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Turn in Your CHOP CHOP Corrections! • Make sure you have the proper heading • Make sure you have titled your paperChop Chop Corrections • Make sure you staple your corrections ON TOP of your Chop Chop Quiz Student Progress Chart Lesson Reflection 3-10 Math Learning Goal Students will understand decimals. Students will understand decimals by being able to do the following: • Learn to write, compare, and order decimals using place value and number lines (3-1) • Learn to estimate decimal sums, differences, products, and quotients (3-2) • Learn to add and subtract decimals (3-3) • Learn to multiply and divide decimals by powers of ten and to convert metric measurements (3-4) • Learn to write large numbers in scientific notation (3-5) • Learn to multiply decimals by whole numbers and by decimals (3-6) • Learn to divide decimals by whole numbers (3-7) • Learn to divide whole numbers and decimals by decimals (3-8) • Learn to solve problems by interpreting the quotient (3-9) • Learn to solve equations involving decimals (3-10) 3-10 Solving Decimal Equations Today’s Learning Goal Assignment Learn to solve equations involving decimals. Course 1 3-10 Solving Decimal Equations th 6 Grade Math HW Page 136 #9-20 all Course 1 3-10 Solving Decimal Equations Warm up Problem of the Day Lesson Presentation Course 1 3-10 Solving Decimal Equations Warm Up Solve. 1. x – 3 = 11 x = 14 2. 18 = x + 4 x = 14 3. x = 42 x = 294 4. 2x = 52 x = 26 5. x – 82 = 172 x = 254 7 Course 1 3-10 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 6.75 1.5 2.25 3.75 5.25 6 Course 1 0.75 4.5 3-10 Solving Decimal Equations Today’s Learning Goal Assignment Learn to solve equations involving decimals. Course 1 3-10 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 –$45.20 m = $24.75 Course 1 3-10 Solving Decimal Equations Remember! Use inverse operations to get the variable alone on one side of the equation. Course 1 3-10 Solving Decimal Equations Additional Example 1A: Solving One-Step Equations with Decimals Solve the equation. Check your answer. A. k – 6.2 = 9.5 k – 6.2 = 9.5 + 6.2 + 6.2 k = 15.7 Check k – 6.2 = 9.5 ? 15.7 – 6.2 = 9.5 ? 9.5 = 9.5 Course 1 6.2 is subtracted from k. Add 6.2 to both sides to undo the subtraction. Substitute 15.7 for k in the equation. 15.7 is the solution. 3-10 Solving Decimal Equations Additional Example 1B: Solving One-Step Equations with Decimals Solve the equation. Check your answer. B. 6k = 7.2 k is multiplied by 6. 6k = 7.2 Divide both sides by 6 to 6k = 7.2 undo the multiplication. 6 6 k = 1.2 Check 6k = 7.2 ? 6(1.2) = 7.2 ? 7.2 = 7.2 Course 1 Substitute 1.2 for k in the equation. 1.2 is the solution. 3-10 Solving Decimal Equations Additional Example 1C: Solving One-Step Equations with Decimals Solve the equation. Check your answer. m C. = 0.6 m is divided by 7. 7 m Multiply both sides by 7 · 7 = 0.6 · 7 7 to undo the division. m = 4.2 Check m = 0.6 7 4.2 ? = 0.6 7 ? 0.6 = 0.6 Course 1 Substitute 4.2 for m in the equation. 4.2 is the solution. 3-10 Solving Decimal Equations Try This: Example 1A Solve the equation. Check your answer. A. n – 3.7 = 8.6 n – 3.7 = 8.6 + 3.7 + 3.7 n = 12.3 Check n – 3.7 = 8.6 ? 12.3 – 3.7 = 8.6 ? 8.6 = 8.6 Course 1 3.7 is subtracted from n. Add 3.7 to both sides to undo the subtraction. Substitute 12.3 for n in the equation. 12.3 is the solution. 3-10 Solving Decimal Equations Try This: Example 1B Solve the equation. Check your answer. B. 7h = 8.4 7h = 8.4 7h = 8.4 7 7 h = 1.2 h is multiplied by 7. Divide both sides by 7 to undo the multiplication. Check 7h = 8.4 ? 7(1.2) = 8.4 ? 8.4 = 8.4 Course 1 Substitute 1.2 for h in the equation. 1.2 is the solution. 3-10 Solving Decimal Equations Try This: Example 1C Solve the equation. Check your answer. w C. = 0.3 9 w · 9 = 0.3 · 9 9 w = 2.7 Check w = 0.3 9 2.7 ? = 0.3 9 ? 0.3 = 0.3 Course 1 w is divided by 9. Multiply both sides by 9 to undo the division. Substitute 2.7 for w in the equation. 2.7 is the solution. 3-10 Solving Decimal Equations Remember! The area of a rectangle is its length times its width. w l A = lw Course 1 3-10 Solving Decimal Equations Additional Example 2A: Measurement Application Solve the equation. Check your answer. A. The area of Emily’s floor is 33.75 m2. If its length is 4.5 meters, what is its width? area = length · width 33.75 = 4.5 · w 33.75 = 4.5w Write the equation for the problem. Let w be the width of the room. 33.75 = 4.5w 4.5 4.5 7.5 = w Divide both sides by 4.5 to undo the multiplication. The width of Emily’s floor is 7.5 meters. Course 1 3-10 Solving Decimal Equations Additional Example 2B: Measurement Application Solve the equation. Check your answer. B. If carpet costs $23 per square meter, what is the total cost to carpet the floor? total cost = area · cost of carpet per square meter C = 33.75 · 23 Let C be the total cost. Write the equation for the problem. C = 776.25 Multiply. The cost of carpeting the floor is $776.25. Course 1 3-10 Solving Decimal Equations Try This: Example 2A Solve the equation. Check your answer. A. The area of Yvonne’s bedroom is 181.25 ft2. If its length is 12.5 feet, what is its width? area = length · width 181.25 = 12.5 · w 181.25 = 12.5w Write the equation for the problem. Let w be the width of the room. 181.25 = 12.5w 12.5 12.5 14.5 = w Divide both sides by 12.5 to undo the multiplication. The width of Yvonne’s bedroom is 14.5 feet. Course 1 3-10 Solving Decimal Equations Try This: Example 2B Solve the equation. Check your answer. B. If carpet costs $4 per square foot, what is the total cost to carpet the bedroom? total cost = area · cost of carpet per square foot C = 181.25 · 4 Let C be the total cost. Write the equation for the problem. C = 725 Multiply. The cost of carpeting the bedroom is $725. Course 1 3-10 Solving Insert Decimal Lesson Equations Title Here Lesson Quiz Solve each equation. Check your answer. 1. x – 3.9 = 14.2 x = 18.1 2. x = 8.3 4 3. x – 4.9 = 16.2 x = 33.2 4. 7x = 47.6 x = 6.8 x = 21.1 5. The area of the floor in Devon’s room is 35.7 m2. If the width is 4.2 m, what is the length of the bedroom? 8.5 m Course 1