Shorter Course in Algebra |
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Common terms and phrases
a+b+c a²+2ab+b² a²b² a²x² ab+b² ab² ab³ ac² arithmetical series cents change the sign coefficient common factor Complete the square contain cube root denominator difference digits divisible divisor exponent Extract the root feet Find the H. C. F. Find the number geometrical geometrical series greater number Hence highest common factor leaps miles minute-spaces in arc monomial multiplicand Multiply negative number nth root number is expressed number of dollars number of minute-spaces number of terms numbers whose product obtained polynomial positive number pounds quadratic equation quotient ratio remainder Resolve into factors result second term Simplify smaller number Solve the equation square root Subtract surds twice units unknown quantity x²y x²y² x³y xy² xy³
Popular passages
Page viii - Find two numbers such that, when the greater is divided by the less, the quotient is 4, and the remainder 3 ; and when the sum of the two numbers is increased by 38, and the result divided by the greater of the two numbers, the quotient is 2 and the remainder 2," is much simplified by the use of letters to represent the unknown numbers.
Page 145 - The sum of the two digits of a number is 6, and if the number be divided by the sum of the digits the quotient is 4.
Page 45 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Page 220 - ... 16. There are two roads from A to B, one of them 14 miles longer than the other ; and two roads from B to C, one of them 8 miles longer than the other. The distance from A to B is to the distance from B to C, by the shorter roads, as 1 to 2 ; by the longer roads, as 2 to 3.
Page 95 - Reduce the fractions to equivalent fractions having the lowest common denominator. Subtract the numerator of the subtrahend from the numerator of the minuend.
Page 134 - From each equation obtain the value of one of the unknown quantities in terms of the other. Form an equation from these equal values, and reduce the equation.
Page 33 - The product of the sum and difference of two numbers is equal to the difference of their squares.
Page 54 - Any term may be transposed from one side of an equation to the other provided its sign be changed.
Page 123 - A sets out and travels at the rate of 7 miles in 5 hours. Eight hours afterwards B sets out from the same place and travels in the same direction, at the rate of 5 miles in 3 hours. In how many hours will B overtake A ? 41.
Page 170 - It will be seen that this third term is the square of the quotient obtained from dividing the second term by twice the square root of the first term.