34. A plus term and a minus term cancel each other when combined, if both terms stand for the same number. 35. The Numerical Value of an Expression. The result obtained by putting particular values for the letters of an expression and performing the indicated operations is called the numerical value of the expression. Numerical Values of Simple Expressions. = 1. If a 3, find the numerical values of 4 a and a1. 4a= 4 × a = 4 × 3 = 12; a2 = a xaxaxa = 3 × 3 3 × 3 = 81. 5, b = 6, c = 7, find the numerical value of the 3. If x = 2, y = 3, find the numerical value of 5 x2y3. 5 x2y85 x 22 x 38 = 5 x 4 × 27 = : 540. 4. If x=4, y = 6, find the numerical value of x2y. = × 42 × 6 × 16 × 6 = 64. x2y = 5. If x=2, y = 3, z= 4, find the numerical value of 8x3y ÷ 3x3. 6. If x = 3, find the numerical values of √4x2; √4x2; and 2√(9x2). NOTE. √4x2 = √4 x 32√36 = 6. 2√(9 x2) = 2√(9 x 32) = 2 × 9 = 18. When no vinculum or parenthesis is used, a radical sign affects only the symbol immediately following it. EXERCISE 1. If a = 1, b = 2, c = 3, d = 4, x = 5, y = 6, z = 0, find 36. Each term should be written in the algebraic form by omitting the sign x between a numerical factor and a literal factor or between two literal factors. The operations indicated in a term must be performed before the operation indicated by the sign prefixed to the term. 37. The parts of a term are combined in the order of the signs and from left to right. The terms of an expression are combined in the order of the signs and from left to right. Thus, 60 – 40 ÷ 5 × 3 — 20 = 60 − 4o × 3 — 20 = 16. 38. The terms may be arranged in any order before combining them. This is called the commutative law for addition and subtraction. 6b Numerical Values of Compound Expressions. 1. If b = 10, c = 2, y = 5, find the numerical value of (8y2c) c2cy. въ (8y2c) c- · 2 cy = 6 × 10 − 40 × 2 2 X 2 X 5 2. If x=7, y = 5, find the numerical value of If a = 1, b = 2, c = 3, find the value of: If a = 1, b = 2, c = = 3, d = 0, find the value of: Parentheses. 39. A parenthesis preceded by the sign +. If a man has 10 dollars and afterwards collects 3 dollars and then 2 dollars, it makes no difference whether he puts the 3 dollars and the 2 dollars together and adds their sum to his 10 dollars, or adds the 3 dollars to his 10 dollars, and then the 2 dollars. The first process is represented by 10+ (3+2). Hence, 10 + (3 + 2) = 10 + 3 + 2. (1) If a man has 10 dollars and afterwards collects 3 dollars and then pays a bill of 2 dollars, it makes no difference whether he pays the 2 dollars from the 3 dollars collected and adds the remainder to his 10 dollars, or adds the 3 dollars collected to his 10 dollars and pays from this sum his bill of 2 dollars. The first process is represented by 10+ (3 − 2). 10+ (3-2) = 10 +32. If we use general symbols in (1) and (2), we have, a + (b + c) = a+b+c, (2) We have the general rule for a parenthesis preceded by +: If an expression within a parenthesis is preceded by the sign+, the parenthesis may be removed without making any change in the signs of the terms of the expression. Instead of a parenthesis, any other sign of aggregation may be used and the same rule will apply. 40. A parenthesis preceded by the sign- If a man with 10 dollars has to pay two bills, one of 3 dollars and one of 2 dollars, it makes no difference whether he takes 3 dollars and 2 dollars at one time, or takes 3 dollars and 2 dollars in succession, from his 10 dollars. The first process is represented by 10-(3+2). If a man has 10 dollars consisting of two 5-dollar bills, and has a debt of 3 dollars to pay, he can pay his debt by giving a 5-dollar bill and receiving 2 dollars. This process is represented by 105+2. Since the debt paid is 3 dollars, that is, (5-2) dollars, the number of dollars he has left can be expressed by If we use general symbols in (1) and (2), we have, and a ·(b+c) = abc, (b −c) = o − b + c. We have the general rule for a parenthesis preceded by (2) If an expression within a parenthesis is preceded by the sign, the parenthesis may be removed, provided the sign before each term within the parenthesis is changed, the sign to and the sign to +. + NOTE. If the vinculum is used, the sign prefixed to the first term under the vinculum must be understood as the sign before the vinculum. Thus, a+b c has the same meaning as a and + (b − c), a-b -c has the same meaning as a - - (bc). |