Solving Sample Equations On Algebra And Expounding On Properties Of Real Numbers (Math Problem Sample)

Algebra
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Algebra
1 2a (a – 5) + 4 (a – 5)
= 2a (a) – 2a (5) + 4 (a) – 4 (5) Using the distributive property, multiply the terms
within the parentheses with term outside, to remove
parentheses.
= 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 the
terms within the parentheses with term
outside, 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 the
multiplication by
0.05 and 0.8
= 0.015m + 1.75n + 0.072n + 17.6m
= 0.015m + 17.6m + 1.75n + 0.072n Group the like terms, both coefficients
m and n.
= 17.615m + 1.822n Combine like terms
Properties of Real Numbers
Properties 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 operations 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 ...