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a²b added algebraic amount average axis bushels cents certain changed coefficient consecutive contains cost denominator denoted diagram difference distance divided dollars Draw earned equals equation example exceeds EXERCISE expression factors feet Find the number find the value formula four fraction girl give given grade graph Hence hour inches increased length less letters method miles month Multiply nearest obtain pounds problems profits pupil quantity quotient received rectangle Reduce remainder represent result rule Separate short side Simplify sold Solve solve Exs space square square root subtracted symbols temperature third travels twice United unknown weight wide width Write x²y yards
Page 102 - ... the square of the second. _ Again, (a — by = (a — 5) (a — 5) = a2 — 2a6 + 52. (2) That is, The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Page 213 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, the sum, difference, product, and quotient so obtained, will be all equal to each other.
Page 164 - To reduce a mixed number to its equivalent improper fraction. RULE.* Multiply the whole number by the denominator of the fraction, and add the numerator to the product, then that sum written above the denominator will form the fraction required. EXAMPLES. 1. Reduce 27$ to its equivalent improper fraction...
Page 243 - If the greater of two numbers is divided by the less, the quotient is 3 and the remainder 3, but if 3 times the greater be divided by 4 times the less, the quotient is 2 and the remainder 20.
Page 271 - Resolve the quantity under the radical sign into two factors, one of which is the highest perfect power of the same degree as the radical. Extract the required root of this factor, and prefix the result to the indicated root of the other.
Page 220 - In one of the given equations obtain the value of one of the unknown quantities in terms of the other unknown quantity; Substitute this value in the other equation and solve.
Page 303 - Degree of a Term; Homogeneous Expressions. The degree of a term is determined by the number of literal factors which the term contains. Hence, the degree of a term is equal to the sum of the exponents of the literal factors...
Page 43 - The work is checked by letting a and 6 each = 1. Hence, the process for addition may be stated as follows: Arrange the terms to be added in columns, placing similar terms in the same column; Find the algebraic sum of the numerical coefficients of each column and prefix this result to the literal factors common to the terms in the column. Sometimes the algebraic sum of the coefficients of each group of similar terms is found without arranging the terms in columns. EXERCISE 9 Add and check each result:...