Learn the following active words and word combinations

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to add – складывать

addend – слагаемое

to check – проверять

to consider – рассматривать

to define – определять

difference – разность

to express – выражать

minuend – уменьшаемое

to proceed – продолжать

to produce – производить

to signify – означать, значить

single – единственный, единый

to subtract – вычитать

subtraction – вычитание

subtrahend – вычитаемое

Give the Russian equivalents for the following words and expressions from the text.

directed, signify, direction, undirected, in front of, operation, equivalent, change, quantity, thus, obtain.

Find the answers to these questions after quickly reading the text.

1. What do directed numbers signify?

2.What is algebraic addition?

Read and translate the text.

Positive and negative numbers are sometimes known as directed numbers because they signify direction. In arithmetic only undirected numbers with no sign in front of them are used. In algebra, the sign is considered as well as the size of the number. For example, in arithmetic, 7 + 5 = 12. The plus sign is the sign of operation.

In algebra the same process becomes (+7) + (+5) = +12. The first and the third plus signs show direction; the second plus sign is the sign of operation.

In algebra we add signed numbers, as + 9 and – 7. The relation is expressed thus: (+9) + (– 7) = +2.

From our study of positive and negative numbers we interpret it as 9 steps up and 7 steps down, which results in 2 steps up. Algebraicaddition is a combination of several algebraic expressions into a single equivalent expression.

Subtraction is defined as the inverse of addition. That is, to subtract a number a from a number b means to find a number, which, when added to a gives b. To subtract signed numbers, we change the sign of the subtrahend and proceed as in addition.

Examples:	+5 – +3		+5 – -3		-5 – +3		-5 – -3
	+2		+8		-8		-2

To subtract one algebraic expression from another, we change the signs of the subtrahend, and proceed as in addition.

To check a subtraction, we add the difference to the subtrahend; the result produces another quantity – the minuend. Thus, if we subtract 3ab from 10ab, we obtain 7ab, for 7ab added to3ab produces 10ab.

Find in the text English equivalents for the following Russian words and word combinations.

вычитаемое, величина, уменьшаемое, алгебраическое сложение, эквивалентное выражение, вычитать, разность, сложение, складывать, слагаемое, сумма, числительное, числа со знаками, относительные числа.

Match the words with their definitions.

algebra	a number or quantity to be subtracted from another one
to add	to take away or deduct (one number or quantity from another)
addition	the result obtained by adding numbers or quantities
addend	the amount by which one quantity differs from another
to subtract	to join or unite (to) so as to increase the quantity, number, size, etc. or change the total effect
subtraction	a number or quantity from which another is to be subtracted
subtrahend	equal in quantity, value, force, meaning
minuend	an adding of two or more numbers to get a number called the sum
difference	a number or quantity to be added to another
sum	the mathematical process of finding the difference between the two numbers or quantities
equivalent	a mathematical system using symbols, esp. letters, to generalize certain arithmetical operations and relationships