- •Arithmetic
- •How the use of numbers began
- •Exercises
- •How we read and write numbers
- •Exercises
- •Adding, subtracting, multiplying and dividing the whole numbers
- •Exercises
- •Fractions and their meaning
- •Exercises
- •Types of fractions
- •Exercises
- •Addition, subtraction, multiplication and division of fractions
- •Exercises
- •Changing fractions
- •Decimal fractions
- •Exercises
- •Adding, subtracting, multiplying and dividing decimal fractions
- •Exercises
- •What is per cent?
- •Exercises
- •Scale drawing
- •Exercises
- •Exercises
- •Algebra
- •The nature of algebra
- •Exercises
- •Signs used in algebra
- •Exercises
- •Equations
- •Exercises
- •Monomial and polynomial
- •Exercises
- •Factors, coefficients and combining terms
- •Exercises
- •The formula
- •Exercises
- •Systems of two linear equations1 in two unknowns
- •Exercises
- •Squares and square roots
- •Exercises
- •Logarithms
- •Exercises
- •The slide-rule
- •Exercises
- •Geometry
- •Points and lines
- •Measuring and constructing angles with a protractor
- •Exercises
- •Kinds of polygons
- •Exercises
- •Circles
- •Exercises
- •Geometric solids
- •Exercises
- •Symmetry
- •Exercises
- •Similar fioures
- •Exercises
- •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:
reduce, value, both, other, mixed, proper, improper.
II. Give all possible derivatives of the following words:
value, convenience, to represent, to express, to divide.
III. Make up sentences of your own using the words and expressions given below:
evenly, to reduce to, for the convenience, expressed in, is equal to.
IV. Answer the following questions:
1. What is a common fraction called? 2. What is a proper fraction called? 3. Is the value of a proper fraction more or less than 1? 4. What do we call mixed numbers? 5. How do you reduce a fraction to its lower terms?
V. Put 6 questions to the text.
VI. Translate into Russian:
Fractions indicate division, the numerator being a dividend, the denominator a divisor, and the value of the fraction the quotient.
A fraction can be reduced to lower terms if the numerator and the denominator are divisible by a single number, that is if they have a common divisor. In order to reduce a fraction to its lowest terms, therefore, it is seen at once that the greatest common divisor must be used.
VII. Translate Into English:
Дробь, у которой числитель меньше знаменателя, называется правильной дробью. Правильная дробь меньше единицы.
Дробь, у которой числитель равен знаменателю или больше его, называется неправильной дробью. Таким образом, неправильная дробь или равна единице, или больше ее.
Числа, которые состоят из целого числа и дроби, называются смешанными числами.
Сокращением дроби называется замена ее другой, равной ей дробью с меньшими членами, путем деления числителем и знаменателем на одно и тоже число. Это число называется наибольшим общим делителем.
TEXT
Addition, subtraction, multiplication and division of fractions
To add fractions having the same denominator (like fractions) add their numerators and write the sum over the common denominator (do not add the denominators). Reduce the Resulting fraction to lowest terms.
To add fractions having different denominators (unlike fractions) the fractions must be changed1 to equivalent fractions which have the same or a common denominator. The least number which will be a common denominator, for example, of 2/3 and 3/5 is 15. 15 is the least common denominator, or lowest common denominator of 2/3 and 3/5. The least common denominator is sometimes denoted by the letters L.C.D.
To subtract fractions having the same denominator subtract the numerators and write the difference over the common denominator (do not subtract denominators).
To subtract fractions having different denominators first change the fractions to equivalent fractions having a common denominator. To subtract the fractions when they have a common denominator, subtract the numerators and write the difference over the denominator.
To multiply a mixed number and a fraction: 1) reduce the fraction to its lowest terms; 2) change the mixed number to an improper fraction; 3) multiply the two numerators to obtain the numerator of the answer; 4) multiply the denominators to obtain the denominator of the answer; 5) reduce the fraction obtained when possible. Reduction can be done by dividing a numerator and denominator by the same number. The numbers that are divided are crossed out, and the quotients are written as the new numerator and the new denominator.
To divide a whole number by a fraction, multiply the whole number by the denominator of the fraction and divide the result by the numerator of the fraction.
Note:
1 must be changed - должны быть превращены.