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 \({3 \over 4 a} + {9 \over 4 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({3 \over 4 a} + {9 \over 4 a} = {12 \over 4 a} = {3 \over a}\) 1p 1p b \({3 \over a} - {4 \over 7 a}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({3 \over a} - {4 \over 7 a} = {21 \over 7 a} - {4 \over 7 a} = {17 \over 7 a}\) 1p 1p c \({7 \over 8 p} - {2 \over 5 q}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 8 p} - {2 \over 5 q} = {35 q \over 40 p q} - {16 p \over 40 p q} = {35 q - 16 p \over 40 p q}\) 1p 1p d \(2 - {5 \over 3 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(2 - {5 \over 3 x} = {2 \over 1} - {5 \over 3 x} = {6 x \over 3 x} - {5 \over 3 x} = {6 x - 5 \over 3 x}\) 1p opgave 2 Herleid tot één breuk. 1p \({3 x \over y} - {2 \over 4 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({3 x \over y} - {2 \over 4 y} = {12 x \over 4 y} - {2 \over 4 y} = {12 x - 2 \over 4 y} = {6 x - 1 \over 2 y}\) 1p opgave 3 Herleid. 1p a \({8 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({8 a \over a} = {8 \over 1} = 8\) 1p 1p b \({x \over 4 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 4 x} = {1 \over 4}\) 1p 1p c \({8 p \over 10 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({8 p \over 10 p} = \frac{4}{5}\) 1p 1p d \({-32 x \over 4 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-32 x \over 4 x} = -8\) 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 \({10 y \over 14 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({10 y \over 14 x y} = {5 \over 7 x}\) 1p 1p c \({-27 p q r \over 3 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-27 p q r \over 3 q r} = -9 p\) 1p 1p d \({7 x y \over y} + {3 x z \over z}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({7 x y \over y} + {3 x z \over z} = 7 x + 3 x = 10 x\) 1p

1 vwo

6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

\({3 \over 4 a} + {9 \over 4 a}\)

Optellen (1)

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

\({3 \over 4 a} + {9 \over 4 a} = {12 \over 4 a} = {3 \over a}\)

\({3 \over a} - {4 \over 7 a}\)

Optellen (2)

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

\({3 \over a} - {4 \over 7 a} = {21 \over 7 a} - {4 \over 7 a} = {17 \over 7 a}\)

\({7 \over 8 p} - {2 \over 5 q}\)

Optellen (3)

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

\({7 \over 8 p} - {2 \over 5 q} = {35 q \over 40 p q} - {16 p \over 40 p q} = {35 q - 16 p \over 40 p q}\)

\(2 - {5 \over 3 x}\)

Optellen (4)

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

\(2 - {5 \over 3 x} = {2 \over 1} - {5 \over 3 x} = {6 x \over 3 x} - {5 \over 3 x} = {6 x - 5 \over 3 x}\)

opgave 2

Herleid tot één breuk.

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

Optellen (6)

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

○

\({3 x \over y} - {2 \over 4 y} = {12 x \over 4 y} - {2 \over 4 y} = {12 x - 2 \over 4 y} = {6 x - 1 \over 2 y}\)

opgave 3

Herleid.

\({8 a \over a}\)

Vereenvoudigen (1)

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

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

\({x \over 4 x}\)

Vereenvoudigen (2)

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

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

\({8 p \over 10 p}\)

Vereenvoudigen (3)

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

\({8 p \over 10 p} = \frac{4}{5}\)

\({-32 x \over 4 x}\)

Vereenvoudigen (4)

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

\({-32 x \over 4 x} = -8\)

opgave 4

Herleid.

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

Vereenvoudigen (5)

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

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

\({10 y \over 14 x y}\)

Vereenvoudigen (6)

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

\({10 y \over 14 x y} = {5 \over 7 x}\)

\({-27 p q r \over 3 q r}\)

Vereenvoudigen (7)

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

\({-27 p q r \over 3 q r} = -9 p\)

\({7 x y \over y} + {3 x z \over z}\)

Vereenvoudigen (8)

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

\({7 x y \over y} + {3 x z \over z} = 7 x + 3 x = 10 x\)