Elementary Algebra |
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Page 95
... integers . we mean a equal parts , b of which make up the unit ... ( 1 ) ; But ma mb b parts in ( 1 ) = mb parts in ( 2 ) ; ... 1 part . . . = m .. ..... ... ( 2 ) . ... a parts that is , Conversely , .... = ma a ma b mb ma a = mbb ...
... integers . we mean a equal parts , b of which make up the unit ... ( 1 ) ; But ma mb b parts in ( 1 ) = mb parts in ( 2 ) ; ... 1 part . . . = m .. ..... ... ( 2 ) . ... a parts that is , Conversely , .... = ma a ma b mb ma a = mbb ...
Page 98
... integer : multiply the numerator by that integer ; or , if the denominator be divisible by the integer , divide the denominator by it . The rule may be proved as follows : α ( 1 ) / represents a equal parts , b of which make up the unit ...
... integer : multiply the numerator by that integer ; or , if the denominator be divisible by the integer , divide the denominator by it . The rule may be proved as follows : α ( 1 ) / represents a equal parts , b of which make up the unit ...
Page 99
... integer : divide the numerator , if it be divisible , by the integer ; or , if the numerator be not divisible , multiply the denominator by that integer . The rule may be proved as follows : ac ( 1 ) represents ac equal parts , b of ...
... integer : divide the numerator , if it be divisible , by the integer ; or , if the numerator be not divisible , multiply the denominator by that integer . The rule may be proved as follows : ac ( 1 ) represents ac equal parts , b of ...
Page 114
... integers ; but cases frequently occur in which the numerator or denominator of a fraction is itself fractional . 137. DEFINITION . A fraction whose numerator and deno- minator are whole numbers is called a Simple Fraction . A fraction ...
... integers ; but cases frequently occur in which the numerator or denominator of a fraction is itself fractional . 137. DEFINITION . A fraction whose numerator and deno- minator are whole numbers is called a Simple Fraction . A fraction ...
Page 115
... integers , a fraction may be regarded as repre- senting the quotient of the numerator by the denominator . We now see that a complex fraction may be regarded in the same sense . 142. The student should especially notice the following ...
... integers , a fraction may be regarded as repre- senting the quotient of the numerator by the denominator . We now see that a complex fraction may be regarded in the same sense . 142. The student should especially notice the following ...
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Common terms and phrases
a+3b a+b+c a₁ a²+b² arithmetic means arithmetical arranged ascending powers b₁ beginner Binomial Theorem cents CHAPTER coefficients column compound expression continued fraction convergent cube root decimal denote digits dimes Divide dividend division divisor equal EXAMPLES XI Find the highest find the number Find the square Find the sum find the value following expressions given expressions greater harmonic mean Hence highest common factor integer less letters logarithm lowest common multiple method miles an hour Multiply number of terms numerator and denominator obtain partial fractions prefixed prove quadratic quadratic equation quotient ratio remainder Resolve into factors result rule of signs second term Simplify SIMULTANEOUS EQUATIONS solution square root subtraction Suppose surds symbols Transposing unknown quantity walk whence write yards zero
Popular passages
Page 331 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 256 - In a quadratic equation wJiere the coefficient of the first term is unity, (i) the sum of the roots is equal to the coefficient of x with its sign changed ; (ii) the product of the roots is equal to the third term.
Page 168 - Thus the 4th root (2x2) = the square root of the square root ; the sixth root (3x2) = the cube root of the square root, or the square root of the cube root.
Page 178 - A basket of oranges is emptied by one person taking half of them and one more, a second person taking half of the remainder and one more, and a third person taking half of the remainder and six more. How many did the basket contain at first ? 17.
Page 179 - Two vessels contain mixtures of wine and water ; in one there is three times as much wine as water, in the other five times as much water as wine. Find how much must be drawn off from each to fill a third vessel which holds seven gallons, in order that its contents may be half wine and half water.
Page 280 - The pressure of wind on a plane surface varies jointly as the area of the surface, and the square of the wind's velocity. The pressure on a square foot is 1...
Page 213 - Art. 167 we saw that if the number of unknown quantities is greater than the number of independent equations, there will be an unlimited number of solutions, and the equations will be indeterminate. By introducing conditions, however, we can limit the number of solutions. When positive integral values of the unknown quantities are required, the equations are called simple indeterminate equations. The introduction of this restriction enables us to express the solutions in a very simple form. Ex. 1....