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 \({6 \over 7 p} - {3 \over 7 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({6 \over 7 p} - {3 \over 7 p} = {3 \over 7 p}\) 1p 1p b \({5 \over a} + {8 \over 2 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({5 \over a} + {8 \over 2 a} = {10 \over 2 a} + {8 \over 2 a} = {18 \over 2 a} = {9 \over a}\) 1p 1p c \({7 \over 9 a} - {6 \over 5 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 9 a} - {6 \over 5 b} = {35 b \over 45 a b} - {54 a \over 45 a b} = {35 b - 54 a \over 45 a b}\) 1p 1p d \(8 + {5 \over 6 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(8 + {5 \over 6 x} = {8 \over 1} + {5 \over 6 x} = {48 x \over 6 x} + {5 \over 6 x} = {48 x + 5 \over 6 x}\) 1p opgave 2 Herleid tot één breuk. 1p \({5 x \over y} + {7 \over 9 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({5 x \over y} + {7 \over 9 y} = {45 x \over 9 y} + {7 \over 9 y} = {45 x + 7 \over 9 y}\) 1p opgave 3 Herleid. 1p a \({4 p \over p}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({4 p \over p} = {4 \over 1} = 4\) 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 \({10 a \over 35 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({10 a \over 35 a} = \frac{2}{7}\) 1p 1p d \({20 x \over -4 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({20 x \over -4 x} = -5\) 1p opgave 4 Herleid. 1p a \({-40 a b \over 45 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({-40 a b \over 45 a c} = -{8 b \over 9 c}\) 1p 1p b \({14 b \over -18 a b}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({14 b \over -18 a b} = -{7 \over 9 a}\) 1p 1p c \({15 p q r \over 5 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({15 p q r \over 5 q r} = 3 p\) 1p 1p d \({2 x y \over y} - {5 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({2 x y \over y} - {5 x z \over z} = 2 x - 5 x = -3 x\) 1p

1 vwo

6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

\({6 \over 7 p} - {3 \over 7 p}\)

Optellen (1)

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

\({6 \over 7 p} - {3 \over 7 p} = {3 \over 7 p}\)

\({5 \over a} + {8 \over 2 a}\)

Optellen (2)

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

\({5 \over a} + {8 \over 2 a} = {10 \over 2 a} + {8 \over 2 a} = {18 \over 2 a} = {9 \over a}\)

\({7 \over 9 a} - {6 \over 5 b}\)

Optellen (3)

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

\({7 \over 9 a} - {6 \over 5 b} = {35 b \over 45 a b} - {54 a \over 45 a b} = {35 b - 54 a \over 45 a b}\)

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

Optellen (4)

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

\(8 + {5 \over 6 x} = {8 \over 1} + {5 \over 6 x} = {48 x \over 6 x} + {5 \over 6 x} = {48 x + 5 \over 6 x}\)

opgave 2

Herleid tot één breuk.

\({5 x \over y} + {7 \over 9 y}\)

Optellen (6)

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

○

\({5 x \over y} + {7 \over 9 y} = {45 x \over 9 y} + {7 \over 9 y} = {45 x + 7 \over 9 y}\)

opgave 3

Herleid.

\({4 p \over p}\)

Vereenvoudigen (1)

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

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

\({x \over 7 x}\)

Vereenvoudigen (2)

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

\({x \over 7 x} = {1 \over 7}\)

\({10 a \over 35 a}\)

Vereenvoudigen (3)

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

\({10 a \over 35 a} = \frac{2}{7}\)

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

Vereenvoudigen (4)

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

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

opgave 4

Herleid.

\({-40 a b \over 45 a c}\)

Vereenvoudigen (5)

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

\({-40 a b \over 45 a c} = -{8 b \over 9 c}\)

\({14 b \over -18 a b}\)

Vereenvoudigen (6)

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

\({14 b \over -18 a b} = -{7 \over 9 a}\)

\({15 p q r \over 5 q r}\)

Vereenvoudigen (7)

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

\({15 p q r \over 5 q r} = 3 p\)

\({2 x y \over y} - {5 x z \over z}\)

Vereenvoudigen (8)

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

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