Solving Equations with Decimals and Fractions - Easy Guide

Welcome to our lesson on converting decimals to fractions!Decimals and fractions are just different ways to write the same numbers.Let's start with a simple example: converting zero point five to a fraction.For zero point seven five, we follow the same process, but move the decimal point two places.With zero point one two five, we move the decimal three places and simplify to one eighth.Here are some common decimal-to-fraction conversions you should memorize.And here are the general rules for converting any decimal to a fraction.Now it's your turn! Try converting zero point six to a fraction using these rules.In our next section, we'll learn how to use these conversions when solving equations.Keep these conversion patterns in mind as we move forward!When solving equations with both decimals and fractions, we follow three fundamental rules.Let's look at our first example: zero point five x plus three fourths equals two.To eliminate the fraction three fourths, we multiply every term by four.This gives us two x plus three equals eight.In our second example, we have one point two five x minus two fifths equals three.First, we convert one point two five to a fraction: one hundred twenty five over one hundred.Then multiply all terms by one hundred to eliminate the fractions.Our final example combines both decimal and fraction conversions: zero point eight x plus one half equals one point five.First, we convert all decimals to fractions.Then multiply everything by ten to eliminate the fractions.Let's solve this equation step by step: two point five x plus one-third equals four.To clear the fraction, we multiply every term by six, our least common denominator.Now we can solve for x by subtracting two from both sides and dividing by fifteen.Always check your answer by plugging it back into the original equation.Let's look at some common mistakes to avoid when solving these equations.Here's another example where students often make mistakes: zero point seven five x minus two-fifths equals three.A common mistake is forgetting to multiply all terms by the LCD. Here's what NOT to do:Instead, here's the correct approach, multiplying everything by five:Let's review the key points for solving equations with mixed numbers.Thanks for learning equation solving techniques with Spark.E!