Solving Equations With Fractions Examples Oct 30 2020 0183 32 In this lesson we ll look at how to solve equations with numerical fractions as coefficients and terms Remember that multiplying a fraction by its reciprocal will always give you a value of 1 For example 4 5 has a reciprocal of 5 4 because frac 4 5 cdot frac 5 4 1
The following are examples of fractional equations a frac 3 x frac 9 20 b frac x 2 x 2 frac 3 5 c frac 3 x 3 frac 4 x 5 d frac 3 4 frac 1 8 x 0 e frac x 6 frac 2 3 x frac 2 3 The Cross Product property can be used to solve fractional equations When we have an equation with a fraction coefficient we can use the Multiplication Property of Equality to make the coefficient equal to 1 For example in the equation 3 4x 24 The coefficient of x is 3 4 To solve for x we need its coefficient to be 1 Since the product of a number and its reciprocal is 1 our strategy here will be to
Solving Equations With Fractions Examples
Solving Equations With Fractions Examples
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Example 1 Solve for x x 3 x 2 5 6 Solution Clear of fractions as follows Multiply both sides of the equation every term by the LCM of denominators Each denominator will then divide into its multiple We will then have an equation without fractions The LCM of 3 and 5 is 15 Therefore multiply both sides of the equation by 15
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Solving Equations With Fractions Examples
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Example 1 equations with one operation Solve for x text cfrac x 5 4 x 5x 4 Identify the operations that are being applied to the unknown variable Looking at the left hand side of the equation the x x is divided by 5 5 2 Apply the inverse operations one at a time to both sides of the equation
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Equations With Fractions Example 1 Watch on Hopefully you were able to follow that example I know it s tough but if you can get rid of the fraction it will make these problems so much easier Keep going you ll get the hang of
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May 28 2023 0183 32 For any real numbers a b and c if a b then ac bc When you add subtract multiply or divide the same quantity from both sides of an equation you still have equality In the next few examples we ll translate sentences into equations and then solve the
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Aug 15 2020 0183 32 Example 1 Solve for x x frac 5 6 frac 1 3 Solution To undo subtracting 5 6 add 5 6 to both sides of the equation and simplify
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The general rule for solving equations with fractions whether it be only on one side or both is to try to get rid of all of them The most common way to find the lowest common multiple LCM of all of the fractions and then multiply
We can solve linear equations with fractions with the following steps Step 1 Remove the fractions We multiply the entire equation by the least common multiple to remove the fractions Step 2 Simplify We remove the parentheses and other grouping signs and combine like terms How to Solve Equations with Fraction Coefficients Solve 1 6 y 1 3 5 6 Try It 2 95 Solve 1 4 x 1 2 5 8 Try It 2 96 Solve 1 8 x 1 2 1 4 Notice in Example 2 48 once we cleared the equation of fractions the equation was like those we solved earlier in this chapter We changed the problem to one we already knew how to solve
Equations involving one fraction Example Question Equations with fractions on both sides Example Question Practise solving equations using fractions Quiz Game Divided