Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Warm Up Simplify Write each decimal as a fraction in simplest form – – 11 50

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. California Standards

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers A (–1.2) Think: Find the difference of |1.2| and |3|. 0.9 Add or subtract. Additional Example 1: Adding and Subtracting Decimals – 1.2 is greater than 0.3; use the sign of 1.2. B – 4.39 Line up the decimal points. Use a zero as a placeholder. – Subtract.

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers A Line up the decimal points Add or subtract. Check It Out! Example Add. B – 3.29 Line up the decimal points. Use a zero as a placeholder. – Subtract.

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers In August 2001, at the World University Games in Beijing, China, Jimyria Hicks ran the 200-meter dash in seconds. Her best time at the U.S. Senior National Meet in June of the same year was seconds. How much faster did she run in June? She ran 0.73 second faster in June – Line up the decimal points. Additional Example 2: Sports Application

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Tom ran the 100-meter dash in 11.5 seconds last year. This year he improved his time by seconds. How fast did Tom run the 100-meter dash this year? Check It Out! Example 2 Tom ran the 100-meter dash in seconds this year. Subtract from 11.5 to determine the new time – Add two zeros so the decimals align. 00

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Remember! Subtracting a number is the same as adding its opposite.

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Additional Example 3: Adding and Subtracting Fractions with Like Denominators Subtract numerators. Keep the denominator –– –– 5959 = – 7979 = – 3737 –2 – 5 9 = 6 + (–3) 7 = can be written as. – 3737 –3 7 Add or subtract. Write each answer in simplest form –3 7 A. B.

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers = – (–4) 9 = –4 9 Check It Out! Example 3 Subtract numerators. Keep the denominator –– –– 3535 = – 4545 –1 – 3 5 = Add or subtract. Write each answer in simplest form A. B. can be written as. – 4949 –4 9

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers 12.1 – x for x = –0.1 Substitute –0.1 for x – (–0.1) 12.2 Think: 12.1 – (–0.1) = Evaluate the expression for the given value of the variable. Additional Example 4A: Evaluating Expressions with Rational Numbers

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers 4545 = Add numerators, keep the denominator Simplify. + m for m = = Substitute 3 for m (10) = = Evaluate the expression for the given value of the variable. Additional Example 4B: Evaluating Expressions with Rational Numbers

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers 52.3 – y for y = –7.8 Substitute –7.8 for y – (–7.8) 60.1 Think: 52.3 – (–7.8) = Check It Out! Example 4A Evaluate the expression for the given value of the variable.

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Add numerators, keep the denominator Simplify. + m for m = = Substitute 5 for m (8) = = Check It Out! Example 4B Evaluate the expression for the given value of the variable = 6

Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Add or subtract. 1. – (–2.8) 7.2 – x for x = – – – 64.9 Lesson Quiz Evaluate – Sarah’s best broad jump is 1.6 meters, and Jill’s best is 1.47 meters. How much farther can Sarah jump than Jill? m