The First Steps in Algebra |
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Common terms and phrases
a+b+c a²b a²b² a³b a³b³ ab+b² ab² ab³ ac² algebraic expression algebraic numbers arithmetical mean arithmetical progression binomial called cents coefficient common factor compound expression cube root decimal denominator difference Divide dividend divisor equation Exercise Extract the square feet Find the numbers Find the product Find the square Find the sum find the value formula fraction geometrical geometrical progression given number greater number Hence highest common factor integral number leaps letters means miles an hour minus monomial multiplicand Multiply negative numbers number of dollars oranges parenthesis Polynomials quadratic quadratic equation quotient ratio remainder Resolve into factors result second term smaller number Solve square root stands Subtract trial-divisor units unknown number x²y x²y² x³y x³y³ xy² xy³ yards
Popular passages
Page 167 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Page 161 - ... connected by the brace, and annexing two ciphers to the result. The last two figures of the root are found by division. The rule in such cases is, that two less than the number of figures already obtained may be found without error by division, the divisor to be employed being three times the square of the part of the root already found.
Page 21 - It becomes necessary in solving an equation to bring all the terms that contain the symbol for the unknown number to one side of the equation, and all the other terms to the other side. This is called transposing the terms. We will illustrate by examples : (1) Find the number for which x stands when...
Page 87 - The least common multiple of two or more numbers is the least number that is exactly divisible by each of them.
Page 88 - Separate each number into its prime factors. Find the product of these factors, taking each factor the greatest number of times it occurs in any one of the given numbers.
Page 170 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 117 - The area of a rectangle is equal to the product of the length by the breadth.
Page 79 - Extract the square roots of the first and last terms, and connect these square roots by the sign of the middle term.
Page 65 - RULE 3. The product of the sum and difference of two numbers is the difference of their squares.
Page 43 - Here the product and one factor are given and the other factor is required. "We may therefore take for the general definition of division The operation by which when the product and one factor are given the other factor is found. With reference to this operation the product is called the dividend, the given factor the divisor, and the required factor the quotient.