## The First Steps in Algebra |

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a+b+c a²b² ab² ab³ added algebraic Arithmetic Arrange bills called cents changed CHAPTER coefficient common factor complete contains count cube root denominator difference Divide dividend division divisor dollars equal equation examples Exercise expression Extract factors feet figures Find the numbers Find the sum formula four fraction geometrical given gives greater groups Hence increased indicated integral interest leaps length less letters means Multiply negative NOTE obtained oranges Page parenthesis places positive preceded principal problem progression proportion quantities quotient ratio Reduce remainder represented Resolve into factors result RULE side simple smaller Solve square root stands Subtract term third twice units Write 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.