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 \({2 \over 9 x} + {6 \over 9 x}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({2 \over 9 x} + {6 \over 9 x} = {8 \over 9 x}\) 1p 1p b \({9 \over x} - {6 \over 8 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({9 \over x} - {6 \over 8 x} = {72 \over 8 x} - {6 \over 8 x} = {66 \over 8 x} = {33 \over 4 x}\) 1p 1p c \({6 \over 4 p} + {7 \over 8 q}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({6 \over 4 p} + {7 \over 8 q} = {12 q \over 8 p q} + {7 p \over 8 p q} = {12 q + 7 p \over 8 p q}\) 1p 1p d \(7 - {5 \over 3 a}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(7 - {5 \over 3 a} = {7 \over 1} - {5 \over 3 a} = {21 a \over 3 a} - {5 \over 3 a} = {21 a - 5 \over 3 a}\) 1p opgave 2 Herleid tot één breuk. 1p \({6 a \over b} + {5 \over 2 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({6 a \over b} + {5 \over 2 b} = {12 a \over 2 b} + {5 \over 2 b} = {12 a + 5 \over 2 b}\) 1p opgave 3 Herleid. 1p a \({5 x \over x}\) Vereenvoudigen (1) 00h5 - Breuken herleiden - basis - 0ms - dynamic variables a \({5 x \over x} = {5 \over 1} = 5\) 1p 1p b \({x \over 3 x}\) Vereenvoudigen (2) 00h6 - Breuken herleiden - basis - 0ms - dynamic variables b \({x \over 3 x} = {1 \over 3}\) 1p 1p c \({15 a \over -24 a}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({15 a \over -24 a} = -\frac{5}{8}\) 1p 1p d \({12 a \over 2 a}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({12 a \over 2 a} = 6\) 1p opgave 4 Herleid. 1p a \({12 p q \over 20 p r}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({12 p q \over 20 p r} = {3 q \over 5 r}\) 1p 1p b \({-10 y \over -15 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-10 y \over -15 x y} = {2 \over 3 x}\) 1p 1p c \({27 x y z \over -3 y z}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({27 x y z \over -3 y z} = -9 x\) 1p 1p d \({6 p q \over q} + {7 p r \over r}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({6 p q \over q} + {7 p r \over r} = 6 p + 7 p = 13 p\) 1p

1 vwo

6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

\({2 \over 9 x} + {6 \over 9 x}\)

Optellen (1)

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

\({2 \over 9 x} + {6 \over 9 x} = {8 \over 9 x}\)

\({9 \over x} - {6 \over 8 x}\)

Optellen (2)

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

\({9 \over x} - {6 \over 8 x} = {72 \over 8 x} - {6 \over 8 x} = {66 \over 8 x} = {33 \over 4 x}\)

\({6 \over 4 p} + {7 \over 8 q}\)

Optellen (3)

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

\({6 \over 4 p} + {7 \over 8 q} = {12 q \over 8 p q} + {7 p \over 8 p q} = {12 q + 7 p \over 8 p q}\)

\(7 - {5 \over 3 a}\)

Optellen (4)

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

\(7 - {5 \over 3 a} = {7 \over 1} - {5 \over 3 a} = {21 a \over 3 a} - {5 \over 3 a} = {21 a - 5 \over 3 a}\)

opgave 2

Herleid tot één breuk.

\({6 a \over b} + {5 \over 2 b}\)

Optellen (6)

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

○

\({6 a \over b} + {5 \over 2 b} = {12 a \over 2 b} + {5 \over 2 b} = {12 a + 5 \over 2 b}\)

opgave 3

Herleid.

\({5 x \over x}\)

Vereenvoudigen (1)

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

\({5 x \over x} = {5 \over 1} = 5\)

\({x \over 3 x}\)

Vereenvoudigen (2)

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

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

\({15 a \over -24 a}\)

Vereenvoudigen (3)

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

\({15 a \over -24 a} = -\frac{5}{8}\)

\({12 a \over 2 a}\)

Vereenvoudigen (4)

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

\({12 a \over 2 a} = 6\)

opgave 4

Herleid.

\({12 p q \over 20 p r}\)

Vereenvoudigen (5)

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

\({12 p q \over 20 p r} = {3 q \over 5 r}\)

\({-10 y \over -15 x y}\)

Vereenvoudigen (6)

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

\({-10 y \over -15 x y} = {2 \over 3 x}\)

\({27 x y z \over -3 y z}\)

Vereenvoudigen (7)

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

\({27 x y z \over -3 y z} = -9 x\)

\({6 p q \over q} + {7 p r \over r}\)

Vereenvoudigen (8)

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

\({6 p q \over q} + {7 p r \over r} = 6 p + 7 p = 13 p\)