8} ⋅ -{7 \over y}\)

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

b

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

1p

1p

c

\({1 \over 5} ⋅ x\)

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

c

\({1 \over 5} ⋅ x = {x \over 5}\)

1p

1p

d

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

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

d

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

1p

opgave 2

Herleid tot één breuk.

1p

\({7 \over 4} : a\)

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

○

\({7 \over 4} : a = {7 \over 4} : {a \over 1} = {7 \over 4} ⋅ {1 \over a} = {7 \over 4 a}\)

1p

3 havo 5.2 Breuken met letters herleiden

Breuken herleiden (1)

opgave 1

Herleid tot één breuk.

1p

\({7 p \over 3} + {p + 6 \over 5}\)

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

○

\({7 p \over 3} + {p + 6 \over 5} = {35 p \over 15} + {3 (p + 6) \over 15} = {35 p + 3 (p + 6) \over 15} = {38 p + 18 \over 15}\)

1p

"