1.1 Übungen

Aus Online Mathematik Brückenkurs 1

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Übung 1.1:1

Berechne folgendes (ohne Taschenrechner)

a) \displaystyle 3-7-4+6-5 b) \displaystyle 3-(7-4)+(6-5)
c) \displaystyle 3-(7-(4+6)-5) d) \displaystyle 3-(7-(4+6))-5
Answer
Antwort 1.1:1
Lösung a
Solution 1.1:1a
Lösung b
Solution 1.1:1b
Lösung c
Solution 1.1:1c
Lösung d
Solution 1.1:1d


Übung 1.1:2

Simplify

a) \displaystyle (3-(7-4))(6-5) b) \displaystyle 3-(((7-4)+6)-5)
c) \displaystyle 3\cdot(-7)-4\cdot(6-5) d) \displaystyle 3\cdot(-7)-(4+6)/(-5)
Answer
Antwort 1.1:2
Lösung a
Solution 1.1:2a
Lösung b
Solution 1.1:2b
Lösung c
Solution 1.1:2c
Lösung d
Solution 1.1:2d


Übung 1.1:3

Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?

a) \displaystyle 8 b) \displaystyle -4 c) \displaystyle 8-4
d) \displaystyle 4-8 e) \displaystyle 8\cdot(-4) f) \displaystyle (-8)\cdot(-4)
Answer
Antwort 1.1:3
Lösung a
Solution 1.1:3a
Lösung b
Solution 1.1:3b
Lösung c
Solution 1.1:3c
Lösung d
Solution 1.1:3d
Lösung e
Solution 1.1:3e
Lösung f
Solution 1.1:3f


Übung 1.1:4

Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?

a) \displaystyle \frac{4}{-8} b) \displaystyle \frac{-8}{-4} c) \displaystyle \frac{\sqrt{2}}{3}
d) \displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2 e) \displaystyle -\pi f) \displaystyle \pi+1
Answer
Antwort 1.1:4
Lösung a
Solution 1.1:4a
Lösung b
Solution 1.1:4b
Lösung c
Solution 1.1:4c
Lösung d
Solution 1.1:4d
Lösung e
Solution 1.1:4e
Lösung f
Solution 1.1:4f


Übung 1.1:5

Arrange the following numbers in ascending order

a) \displaystyle 2, \displaystyle \tfrac{3}{5}, \displaystyle \tfrac{5}{3} och \displaystyle \tfrac{7}{3}
b) \displaystyle -\tfrac{1}{2}, \displaystyle -\tfrac{1}{5}, \displaystyle -\tfrac{3}{10} och \displaystyle -\tfrac{1}{3}
c) \displaystyle \tfrac{1}{2}, \displaystyle \tfrac{2}{3}, \displaystyle \tfrac{3}{5}, \displaystyle \tfrac{5}{8} och \displaystyle \tfrac{21}{34}
Answer
Antwort 1.1:5
Lösung a
Solution 1.1:5a
Lösung b
Solution 1.1:5b
Lösung c
Solution 1.1:5c


Übung 1.1:6

Give the decimal expansion of the following to three decimal places.

a) \displaystyle \frac{7}{6} b) \displaystyle \frac{9}{4} c) \displaystyle \frac{2}{7} d) \displaystyle \sqrt{2}
Answer
Antwort 1.1:6
Lösung a
Solution 1.1:6a
Lösung b
Solution 1.1:6b
Lösung c
Solution 1.1:6c
Lösung d
Solution 1.1:6d


Übung 1.1:7

Which of the following numbers are rational? Give them as a fraction of two integers.

a) \displaystyle 3\textrm{.}14
b) \displaystyle 3\textrm{.}1416\,1416\,1416\,\ldots
c) \displaystyle 0\textrm{.}2\,001\,001\,001\,\ldots
d) \displaystyle 0\textrm{.}10\,100\,1000\,10000\,1\ldots\, (one 1:, one 0:, one 1:, two 0:s, one 1:, three 0:s etc.)
Answer
Antwort 1.1:7
Lösung a
Solution 1.1:7a
Lösung b
Solution 1.1:7b
Lösung c
Solution 1.1:7c
Lösung d
Solution 1.1:7d
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