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3-8 Solving Decimal Equations Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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3-8 Solving Decimal Equations Warm Up Solve. 1. x – 3 = 11 2. 18 = x + 4 3. = 42 4. 2x = 52 5. x – 82 = 172 x = 14 x 7 x = 294 x = 26 x = 254

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3-8 Solving Decimal Equations Problem of the Day Find the missing entries in the magic square. 11.25 is the sum of every row, column, and diagonal. 3 3.755.25 6 6.75 1.5 2.25 0.754.5

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3-8 Solving Decimal Equations I can solve equations involving decimals.

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3-8 Solving Decimal Equations You can solve equations with decimals using inverse operations just as you solved equations with whole numbers. $45.20 + m = $69.95 –$45.20 m = $24.75

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3-8 Solving Decimal Equations Use inverse operations to get the variable alone on one side of the equation. Remember!

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3-8 Solving Decimal Equations Additional Example 1A: Solving One-Step Equations with Decimals Solve the equation. Check your answer. k – 6.2 = 9.5 6.2 is subtracted from k. Add 6.2 to both sides to undo the subtraction. + 6.2 k = 15.7 Check k – 6.2 = 9.5 Substitute 15.7 for k in the equation. 15.7 – 6.2 = 9.5 ? 9.5 = 9.5 ? 15.7 is the solution.

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3-8 Solving Decimal Equations Additional Example 1B: Solving One-Step Equations with Decimals Solve the equation. Check your answer. 6k = 7.2 k is multiplied by 6. Divide both sides by 6 to undo the multiplication. k = 1.2 Check 6k = 7.2 Substitute 1.2 for k in the equation. 6(1.2) = 7.2 ? 7.2 = 7.2 ? 1.2 is the solution. 66 6k = 7.2

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3-8 Solving Decimal Equations Additional Example 1C: Solving One-Step Equations with Decimals Solve the equation. Check your answer. = 0.6 m is divided by 7. Multiply both sides by 7 to undo the division. m = 4.2 Check Substitute 4.2 for m in the equation. 0.6 = 0.6 ? 4.2 is the solution. · 7 m 7 m 7 = 0.6 m 7 4.2 7 ?

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3-8 Solving Decimal Equations Check It Out: Example 1A Solve the equation. Check your answer. n – 3.7 = 8.6 3.7 is subtracted from n. Add 3.7 to both sides to undo the subtraction. + 3.7 n = 12.3 Check n – 3.7 = 8.6 Substitute 12.3 for n in the equation. 12.3 – 3.7 = 8.6 ? 8.6 = 8.6 ? 12.3 is the solution.

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3-8 Solving Decimal Equations Check It Out: Example 1B Solve the equation. Check your answer. 7h = 8.4 h is multiplied by 7. Divide both sides by 7 to undo the multiplication. h = 1.2 Check 7h = 8.4 Substitute 1.2 for h in the equation. 7(1.2) = 8.4 ? 8.4 = 8.4 ? 1.2 is the solution. 77 7h = 8.4

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3-8 Solving Decimal Equations Check It Out: Example 1C Solve the equation. Check your answer. = 0.3 w is divided by 9. Multiply both sides by 9 to undo the division. w = 2.7 Check Substitute 2.7 for w in the equation. 0.3 = 0.3 ? 2.7 is the solution. · 9 w 9 w 9 = 0.3 w 9 2.7 9 ?

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3-8 Solving Decimal Equations The area of a rectangle is its length times its width. A = lw Remember! w l

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3-8 Solving Decimal Equations Additional Example 2A: Measurement Application The area of Emily’s floor is 33.75 m 2. If its length is 4.5 meters, what is its width? 33.75 = 4.5w Write the equation for the problem. Let w be the width of the room. Divide both sides by 4.5 to undo the multiplication. 7.5 = w 4.5 33.75 = 4.5 · w area = length · width 33.75 = 4.5w The width of Emily’s floor is 7.5 meters.

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3-8 Solving Decimal Equations Additional Example 2B: Measurement Application If carpet costs $23 per square meter, what is the total cost to carpet the floor? Let C be the total cost. Write the equation for the problem. Multiply.C = 776.25 C = 33.75 · 23 total cost = area · cost of carpet per square meter The cost of carpeting the floor is $776.25.

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3-8 Solving Decimal Equations Check It Out: Example 2A The area of Yvonne’s bedroom is 181.25 ft 2. If its length is 12.5 feet, what is its width? 181.25 = 12.5w Write the equation for the problem. Let w be the width of the room. Divide both sides by 12.5 to undo the multiplication. 14.5 = w 12.5 181.25 = 12.5 · w area = length · width 181.25 = 12.5w The width of Yvonne’s bedroom is 14.5 feet.

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3-8 Solving Decimal Equations Check It Out: Example 2B If carpet costs $4 per square foot, what is the total cost to carpet the bedroom? Let C be the total cost. Write the equation for the problem. Multiply.C = 725 C = 181.25 · 4 total cost = area · cost of carpet per square foot The cost of carpeting the bedroom is $725.

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3-8 Solving Decimal Equations Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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3-8 Solving Decimal Equations Lesson Quiz Solve each equation. Check your answer. 1. x – 3.9 = 14.2 2. = 8.3 3. x – 4.9 = 16.2 4. 7x = 47.6 5. The area of the floor in Devon’s room is 35.7 m 2. If the width is 4.2 m, what is the length of the bedroom? x 4 x = 18.1 x = 33.2 x = 21.1 x = 6.8 8.5 m

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3-8 Solving Decimal Equations 1. Solve the equation. m – 8.7 = 17.8 A. m = 9.1 B. m = 25.5 C. m = 26.5 D. m = 27 Lesson Quiz for Student Response Systems

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3-8 Solving Decimal Equations 2. Solve the equation. A. q = 36.6 B. q = 33.6 C. q = 30.6 D. q = 11.6 Lesson Quiz for Student Response Systems q6q6 = 5.6

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3-8 Solving Decimal Equations 3. Solve the equation. s – 9.9 = 18.7 A. s = 28.6 B. s = 27.9 C. s = 27.7 D. s = 8.8 Lesson Quiz for Student Response Systems

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3-8 Solving Decimal Equations 4. Solve the equation. 8u = 73.6 A. u = 5.8 B. u = 9.2 C. u = 65.6 D. u = 81.8 Lesson Quiz for Student Response Systems

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3-8 Solving Decimal Equations 5. Laura bought 9.7 yards of fabric for $76.63. What is the cost per yard? A. $9.90 B. $9.70 C. $7.90 D. $7.70 Lesson Quiz for Student Response Systems

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