Solving Equations by Adding or Subtracting Decimals

1. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 (For help, go to Skills Handbook page 730.) Simplify. 1. 2.8 + 7.06 2. 0.65 + 1.8 3. 4.52 – 2.48 4. 3.7 – 0.62 Check Skills You’ll Need 3-5

2. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Solutions 1. 2.80 2. 0.65 + 7.06 + 1.80 9.86 2.45 3. 4.52 4. 3.70 – 2.48 – 0.62 2.04 3.08 3-5

3. 6.8 – 6.8 + p = –9.7 – 6.8 Subtract 6.8 from each side. p = –16.5 Simplify. Check 6.8 + p = –9.7 Replace p with –16.5. 6.8 + (–16.5) –9.7 –9.7 = –9.7 Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Solve 6.8 + p = –9.7. 6.8 + p = –9.7 Quick Check 3-5

4. x + 8.75 – 8.75 = 14.5 – 8.75 Subtract 8.75 from each side. x = 5.75 Simplify. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Ping has a board that is 14.5 ft long. She saws off a piece that is 8.75 ft long. Use the diagram below to find the length of the piece that is left. x + 8.75 = 14.5 The length of the piece that is left is 5.75 ft. Quick Check 3-5

5. –23.34 + 16.99 = q – 16.99 + 16.99 Add 16.99 to each side. –6.35 = q Simplify. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Solve –23.34 = q – 16.99. –23.34 = q – 16.99 Quick Check 3-5

6. Words previous balance minus check is new balance Let p = previous balance. Equation p – $49.98 = $169.45   p – 49.98 + 49.98 = 169.45 + 49.98 Add 49.98 to each side. p = 219.43 Simplify. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Quick Check Alejandro wrote a check for $49.98. His new account balance is $169.45. What was his previous balance? p – 49.98 = 169.45 Alejandro had $219.43 in his account before he wrote the check. 3-5

7. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Solve each equation. 1.a + 10 = 7.9 2. –1.01 = c – 9 3.s – (–2.6) = 1.6 4. 3.02 + d = 2.91 5. –23.7 = 13.3 + g – 2.1 7.99 – 1 – 0.11 – 37 3-5

8. daily milk consumption numberof days Words times is 250 gallons Let x = number of days. 250 x Equation • = 85.8 Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 Every day the school cafeteria uses about 85.8 gallons of milk. About how many days will it take for the cafeteria to use the 250 gallons in the refrigerator? 3-6

9. 85.8x 85.8 250 85.8 = Divide each side by 85.8. x = 2.914 . . . Simplify. x 3 Round to the nearest whole number. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 (continued) 85.8x = 250 The school will take about 3 days to use 250 gallons of milk. Quick Check 3-6

10. –37.5 = Multiply each side by –1.2. –37.5(–1.2) = (–1.2) 45 = c Simplify. c –1.2 c –1.2 c –1.2 Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 Solve –37.5 = . Quick Check 3-6

11. a = h n h n h 15 0.133 = Replace a with 0.133 and n with 15. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 A little league player was at bat 15 times and had a batting average of 0.133 (rounded to the nearest thousandth). The batting average formula is a = , where a is the batting average, h is the number of hits, and n is the number of times at bat. Use the formula to find the number of hits she made. 3-6

12. 0.133(15) = (15) Multiply each side by 15. Simplify. 1.995 = h 2 h Since h (hits) represents an integer, round to the nearest integer. h 15 Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 (continued) The little league player made 2 hits. Quick Check 3-6

13. p –2.5 Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 Solve each equation. 1. 9b = –30.6 2. –10.8 = 3. 2.45 = –0.7k4. = 240 5.y ÷ (–0.3) = 146.7 –3.4 27 t 3.7 –3.5 888 – 44.01 3-6