- •Arithmetic
- •How the use of numbers began
- •Exercises
- •How we read and write numbers
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Adding, subtracting, multiplying and dividing the whole numbers
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Fractions and their meaning
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Types of fractions
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Addition, subtraction, multiplication and division of fractions
- •Exercises
- •Changing fractions
- •I. Read the following words paying attention to the pronunciation:
- •Decimal fractions
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Adding, subtracting, multiplying and dividing decimal fractions
- •Exercises
- •I Read the following words paying attention to the pronunciation:
- •What is per cent?
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Scale drawing
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Algebra
- •The nature of algebra
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Signs used in algebra
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Equations
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Monomial and polynomial
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Factors, coefficients and combining terms
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •The formula
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Systems of two linear equations1 in two unknowns
- •Exercises
- •Read the following words paying attention to the pronunciation:
- •Squares and square roots
- •Exercises
- •Read the following words paying attention to the pronunciation:
- •Logarithms
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •The slide-rule
- •Exercises
- •Geometry
- •Points and lines
- •Measuring and constructing angles with a protractor
- •Exercises
- •Read the following words paying attention to the pronunciation:
- •Kinds of polygons
- •Exercises
- •Circles
- •Exercises
- •Geometric solids
- •Exercises
- •Symmetry
- •Exercises
- •Similar fioures
- •Exercises
- •I. Read the following words paying attention to the pronunciation:
- •Trigonometry
- •Trigonometry and its application
- •Exercises
- •Trigonometric functions
- •Exercises
- •Measurement of angles
- •Exercises
- •Functions of complementary angles
- •Exercises
- •The solution of right triangles
- •Exercises
- •Tables of values of the trigonometric functions
- •Exercises
- •Exercises
- •Supplementary reading
- •Pythagoras
- •Leibnitz
- •Sophia kovalevskaya
- •Nikolai lobachevsky
- •Mathematician No. 1
- •About common fractions
- •Mathematics—handyman for all sciences
- •Ordinary vs. Binary numbers
- •Appendix signs used in mathematics
- •Short mathematics dictionary
- •English – russian vocabulary of mathematical terms
Exercises
I. Read the following words paying attention to the pronunciation:
special, place, particular, decimal, indicate, without, whether, higher, power, leave, greatest, figure, require, determine.
II. Form nouns of the following verbs:
to determine, to place, to indicate, to move, to inspect, to require, to compare.
III. Answer the following questions:
What is the decimal fraction? 2. How do we write decimal fractions? 3. How do you round off a decimal to a particular place? 4. How do you compare decimal fractions? 5. How do you change decimal fractions?
IV. Put 4 questions to the text and answer them.
V. Translate into Russian:
Since fractional parts of thing may be written either as common fractions or as decimal fractions, we should be able to change a decimal fraction to a common fraction.
To change a decimal fraction to a common fraction take out the decimal point and write the decimal number as the numerator of the fraction. For the denominator write the number as shown by the name of the last decimal place. Reduce the common fraction to lowest terms.
VI. Translate into English:
Дроби, знаменателями которых являются числа, выраженные единицей с последующими нулями (одним или несколькими), называются десятичными. Из двух десятичных дробей та больше, у которой число целых больше; при равенстве целых та дробь больше, у которой число десятых больше и т. д.
Перенесение запятой на один знак вправо увеличивает число в десять раз. Чтобы увеличить его в сто раз, нужно перенести запятую на два знака вправо и т. д.
TEXT
Adding, subtracting, multiplying and dividing decimal fractions
Decimal fractions are added in the same way that the whole numbers are added. Since only like decimal fractions can be added, that is hundredths to hundredths, and tenths to tenths, the addends are arranged in a vertical column with the decimal points directly below one another, all the way down to the answer.
Problem: Find the sum of the following numbers: 2.23, 4.8, 9 and 0.067.
2.230
4.800
Annex zeroes and arrange numbers in columns: 9.000
0.067
_______
16.097 answer.
In subtracting decimal fractions we must write decimal fractions so that the decimal point of the minuend, subtrahend and remainder are below each other. Zeroes should be annexed so that both minuend and subtrahend are carried out to the same number of places. Check the answer the same way that you check the subtraction of whole numbers.
In multiplying a decimal fraction or mixed decimals multiply as you do whole numbers. Then, starting at the right, mark off as many decimal places in the product as there are in the multiplier and multiplicand together.
To divide a number by 10 or any power of ten, move the point in the dividend as many places to the left as there are zeroes in the divisor. Add zeroes when needed.