1.1 Exercises

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===Exercise 1.1:3===
===Exercise 1.1:3===
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Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
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Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.
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===Exercise 1.1:4===
===Exercise 1.1:4===
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Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
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Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.{| width="100%" cellspacing="10px"
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===Exercise 1.1:7===
===Exercise 1.1:7===
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Which of the following numbers are rational? Give them as a fraction of two integers.
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Which of the following numbers are rational? Express them as a fraction of two integers.
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Current revision

       Theory          Exercises      


Exercise 1.1:1

Work out (without the help of a calculator)

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
Answer 1.1:1
Solution a
Solution 1.1:1a
Solution b
Solution 1.1:1b
Solution c
Solution 1.1:1c
Solution d
Solution 1.1:1d


Exercise 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
Answer 1.1:2
Solution a
Solution 1.1:2a
Solution b
Solution 1.1:2b
Solution c
Solution 1.1:2c
Solution d
Solution 1.1:2d


Exercise 1.1:3

Determine whether the following are natural numbers, integers, rational numbers or 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
Answer 1.1:3
Solution a
Solution 1.1:3a
Solution b
Solution 1.1:3b
Solution c
Solution 1.1:3c
Solution d
Solution 1.1:3d
Solution e
Solution 1.1:3e
Solution f
Solution 1.1:3f


Exercise 1.1:4

Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.{| width="100%" cellspacing="10px" |a) |width="33%"| \displaystyle \frac{4}{-8} |b) |width="33%"| \displaystyle \frac{-8}{-4} |c) |width="33%"| \displaystyle \frac{\sqrt{2}}{3} |- |d) || \displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2 |e) || \displaystyle -\pi |f) || \displaystyle \pi+1 |}

Answer
Answer 1.1:4
Solution a
Solution 1.1:4a
Solution b
Solution 1.1:4b
Solution c
Solution 1.1:4c
Solution d
Solution 1.1:4d
Solution e
Solution 1.1:4e
Solution f
Solution 1.1:4f


Exercise 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
Answer 1.1:5
Solution a
Solution 1.1:5a
Solution b
Solution 1.1:5b
Solution c
Solution 1.1:5c


Exercise 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
Answer 1.1:6
Solution a
Solution 1.1:6a
Solution b
Solution 1.1:6b
Solution c
Solution 1.1:6c
Solution d
Solution 1.1:6d


Exercise 1.1:7

Which of the following numbers are rational? Express 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
Answer 1.1:7
Solution a
Solution 1.1:7a
Solution b
Solution 1.1:7b
Solution c
Solution 1.1:7c
Solution d
Solution 1.1:7d
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