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 \({4 \over 7 p} + {6 \over 7 p}\) Optellen (1) 008u - Breuken herleiden - basis - 0ms - dynamic variables a \({4 \over 7 p} + {6 \over 7 p} = {10 \over 7 p}\) 1p 1p b \({2 \over x} + {6 \over 3 x}\) Optellen (2) 008v - Breuken herleiden - basis - 0ms - dynamic variables b \({2 \over x} + {6 \over 3 x} = {6 \over 3 x} + {6 \over 3 x} = {12 \over 3 x} = {4 \over x}\) 1p 1p c \({7 \over 9 a} - {3 \over 5 b}\) Optellen (3) 008w - Breuken herleiden - basis - 0ms - dynamic variables c \({7 \over 9 a} - {3 \over 5 b} = {35 b \over 45 a b} - {27 a \over 45 a b} = {35 b - 27 a \over 45 a b}\) 1p 1p d \(5 + {8 \over 3 x}\) Optellen (4) 008x - Breuken herleiden - basis - 0ms - dynamic variables d \(5 + {8 \over 3 x} = {5 \over 1} + {8 \over 3 x} = {15 x \over 3 x} + {8 \over 3 x} = {15 x + 8 \over 3 x}\) 1p opgave 2 Herleid tot één breuk. 1p \({8 a \over b} + {9 \over 5 b}\) Optellen (6) 008z - Breuken herleiden - basis - 0ms - dynamic variables ○ \({8 a \over b} + {9 \over 5 b} = {40 a \over 5 b} + {9 \over 5 b} = {40 a + 9 \over 5 b}\) 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 \({-12 p \over 27 p}\) Vereenvoudigen (3) 00h7 - Breuken herleiden - basis - 0ms - dynamic variables c \({-12 p \over 27 p} = -\frac{4}{9}\) 1p 1p d \({-4 x \over -2 x}\) Vereenvoudigen (4) 00h8 - Breuken herleiden - basis - 0ms - dynamic variables d \({-4 x \over -2 x} = 2\) 1p opgave 4 Herleid. 1p a \({12 a b \over 20 a c}\) Vereenvoudigen (5) 00h9 - Breuken herleiden - basis - 0ms - dynamic variables a \({12 a b \over 20 a c} = {3 b \over 5 c}\) 1p 1p b \({-14 y \over 18 x y}\) Vereenvoudigen (6) 00ha - Breuken herleiden - basis - 0ms - dynamic variables b \({-14 y \over 18 x y} = -{7 \over 9 x}\) 1p 1p c \({-10 p q r \over 5 q r}\) Vereenvoudigen (7) 00hb - Breuken herleiden - basis - 0ms - dynamic variables c \({-10 p q r \over 5 q r} = -2 p\) 1p 1p d \({4 a b \over b} + {2 a c \over c}\) Vereenvoudigen (8) 00hc - Breuken herleiden - basis - 0ms - dynamic variables d \({4 a b \over b} + {2 a c \over c} = 4 a + 2 a = 6 a\) 1p

1 vwo

6.6 Herleiden van breuken

Breuken herleiden (13)

opgave 1

Herleid tot één breuk.

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

Optellen (1)

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

\({4 \over 7 p} + {6 \over 7 p} = {10 \over 7 p}\)

\({2 \over x} + {6 \over 3 x}\)

Optellen (2)

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

\({2 \over x} + {6 \over 3 x} = {6 \over 3 x} + {6 \over 3 x} = {12 \over 3 x} = {4 \over x}\)

\({7 \over 9 a} - {3 \over 5 b}\)

Optellen (3)

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

\({7 \over 9 a} - {3 \over 5 b} = {35 b \over 45 a b} - {27 a \over 45 a b} = {35 b - 27 a \over 45 a b}\)

\(5 + {8 \over 3 x}\)

Optellen (4)

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

\(5 + {8 \over 3 x} = {5 \over 1} + {8 \over 3 x} = {15 x \over 3 x} + {8 \over 3 x} = {15 x + 8 \over 3 x}\)

opgave 2

Herleid tot één breuk.

\({8 a \over b} + {9 \over 5 b}\)

Optellen (6)

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

○

\({8 a \over b} + {9 \over 5 b} = {40 a \over 5 b} + {9 \over 5 b} = {40 a + 9 \over 5 b}\)

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

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

\({-12 p \over 27 p}\)

Vereenvoudigen (3)

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

\({-12 p \over 27 p} = -\frac{4}{9}\)

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

Vereenvoudigen (4)

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

\({-4 x \over -2 x} = 2\)

opgave 4

Herleid.

\({12 a b \over 20 a c}\)

Vereenvoudigen (5)

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

\({12 a b \over 20 a c} = {3 b \over 5 c}\)

\({-14 y \over 18 x y}\)

Vereenvoudigen (6)

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

\({-14 y \over 18 x y} = -{7 \over 9 x}\)

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

Vereenvoudigen (7)

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

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

\({4 a b \over b} + {2 a c \over c}\)

Vereenvoudigen (8)

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

\({4 a b \over b} + {2 a c \over c} = 4 a + 2 a = 6 a\)