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HW # 23 - Rational Numbers worksheet

Week 6, Day Three. HW # 23 - Rational Numbers worksheet Study for QUIZ 2-1 to 2- 6 (review last night’s HW) Warm up. Is the statement below true or false? Explain how you arrived at your conclusion. My number and your number are both divisible

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HW # 23 - Rational Numbers worksheet

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  1. Week 6, Day Three HW # 23- Rational Numbers worksheet Study for QUIZ2-1 to 2-6 (review last night’s HW) Warm up Is the statement below true or false? Explain how you arrived at your conclusion. My number and your number are both divisible by 8. Therefore, the sum of our numbers will be divisible by 4.

  2. Warm Up Response If my number is divisible by 8, then 8 is a factor of my number. Since 4 is a factor of 8, my number would also be divisible by 4. 3. The same would be true for your number. Therefore, even if I add the numbers together, 4 would remain a factor of the sum. EX: 16 + 32 = 48 which is divisible by 4 (and 8)

  3. Homework Check You should have checked your answers online last night. PLEASE be sure that you do this. If you did not get a majority of the problems correct, fill out a Hall Pass in your Panther Planner and come see me! There is a quiz on Day Four!

  4. Goals for Today • Mystery Numbers • Solving Equations • (both single and multi-step)

  5. Mystery Numbers Each group has a different statement. Decide if the statement is TRUE or FALSE. Prove your answer. Be sure to use complete sentences and math vocabulary.

  6. 3 4 2 3 3 8 d 3 5 5 12 = 2 j = –15 4 1 y = 2 5 15 1 d = 9 2 2-7 Lesson Quiz Solve. 1.x – 23.3 = 17.8 2.j + = –14 x = 41.1 4. 3. 9y = Include an explanation of why you did what you did for #4. 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

  7. 2-7 EXTRA PRACTICE EXAMPLES

  8. – 4.6 –4.6 = 4.4 m Remember! 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. Additional Examples 1A: Solving Equations with Decimals Solve. m + 4.6 = 9 m + 4.6 = 9 Since 4.6 is added to m, subtract 4.6 from both sides to undo the addition.

  9. –32.8 8.2 8.2p 8.2 = p = –4 Additional Examples 1B: Solving Equations with Decimals Solve. 8.2p = –32.8 Since p is multiplied by 8.2, divide both sides by 8.2.

  10. x 1.2 = 15 x 1.2 = 1.2 •15 1.2 • Additional Examples 1C: Solving Equations with Decimals Solve. Since x is divided by 1.2, multiply both sides by 1.2. x = 18

  11. 75.9 5.5 5.55.5 b = –9.1 –9.1 = 13.8 b = = –6.1 m Check It Out! Example 1 Solve. A. m + 9.1 = 3 Since 9.1 is added to m, subtract 9.1 from both sides to undo the addition. m + 9.1 = 3 B. 5.5b = 75.9 Since b is multiplied by 5.5, divide both sides by 5.5.

  12. y 4.5 = 4.5 •90 4.5 • Check It Out! Example 1C Solve. y 4.5 = 90 C. Since y is divided by 4.5, multiply both sides by 4.5. y = 405

  13. 3 7 2 7 n + = – 5 7 n = – 2 7 2 7 3 7 2 7 n + – = – – Since is added to n, subtract from both sides. 27 2 7 Additional Example 2A: Solving Equations with Fractions Solve.

  14. Since is subtracted from y, add to both sides. 1 6 1 6 2 3 1 6 1 6 1 6 y – = + + 5 6 y = 4 6 1 6 y = + Additional Example 2B: Solving Equations with Fractions Solve. 1 6 2 3 y – = Find a common denominator, 6.

  15. Since x is multiplied by , divide both sides by . 5 6 5 8 5 6 5 6 x 5 6 5 6 ÷ = ÷ 6 5 5 8 5 6 6 5 • = x • 3 4 = x Additional Example 2C: Solving Equations with Fractions Solve. 5 8 5 6 x = 1 1 1 3 Multiply by the reciprocal. Simplify. 4 1 1 1

  16. 6 9 2 3 n = – n = – 1 9 1 9 5 9 1 9 n + – = – – Since is added to n, subtract from both sides. 19 1 9 Check It Out! Example 2A Solve. 5 9 1 9 n + = – Simplify.

  17. 1 2 3 4 y – = Since is subtracted from y, add to both sides. 1 2 1 2 3 4 1 2 1 2 1 2 y – = + + 5 4 y = 3 4 2 4 y = + 1 4 y = 1 Check It Out! Example 2B Solve. Find a common denominator, 4. Simplify.

  18. Since x is multiplied by , divide both sides by . 3 8 3 4 3 8 3 8 x 3 8 3 8 ÷ = ÷ 8 3 3 4 3 8 8 3 • = x • Check It Out! Example 2C Solve. 3 4 3 8 x = 1 1 1 2 Multiply by the reciprocal. Simplify. 1 1 1 1 x = 2

  19. 2 3 Rick’s car holds the amount of gasoline as his wife’s van. If the car’s gas tank can hold 24 gallons of gasoline, how much gasoline can the tank in the minivan hold? 2 3 24 Check It Out! Example 3 Write an equation: Capacity of car’s tank Capacity of minivan’s tank 2/3 • = g • =

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