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The solution of equations is the central theme of algebra. In this chapter we will study some techniques for solving equations having one variable.

Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator. In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction of 3 8 , the numerator is 3, and the denominator is 8.

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Solution So, 48 people would be the legal room capacity. Many students think that when they have found the solution to an equation, the problem is finished.

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Use step-by-step calculators for chemistry, calculus, algebra, trigonometry, equation solving, basic math and more. Gain more understanding of your homework with steps and hints guiding you from problems to answers! Wolfram Alpha Pro step-by-step solutions not only give you the answers you're looking for, but also help you learn how to solve problems. Not just answers—step-by-step solutions buttons expand answers and explain how that answer was found. Break steps down even further with intermediate steps. These optional additional explanations for individual pieces of step-by-step solutions help guide you. Explore different ways of finding a solution. Use your classroom's teaching method to guide you through the answer. Your own tutor—hints are also frequently provided to not just provide answers, but also to guide you towards finding the solution yourself. Explore some of the content areas covered by step-by-step solutions, including math, chemistry and physics, or view more examples ».

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Solution Perimeter is the distance around. Remember that checking your solution is an important step in solving equations. For example, looking at the number 0. To convert this fraction into a decimal, first convert it into the fraction of 5 Solving Equations The solution of equations is the central theme of algebra. This is arguably the simplest way to ensure that the fractions have a common denominator. Example 11 The ratio of the number of women to the number of men in a math class is 7 to 8. Now we must eliminate 2x on the right side by subtracting 2x from both sides. Solve proportions. Finally the division rule gives Could we first add 2 to both sides? Example 13 If the legal requirements for room capacity require 3 cubic meters of air space per person, how many people can legally occupy a room that measures 6 meters wide, 8 meters long, and 3 meters high? As mentioned earlier, we wish to present an orderly procedure for solving equations. Note that in this example we used three rules to find the solution. It consists of a numerator and a denominator.

Solve Practice Play. Game Central. Greatest Common Factor.

Then using the division rule, we obtain Here again, we needed to use both the addition rule and the division rule to solve the equation. We must think of eliminating the number 2 from the left side of the equation and also the lx from the right side to obtain x alone on one side. Keep in mind that we wish to obtain x alone on one side of the equation. Solution What number do we divide 2 by to obtain 7? The least common multiple is the first shared multiple of these three numbers. Here again, we needed to use both the addition rule and the division rule to solve the equation. Many of the exercises in previous sections have required the use of more than one rule in the solution process. Using the division rule, we obtain To eliminate the fraction we need to multiply by a number that is divisible by the denominator. We substitute for x in the first equation obtaining The equations are equivalent, so the solution is correct. Many equations can be solved mentally. To convert this fraction into a decimal, first convert it into the fraction of 5 We now have an equivalent equation that contains only whole numbers. Remember that when we multiply a whole number by a fraction, we use the rule We are now ready to solve an equation involving fractions. Could we first add 2 to both sides? If the margin M was one-fifth of the cost C , find the cost of the article.