Four Basic Operations of Arithmetic

Many thousands of years ago this was a world without numbers. Today, using the same numbers in many different ways, man can build bridges, skyscrapers, fly off the Earth like a bird, even measure the distance to the Moon. So you see, mathematics and numbers, are very important to life nowadays.

Until XVI century people in Europe used Roman numerals. The Roman system of numbers is based upon the letters I, V, X, L, C, D, and M. These letters were mixed together to form many different combinations. The arithmetic symbols now in use were derived from the Arabs and the Hindus, the latter of whom introduced the symbol 0.The invention of this symbol for zero was very important, because it enabled the nine Hindu symbols 1, 2, 3, 4, 5, 6, 7, 8 and 9 to represent any number, no matter how great. The work of a zero is to keep the other nine symbols in their proper place. The Hindu-Arabic numeration systemis adecimal system: that is, it is based on tens. In this system the value a digit represents is determined by the place it has in the number; if a digit is moved to the left one place, the value it represents becomes ten times as great.

The invention of our present notation for the decimal number system made possible simple and systematic operations with numbers. Arithmetic is the elementary branch of mathematics dealing with the properties of numbers and their operations. We work with only positive numbers in arithmetic. Negative numbers appear in algebra. An operation is a way of thinking of two numbers and getting one number. The fundamental operations of arithmetic are addition, subtraction, multiplication, division.

There are special signs to indicate operations with numbers. They are plus (+), minus (-), multiplication (x) and division (:) signs.

The process of finding a simple expression for the sum of two or more numbers is known as addition. In the arithmetic sentence 3+5=8 three and five are addends and eight is the sum.

In the operation of subtraction the number to be made smaller is called the minuend.The subtrahend is the number to be subtracted. The result of the process is the difference. A sentence like 6-4=2 represents an operation of subtraction. Here the difference is the number that when added to the subtrahend gives the minuend. Thus, subtraction is the inverse operation of addition since 2+4=6 and 6-4=2.

In multiplication the number being multiplied is the multiplicand. The number by which we are multiplying the multiplicand is the multiplier. When two or more numbers are multiplied, each of them is called a factor. The number resulting from the multiplication is known as the product. You must remember that the product of any number multiplied by zero is zero. The product of any number multiplied by one is the same number.

In division the number to be divided is called the dividend. The divisor isthe number by which the dividend is to be divided. When we are dividing the dividend by the divisor we get the quotient.You may check division by using multiplication since 4:2=2 and 2x2=4.Therefore, division and multiplication are inverse operations. The remainder is what is left over after the dividend has been divided into equal parts. If there is a remainder, it may be written over the divisor and expressed as a fraction in the quotient. There are some important facts that must be remembered about division. The quotient is 0 (zero) whenever the dividend is 0 and the divisor is not 0. That is, 0:n=0 for all values of n except n=0. Division by 0 is meaningless for all values of n.

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Ex. 6. Analyze the following sentences and translate them into Russian.	\|	Ex. 12. Make the sentences negative and interrogative.

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