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PRE-ALGEBRA

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Solving Equations by Adding and Subtracting Fractions (5-7)

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PRE-ALGEBRA Solving equations with fractions is just like solving equations with any rational numbers. You need to isolate the variable by undoing the addition and / or subtraction operations using the Addition and Subtraction Properties of Equality. Example: During the first week of January, a rain gauge collected in. of rain. By the end of January, the total rainfall was 2 in. How much rain fell after the first week in January? 1212 5858 How do you solve equations in that involve adding or subtracting fractions? Solving Equations by Adding and Subtracting Fractions (5-7)

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PRE-ALGEBRA One school recycles about of its waste paper. The student council set a goal of recycling of the school’s waste paper by the end of the year. By how much does the school need to increase its paper recycling to reach the goal? 1313 3434 Words plus is Let n = the increase. Equation + n = fraction school recycles the increase student goal 3434 1313 Solving Equations by Adding or Subtracting Fractions LESSON 5-7 Additional Examples

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PRE-ALGEBRA (continued) + n = 1313 3434 1313 – + n = – Subtract from each side. 1313 3434 1313 1313 n = Use 3 4 as the common denominator. 3 3 – 1 4 3 4 n = Use the Order of Operations. 9 – 4 12 n = Simplify. 5 12 To meet the student council goal, the school needs to recycle more of its waste paper. 5 12 Solving Equations by Adding or Subtracting Fractions LESSON 5-7 Additional Examples

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PRE-ALGEBRA (continued) Check:Is the answer reasonable? The present fraction of paper waste that is recycled plus the increase must equal the goal. Since + = + = =, the answer is reasonable. 9 12 1313 3434 5 12 4 12 5 12 Solving Equations by Adding or Subtracting Fractions LESSON 5-7 Additional Examples

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PRE-ALGEBRA Solve x – =. 2323 1919 x – + = +Add to each side. 2323 1919 2323 2323 2323 x – = 2323 1919 x = Use 9 as the common denominator. 1 + 6 9 x = Use the Order of Operations. 1 + 6 9 x = Simplify. 7979 Solving Equations by Adding or Subtracting Fractions LESSON 5-7 Additional Examples

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PRE-ALGEBRA Solve q – 6 = –1. 1212 3535 1212 q – 6 = – 1 3535 q = 4 Write as a mixed number. 9 10 3535 q – 6 + 6 = – 1 + 6Add 6 to each side. 1212 1212 1212 1212 6 10 5 10 q = – 1 + 6 Use 2 5 as the common denominator. Solving Equations by Adding or Subtracting Fractions LESSON 5-7 Additional Examples

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PRE-ALGEBRA Solve the following equations. 1. + s = 2.k + = 3.u – = 4.– + g = 5.x – 2 = –4 3737 13 21 2525 7979 1 12 3434 5 11 19 22 1313 4 15 4 21 17 45 5656 7 22 1 14 15 –1 Lesson Quiz Solving Equations by Adding or Subtracting Fractions LESSON 5-7

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