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 \({6 \over 7 a} + {5 \over 7 a}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({6 \over 7 a} + {5 \over 7 a} = {11 \over 7 a}\) 1p 1p b \({7 \over x} - {8 \over 3 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({7 \over x} - {8 \over 3 x} = {21 \over 3 x} - {8 \over 3 x} = {13 \over 3 x}\) 1p 1p c \({6 \over 3 a} + {4 \over 8 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 3 a} + {4 \over 8 b} = {48 b \over 24 a b} + {12 a \over 24 a b} = {48 b + 12 a \over 24 a b} = {4 b + a \over 2 a b}\) 1p 1p d \(7 - {9 \over 8 p}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(7 - {9 \over 8 p} = {7 \over 1} - {9 \over 8 p} = {56 p \over 8 p} - {9 \over 8 p} = {56 p - 9 \over 8 p}\) 1p opgave 2 Herleid tot één breuk. 1p \({2 x \over y} + {7 \over 6 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({2 x \over y} + {7 \over 6 y} = {12 x \over 6 y} + {7 \over 6 y} = {12 x + 7 \over 6 y}\) 1p opgave 3 Herleid. 1p a \({9 a \over a}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({9 a \over a} = {9 \over 1} = 9\) 1p 1p b \({p \over 7 p}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 7 p} = {1 \over 7}\) 1p 1p c \({6 x \over 15 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({6 x \over 15 x} = \frac{2}{5}\) 1p 1p d \({-9 a \over 3 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-9 a \over 3 a} = -3\) 1p opgave 4 Herleid. 1p a \({12 x y \over 27 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({12 x y \over 27 x z} = {4 y \over 9 z}\) 1p 1p b \({25 y \over 40 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({25 y \over 40 x y} = {5 \over 8 x}\) 1p 1p c \({6 a b c \over -2 b c}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({6 a b c \over -2 b c} = -3 a\) 1p 1p d \({4 p q \over q} - {7 p r \over r}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({4 p q \over q} - {7 p r \over r} = 4 p - 7 p = -3 p\) 1p

1 vwo

6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

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

Optellen (1)

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

\({6 \over 7 a} + {5 \over 7 a} = {11 \over 7 a}\)

\({7 \over x} - {8 \over 3 x}\)

Optellen (2)

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

\({7 \over x} - {8 \over 3 x} = {21 \over 3 x} - {8 \over 3 x} = {13 \over 3 x}\)

\({6 \over 3 a} + {4 \over 8 b}\)

Optellen (3)

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

\({6 \over 3 a} + {4 \over 8 b} = {48 b \over 24 a b} + {12 a \over 24 a b} = {48 b + 12 a \over 24 a b} = {4 b + a \over 2 a b}\)

\(7 - {9 \over 8 p}\)

Optellen (4)

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

\(7 - {9 \over 8 p} = {7 \over 1} - {9 \over 8 p} = {56 p \over 8 p} - {9 \over 8 p} = {56 p - 9 \over 8 p}\)

opgave 2

Herleid tot één breuk.

\({2 x \over y} + {7 \over 6 y}\)

Optellen (6)

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

○

\({2 x \over y} + {7 \over 6 y} = {12 x \over 6 y} + {7 \over 6 y} = {12 x + 7 \over 6 y}\)

opgave 3

Herleid.

\({9 a \over a}\)

Vereenvoudigen (1)

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

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

\({p \over 7 p}\)

Vereenvoudigen (2)

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

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

\({6 x \over 15 x}\)

Vereenvoudigen (3)

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

\({6 x \over 15 x} = \frac{2}{5}\)

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

Vereenvoudigen (4)

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

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

opgave 4

Herleid.

\({12 x y \over 27 x z}\)

Vereenvoudigen (5)

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

\({12 x y \over 27 x z} = {4 y \over 9 z}\)

\({25 y \over 40 x y}\)

Vereenvoudigen (6)

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

\({25 y \over 40 x y} = {5 \over 8 x}\)

\({6 a b c \over -2 b c}\)

Vereenvoudigen (7)

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

\({6 a b c \over -2 b c} = -3 a\)

\({4 p q \over q} - {7 p r \over r}\)

Vereenvoudigen (8)

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

\({4 p q \over q} - {7 p r \over r} = 4 p - 7 p = -3 p\)