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 \({4 \over 2 p} + {3 \over 2 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 2 p} + {3 \over 2 p} = {7 \over 2 p}\) 1p 1p b \({6 \over x} + {4 \over 5 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({6 \over x} + {4 \over 5 x} = {30 \over 5 x} + {4 \over 5 x} = {34 \over 5 x}\) 1p 1p c \({7 \over 2 a} + {3 \over 6 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 2 a} + {3 \over 6 b} = {21 b \over 6 a b} + {3 a \over 6 a b} = {21 b + 3 a \over 6 a b} = {7 b + a \over 2 a b}\) 1p 1p d \(5 - {7 \over 9 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(5 - {7 \over 9 a} = {5 \over 1} - {7 \over 9 a} = {45 a \over 9 a} - {7 \over 9 a} = {45 a - 7 \over 9 a}\) 1p opgave 2 Herleid tot één breuk. 1p \({3 x \over y} - {6 \over 7 y}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({3 x \over y} - {6 \over 7 y} = {21 x \over 7 y} - {6 \over 7 y} = {21 x - 6 \over 7 y}\) 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 \({p \over 2 p}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({p \over 2 p} = {1 \over 2}\) 1p 1p c \({-10 x \over -14 x}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-10 x \over -14 x} = \frac{5}{7}\) 1p 1p d \({30 a \over 5 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({30 a \over 5 a} = 6\) 1p opgave 4 Herleid. 1p a \({24 x y \over -27 x z}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({24 x y \over -27 x z} = -{8 y \over 9 z}\) 1p 1p b \({16 y \over 18 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({16 y \over 18 x y} = {8 \over 9 x}\) 1p 1p c \({10 p q r \over -2 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({10 p q r \over -2 q r} = -5 p\) 1p 1p d \({4 a b \over b} + {6 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({4 a b \over b} + {6 a c \over c} = 4 a + 6 a = 10 a\) 1p

1 vwo

6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

\({4 \over 2 p} + {3 \over 2 p}\)

Optellen (1)

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

\({4 \over 2 p} + {3 \over 2 p} = {7 \over 2 p}\)

\({6 \over x} + {4 \over 5 x}\)

Optellen (2)

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

\({6 \over x} + {4 \over 5 x} = {30 \over 5 x} + {4 \over 5 x} = {34 \over 5 x}\)

\({7 \over 2 a} + {3 \over 6 b}\)

Optellen (3)

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

\({7 \over 2 a} + {3 \over 6 b} = {21 b \over 6 a b} + {3 a \over 6 a b} = {21 b + 3 a \over 6 a b} = {7 b + a \over 2 a b}\)

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

Optellen (4)

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

\(5 - {7 \over 9 a} = {5 \over 1} - {7 \over 9 a} = {45 a \over 9 a} - {7 \over 9 a} = {45 a - 7 \over 9 a}\)

opgave 2

Herleid tot één breuk.

\({3 x \over y} - {6 \over 7 y}\)

Optellen (6)

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

○

\({3 x \over y} - {6 \over 7 y} = {21 x \over 7 y} - {6 \over 7 y} = {21 x - 6 \over 7 y}\)

opgave 3

Herleid.

\({9 a \over a}\)

Vereenvoudigen (1)

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

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

\({p \over 2 p}\)

Vereenvoudigen (2)

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

\({p \over 2 p} = {1 \over 2}\)

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

Vereenvoudigen (3)

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

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

\({30 a \over 5 a}\)

Vereenvoudigen (4)

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

\({30 a \over 5 a} = 6\)

opgave 4

Herleid.

\({24 x y \over -27 x z}\)

Vereenvoudigen (5)

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

\({24 x y \over -27 x z} = -{8 y \over 9 z}\)

\({16 y \over 18 x y}\)

Vereenvoudigen (6)

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

\({16 y \over 18 x y} = {8 \over 9 x}\)

\({10 p q r \over -2 q r}\)

Vereenvoudigen (7)

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

\({10 p q r \over -2 q r} = -5 p\)

\({4 a b \over b} + {6 a c \over c}\)

Vereenvoudigen (8)

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

\({4 a b \over b} + {6 a c \over c} = 4 a + 6 a = 10 a\)