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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)

Today’s Learning Goal Assignment Learn to solve equations involving decimals. Course Solving Decimal Equations

6 th Grade Math HW Page 136 #9-20 all Course Solving Decimal Equations

3-10 Solving Decimal Equations Course 1 Warm up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Warm Up Solve. 1. x – 3 = = x = x = x – 82 = 172 x = 14 Course Solving Decimal Equations x 7 x = 14 x = 294 x = 26 x = 254

Problem of the Day Find the missing entries in the magic square is the sum of every row, column, and diagonal. 3 Course Solving Decimal Equations

Today’s Learning Goal Assignment Learn to solve equations involving decimals. Course Solving Decimal Equations

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

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

Course 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 = is subtracted from k. Add 6.2 to both sides to undo the subtraction k = 15.7 Check k – 6.2 = 9.5 Substitute 15.7 for k in the equation – 6.2 = 9.5 ? 9.5 = 9.5 ? 15.7 is the solution.

Course Solving Decimal Equations Additional Example 1B: Solving One-Step Equations with Decimals Solve the equation. Check your answer. B. 6k = 7.2 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

Course Solving Decimal Equations Additional Example 1C: Solving One-Step Equations with Decimals Solve the equation. Check your answer. C. = 0.6 = 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 ?

Course Solving Decimal Equations Try This: Example 1A Solve the equation. Check your answer. A. n – 3.7 = 8.6 n – 3.7 = is subtracted from n. Add 3.7 to both sides to undo the subtraction n = 12.3 Check n – 3.7 = 8.6 Substitute 12.3 for n in the equation – 3.7 = 8.6 ? 8.6 = 8.6 ? 12.3 is the solution.

Course Solving Decimal Equations Try This: Example 1B Solve the equation. Check your answer. B. 7h = 8.4 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

Course Solving Decimal Equations Try This: Example 1C Solve the equation. Check your answer. C. = 0.3 = 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 ?

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

Course Solving Decimal Equations Additional Example 2A: Measurement Application Solve the equation. Check your answer. A. The area of Emily’s floor is m 2. If its length is 4.5 meters, what is its width? = 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 · w area = length · width = 4.5w The width of Emily’s floor is 7.5 meters.

Course 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? Let C be the total cost. Write the equation for the problem. Multiply.C = C = · 23 total cost = area · cost of carpet per square meter The cost of carpeting the floor is $

Course Solving Decimal Equations Try This: Example 2A Solve the equation. Check your answer. A. The area of Yvonne’s bedroom is ft 2. If its length is 12.5 feet, what is its width? = 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 = w = 12.5 · w area = length · width = 12.5w The width of Yvonne’s bedroom is 14.5 feet.

Course 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? Let C be the total cost. Write the equation for the problem. Multiply.C = 725 C = · 4 total cost = area · cost of carpet per square foot The cost of carpeting the bedroom is $725.

Lesson Quiz Solve each equation. Check your answer. 1. x – 3.9 = = x – 4.9 = x = 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? Insert Lesson Title Here Course Solving Decimal Equations x 4 x = 18.1 x = 33.2 x = 21.1 x = m