3-6 Warm Up Problem of the Day Lesson Presentation Solving Equations with Rational Numbers Warm Up Problem of the Day Lesson Presentation Pre-Algebra

3-6 Warm Up Add or subtract. 7 10 5 10 1 5 1. + 3 8 5 16 1 16 2. 2 – 1 Pre-Algebra 3-6 Solving Equations with Rational Numbers 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

Problem of the Day A computer word is made of strings of 0’s and 1’s. How many different words can be formed using 8 characters? (An example is 01010101.) 256

Learn to solve equations with rational numbers.

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

A. B. Solve. m + 9.1 = 3 m + 9.1 = 3 Subtract 9.1 from both sides. Try This: 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. Try This: Examples 1C y 4.5 = 90 y 4.5 = 4.5 • 90 4.5 • Multiply both sides by 4.5 y = 405

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

Additional Examples 2B: Solving Equations with Fractions Solve. 1 6 2 3 B. 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 Examples 2C: Solving Equations with Fractions Solve. 5 6 5 8 C. x = 3 5 6 = 5 8 x 6 5 • Multiply both sides by . 6 5 4 x = 3 4 Simplify.

Solve. A. Try This: 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. B. Try This: 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. C. Try This: Examples 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.

– = – = Original amount of milk Milk for casserole Milk for cereal Additional Examples 3: Solving Word Problems Using Equations Mr. Rios wants to prepare a casserole that requires 2 cups of milk. If he makes the casserole, he will have only cup of milk left for his breakfast cereal. How much milk does Mr. Rios have? 1 2 3 4 5 2 2(2)+1 2 = 1 2 2 Convert fractions: Write an equation: Original amount of milk Milk for casserole Milk for cereal – = 5 2 3 4 – = c

Additional Examples 3 Continued Now solve the equation. 5 2 3 4 c – = 5 2 = c – + 3 4 Add to both sides. 5 2 3 4 c = + 10 4 Find a common denominator, 4. 13 4 1 4 3 , or c = Simplify. Mr. Rios has 3 cups of milk. 1 4

Ratio of car’s tank to van’s tank Try This: Examples 3 Rick’s car holds the amount of gasoline as his wife’s van. If the car’s gas tank can hold 15.5 gallons of gasoline, how much gasoline can the tank in the minivan hold? 2 3 Convert decimal to a fraction: 15.5 = 15 = = 1 2 15(2)+1 31 Write an equation: Van’s gas tank Ratio of car’s tank to van’s tank Capacity of car’s tank • = 2 3 31 2 g • =

Try This: Examples 3 Continued Now solve the equation. 2 3 31 2 g • = Multiply both sides by . 3 2 31 2 2 3 = g • 3 2 g = 93 4 Simplify. 1 4 g = 23 The van’s gas tank holds 23 gallons of gasoline. 1 4

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 2 5. Tamara had 6 bags of mulch for her garden. Each bag contained 8 lb of mulch. What was the total weight of the mulch? 1 3 50 lb