Equations On Algebra Expounding On Properties Of Real Numbers - 550 Words

Solving Sample Equations On Algebra And Expounding On Properties Of Real Numbers (Math Problem Sample) Content: Algebra[Name][Course][Name of Instructor][Date of Submission]Algebra 1 2a (a 5) + 4 (a 5)= 2a (a) 2a (5) + 4 (a) 4 (5) Using the distributive property, multiply the termswithin the parentheses with term outside, to removeparentheses.= 2a2 -10a + 4a 20 Add the like terms (coefficients of a) together, and simplify [commutative property]= 2a2 6a 20 Combine like terms 2 2w 3 + 3(w 4) 5(w 6)= 2w 3 + 3(w) + 3(-4) 5 (w) 5(-6) Using the distributive property, multiply theterms within the parentheses with termoutside, to remove the parentheses.= 2w 3 + 3w 12 5w + 30= 2w + 3w 5w 3 12 + 30 Group like terms together (coefficients of w)= 0 + 15 simplify.= 15 (Answer). 3 0.05(0.3m + 35n) 0.8(-0.09n 22m)= 0.05 (0.3m) + 0.05 (35n ) 0.8 (-0.09n) 0.8 (-22m) Distribution of themultiplication by0.05 and 0.8= 0.015m + 1.75n + 0.072n + 17.6m= 0.015m + 17.6m + 1.75n + 0.072n Group the like terms, both coefficientsm and n.= 17.615m + 1.822n Combine like termsProperties of Real NumbersProperties of real number have been very effective and fundamental in solving algebraic equations. The properties mainly encompass; closure property, which depicts that the sum and multiplication of real numbers is equivalent to real numbers, and associative property, which is thought as a grouping property and emphasizes on the fact that when three numbers are multiplied or added, changing of the group of the number, does not affect the final result (Kaufmann Schwitters, 2011). Besides, commutative property accentuate on the order of addition and multiplication of two integers, which in turn does not affect the result, whereas, zero and one are referred to as the identity elements in operation s that involve addition and multiplication respectively (Kaufmann Schwitters, 2011). Distributive property is also a property of real numbers, and it involves both addition and multiplication, and it shows how to multiply a sum of two numbers using a third number (Gustafson Frisk, 2008). Inverse property, on the other hand, largely entails the summation of a number by its inverse to get the identity element (zero), or multiplication of a number by its inverse to get an identity element, which is one (Gustafson Frisk, 2008).In light with this, Gustafson and Frisk (2008) also attest that the basic to understanding algebra is through knowing the properties that govern the operations of addition, subtraction, multiplication, and division of real numbers. Conventionally, the properties ...