2-7 Warm Up Problem of the Day Lesson Presentation Solving Equations with Rational Numbers Course 3 Warm Up Problem of the Day Lesson Presentation

Warm Up Add or subtract. 7 10 5 10 1 5 1. + 3 8 5 16 1 16 2. 2 – 1 3. 4.8 + 3.6 8.4 4. 2.4 – 0.05 2.35

Learn to solve equations with rational numbers.

Additional Examples 1A: Solving Equations with Decimals. Solve. m + 4.6 = 9 m + 4.6 = 9 Subtract 4.6 from both sides. – 4.6 = 4.4 m = Once you have solved an equation it is a good idea to check your answer. To check your answer, substitute your answer for the variable in the original equation. Remember!

Additional Examples 1B: Solving Equations with Decimals Solve. 8.2p = –32.8 –32.8 8.2 8.2p 8.2 = Divide both sides by 8.2 –4 p =

Additional Examples 1C: Solving Equations with Decimals Solve. = 15 x 1.2 x 1.2 = 1.2 • 15 1.2 • Multiply both sides by 1.2 x = 18

Check It Out: Example 1A & 1B Solve. A. m + 9.1 = 3 m + 9.1 = 3 Subtract 9.1 from both sides. –9.1 = –6.1 m = B. 5.5b = 75.9 75.9 5.5 5.5 5.5 = b Divide both sides by 5.5 13.8 b =

C. Solve. Check It Out: Example 1C y 4.5 = 90 y 4.5 = 4.5 • 90 4.5 • Multiply both sides by 4.5 y = 405

Additional Example 2A: Solving Equations with Fractions Solve. 2 7 3 7 n + = – n – + = – – 2 7 3 7 27 Subtract from both sides. 2 7 n = – 5 7

Additional Example 2B: Solving Equations with Fractions Solve. 1 6 2 3 y – = 1 6 = 2 3 – + y Add to both sides. 1 6 = y 4 6 1 6 + Find a common denominator; 6. y = 5 6 Simplify.

Additional Example 2C: Solving Equations with Fractions Solve. 5 6 5 8 x = 3 5 6 = 5 8 x 6 5 • Multiply both sides by . 6 5 4 x = 3 4 Simplify.

Solve. Check It Out: Example 2A 1 9 5 9 n + = – Subtract from both sides. 1 9 n – + = – – 1 9 5 9 19 n = – 2 3 Simplify – . 6 9

Solve. Check It Out: Example 2B 1 2 3 4 y – = 1 2 = 3 4 – + y Add to both sides. 1 2 = y 3 4 2 4 + Find a common denominator; 4. y = 1 1 4 Simplify.

Solve. Check It Out: Example 2C 3 8 = 6 19 x 3 8 = 6 19 x 2 3 8 = 6 19 8 3 • Multiply both sides by . 8 3 1 x = 16 19 Simplify.

Lesson Quiz: Part 1 Solve. 1. x – 23.3 = 17.8 x = 41.1 2 3 3 4 j = –15 5 12 2. j + = –14 3 5 1 15 y = 3. 9y = d 3 8 1 2 d = 9 4. = 2 4

Lesson Quiz: Part II 2 5 5. Tamara can mow acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? 5 hours