15 września 2015

Vocabulary

Exercises

Exercise 1. Match the words in column A with the words in column B.

Exercise 2. Answer the following questions.

1. What are the four basic arithmetic operations?
2. What else does arithmetic include?
3. What is the most common set of symbols in modern usage?
4. What does it mean that addition is commutative?
5. How does algebra differ from arithmetic?
6. What does it mean that multiplication is commutative?
7. What does it mean that subtraction is noncommutative?
8. What does it mean that division is noncommutative?
9. What do you call the result of addition, subtraction, multiplication and division?
10. What do you call the numbers to be added?
11. What do you call the number to be subtracted from another number?
12. What do you call the number you subtract from another number?
13. What do you call the numbers to be multiplied?
14. In the fraction $\frac{1}{2}$ what do you call 1 and what do you call 2?

Exercise 3. Solve the following equations.

1. 1 + 2 =
2. 24 +13 =
3. 7 × 4 =
4. 25 ÷ 5 =
5. 9 − 3 =
6. 15 − 11 =
7. 6 × 6 =
8. 100 − 84 =
9. 99 ÷ 3 =
10. 37 + 48 =

Exercise 4. Complete the sentences. Practise saying them until you remember them by heart.

• Addition is commutative, meaning that…
• Subtraction is noncommutative, meaning that…
• Multiplication is commutative, meaning that…
• Division is noncommutative, meaning that…

Exercise 5. Translate the second part of the sentences.

Arithmetic…

• … jest najstarszą i najbardziej podstawową gałęzią matematyki.
• … obejmuje działania dodawania, odejmowania, mnożenia i dzielenia.
• … obejmuje również ułamki, liczby ujemne, pierwiastki, procenty i funkcje logarytmiczne.
• … obejmuje także bardziej zaawansowane działania.
• … różni się od algebry tym, że wykorzystuje symbole abstrakcyjne do reprezentacji wartości.

Exercise 6. Solve the following equations.

1. 3 + 9 − 7 =
2. 15 − 12 × 2 =
3. 36 ÷ 4 × 6 =
4. 47 + 11 − 5 + 6 =
5. 9 × 7 − 44 ÷ 11 =
6. 22 + 11 − 13 =
7. 36 − 17 + 1 =
8. 27 ÷ 3 × 6 =
9. 100 − 48 + 13 =
10. 5 × 6 + 48 =

Exercise 7. Translate the following texts into English following the example.

• Dodawanie (oznaczane symbolem plus: „+”) jest jednym z czterech podstawowych działań matematycznych — pozostałe to odejmowanie, mnożenie i dzielenie. Wynikiem dodawania jest suma. Wyrażenie matematyczne „3 + 2 = 5” czytamy na głos „3 dodać 2 równa się 5”.
  
  Addition (signified by the plus symbol „+”) is one of the four elementary arithmetic operations, with the others being subtraction, multiplication and division. The result of addition is the sum. The mathematical expression „3 + 2 = 5” can be read out loud as „3 add 2 is equal to 5”.
• Odejmowanie (oznaczane symbolem minus: „−”) jest jednym z czterech podstawowych działań matematycznych — pozostałe to dodawanie, mnożenie i dzielenie. Wynikiem odejmowania jest różnica. Wyrażenie matematyczne „3 − 1 = 2” czytamy na głos „3 odjąć 1 równa się 2”.
• Mnożenie (oznaczane symbolem „×” lub „·”) jest jednym z czterech podstawowych działań matematycznych — pozostałe to dodawanie, odejmowanie i dzielenie. Wynikiem mnożenia jest iloczyn. Wyrażenie matematyczne „4 × 3 = 12” czytamy na głos „4 razy 3 równa się 12”.
• Dzielenie (oznaczane symbolem „÷”) jest jednym z czterech podstawowych działań matematycznych — pozostałe to dodawanie, odejmowanie i mnożenie. Wynikiem dzielenia jest iloraz. Wyrażenie matematyczne „8 ÷ 2 = 4” czytamy na głos „8 podzielić przez 2 równa się 4”.

Exercise 8. Solve the following equations and read them out loud. Then write them down in full form as in the example.

Example: 1 + 1 = 2; one plus one equals two

1. 2 + 3 =
2. 10 − 6 =
3. 9 ÷ 3 =
4. 7 × 7 =
5. 17 + 22 =
6. 40 − 15 =
7. 72 ÷ 8 =
8. 6 × 6 =
9. 53 + 25 =
10. 34 − 8 =
11. 8 × 7 =
12. 99 ÷ 3 =

Exercise. 9. Provide the plural form of these words.

1. branch
2. property
3. operation
4. point
5. root
6. factor
7. expression
8. percentage
9. abstraction

Exercise 10. Fill in the missing words. The first letter of each missing word has been provided.

Arithmetic is a b………. of mathematics. It consists o………. the study of numbers, and the properties of the o………. between them — a………. (denoted b………. +), s………. (−), m………. (×), and d………. (÷).

Other arithmetic operations include p………. (%), s………. r………. ($\sqrt{x}$), e………. (eg. $x^2$), f………. (e.g. 0.01), n………. n………. (e.g. −3) and logarithmic functions. Arithmetic is performed according t………. an o………. of operations.

In Algebra letters can be used to stand f………. numbers that are either u………. (not known) or may t………. on many values, but the l………. of inverses can be used to discover their v………..

Addition is c………., meaning that order of added numbers does not m………., and it is a………., meaning that the o………. in which addition of more than two numbers is p………. does not matter. The numbers to be added are collectively referred t………. as the terms, the a………. or the summands and the result of addition is r………. to as the s………..

Subtraction is n………., meaning that changing the order of the numbers to s………. changes the s………. of the answer. It is not associative, meaning that the order in which s………. is performed matters. The number being subtracted is known a………. the s………., the number it is subtracted from is the m………., and the result of a subtraction is the d………..

The numbers to be multiplied are called the factors or m……….. The result of a multiplication is called a p………..

In the expression x ÷ y = z, x is called the d………., y is called the d………., and z is called the q……….. And in fractions, as in ½ , 1 is also called the n………., and 2 is called the d………..

Exercise 11. Translate the text into Polish.

Exercise 12. Summarize the text orally using questions from exercise 2 as an outline.

Exercise 13. Translate the following poem into Polish. Show your translation off in a comment at the bottom of the page! This exercise is optional.

I think that I shall never envision
An op unlovely as division.

An op whose answer must be guessed
And then, through multiply, assessed;

An op for which we dearly pay,
In cycles wasted every day.

Division code is often hairy;
Long division’s downright scary.

The proofs can overtax your brain,
The ceiling and floor may drive you insane.

Good code to divide takes a Knuthian hero,
But even God can’t divide by zero!

Źródło: Henry S. Warren Jr., Hacker’s Delight 1st Edition