Getal & Ruimte (13e editie) - 1 vwo

'Breuken herleiden'.

1 vwo	6.6 Herleiden van breuken
Breuken herleiden (13)	opgave 1 Herleid tot één breuk. 1p a \({3 \over 5 a} - {9 \over 5 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 5 a} - {9 \over 5 a} = -{6 \over 5 a}\) 1p 1p b \({2 \over p} + {9 \over 4 p}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({2 \over p} + {9 \over 4 p} = {8 \over 4 p} + {9 \over 4 p} = {17 \over 4 p}\) 1p 1p c \({5 \over 3 x} + {8 \over 6 y}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({5 \over 3 x} + {8 \over 6 y} = {10 y \over 6 x y} + {8 x \over 6 x y} = {10 y + 8 x \over 6 x y} = {5 y + 4 x \over 3 x y}\) 1p 1p d \(2 + {5 \over 7 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(2 + {5 \over 7 x} = {2 \over 1} + {5 \over 7 x} = {14 x \over 7 x} + {5 \over 7 x} = {14 x + 5 \over 7 x}\) 1p opgave 2 Herleid tot één breuk. 1p \({4 a \over b} - {2 \over 5 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({4 a \over b} - {2 \over 5 b} = {20 a \over 5 b} - {2 \over 5 b} = {20 a - 2 \over 5 b}\) 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 \({p \over 8 p}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 8 p} = {1 \over 8}\) 1p 1p c \({4 a \over 10 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({4 a \over 10 a} = \frac{2}{5}\) 1p 1p d \({-12 a \over -4 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-12 a \over -4 a} = 3\) 1p opgave 4 Herleid. 1p a \({-6 x y \over -10 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-6 x y \over -10 x z} = {3 y \over 5 z}\) 1p 1p b \({-4 y \over 6 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-4 y \over 6 x y} = -{2 \over 3 x}\) 1p 1p c \({-15 a b c \over -5 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-15 a b c \over -5 b c} = 3 a\) 1p 1p d \({7 x y \over y} - {6 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 x y \over y} - {6 x z \over z} = 7 x - 6 x = x\) 1p

1 vwo

6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

\({3 \over 5 a} - {9 \over 5 a}\)

Optellen (1)

008u - Breuken herleiden - basis - 0ms - dynamic variables

\({3 \over 5 a} - {9 \over 5 a} = -{6 \over 5 a}\)

\({2 \over p} + {9 \over 4 p}\)

Optellen (2)

008v - Breuken herleiden - basis - 0ms - dynamic variables

\({2 \over p} + {9 \over 4 p} = {8 \over 4 p} + {9 \over 4 p} = {17 \over 4 p}\)

\({5 \over 3 x} + {8 \over 6 y}\)

Optellen (3)

008w - Breuken herleiden - basis - 0ms - dynamic variables

\({5 \over 3 x} + {8 \over 6 y} = {10 y \over 6 x y} + {8 x \over 6 x y} = {10 y + 8 x \over 6 x y} = {5 y + 4 x \over 3 x y}\)

\(2 + {5 \over 7 x}\)

Optellen (4)

008x - Breuken herleiden - basis - 0ms - dynamic variables

\(2 + {5 \over 7 x} = {2 \over 1} + {5 \over 7 x} = {14 x \over 7 x} + {5 \over 7 x} = {14 x + 5 \over 7 x}\)

opgave 2

Herleid tot één breuk.

\({4 a \over b} - {2 \over 5 b}\)

Optellen (6)

008z - Breuken herleiden - basis - 0ms - dynamic variables

○

\({4 a \over b} - {2 \over 5 b} = {20 a \over 5 b} - {2 \over 5 b} = {20 a - 2 \over 5 b}\)

opgave 3

Herleid.

\({3 x \over x}\)

Vereenvoudigen (1)

00h5 - Breuken herleiden - basis - 0ms - dynamic variables

\({3 x \over x} = {3 \over 1} = 3\)

\({p \over 8 p}\)

Vereenvoudigen (2)

00h6 - Breuken herleiden - basis - 0ms - dynamic variables

\({p \over 8 p} = {1 \over 8}\)

\({4 a \over 10 a}\)

Vereenvoudigen (3)

00h7 - Breuken herleiden - basis - 0ms - dynamic variables

\({4 a \over 10 a} = \frac{2}{5}\)

\({-12 a \over -4 a}\)

Vereenvoudigen (4)

00h8 - Breuken herleiden - basis - 0ms - dynamic variables

\({-12 a \over -4 a} = 3\)

opgave 4

Herleid.

\({-6 x y \over -10 x z}\)

Vereenvoudigen (5)

00h9 - Breuken herleiden - basis - 0ms - dynamic variables

\({-6 x y \over -10 x z} = {3 y \over 5 z}\)

\({-4 y \over 6 x y}\)

Vereenvoudigen (6)

00ha - Breuken herleiden - basis - 0ms - dynamic variables

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

\({-15 a b c \over -5 b c}\)

Vereenvoudigen (7)

00hb - Breuken herleiden - basis - 0ms - dynamic variables

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

\({7 x y \over y} - {6 x z \over z}\)

Vereenvoudigen (8)

00hc - Breuken herleiden - basis - 0ms - dynamic variables

\({7 x y \over y} - {6 x z \over z} = 7 x - 6 x = x\)