1. Warm Up Solve. 1. x – 3 = 11 2. 18 = x + 4 3. = 42 4. 2x = 52 5. x – 82 = 172 x = 14 Course 1 3-9 Solving Decimal Equations x 7 x = 14 x = 294 x = 26 x = 254

2. Learn to solve equations involving decimals. Course 1 3-9 Solving Decimal Equations

3. Course 1 3-9 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

4. Course 1 3-9 Solving Decimal Equations Use inverse operations to get the variable alone on one side of the equation. Remember!

5. Course 1 3-9 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.

6. Course 1 3-9 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

7. Course 1 3-9 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 ?

8. Course 1 3-9 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.

9. Course 1 3-9 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.

10. 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? Insert Lesson Title Here Course 1 3-9 Solving Decimal Equations x 4 x = 18.1 x = 33.2 x = 21.1 x = 6.8 8.5 m

11. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Learn to solve equations by multiplying and dividing fractions.

12. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Dividing by a number is the same as multiplying by its reciprocal. Remember!

13. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Additional Example 1A: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. j = 25 3 5 __ j ÷ = 25 ÷ 3 5 __ 3 5 3 5 j = 25 3 5 __ 5 3 5 3 j = j = 25 5 1 3 _____ j = 25 5 3 __ j =, or 41 125 3 ___ 2 3 __ Divide both sides of the equation by. 3 5 __ Multiply by, the reciprocal of. 3 5 __ 5 3

14. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Additional Example 1B: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. 7x = 2 5 __ 7x 1 __ 2 5 1 7 1 7 = x = 2 1 5 7 ____ x = 2 35 __ Multiply both sides by the reciprocal of 7. The answer is in simplest form.

15. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Additional Example 1C: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. = 6 5y5y 8 __ 5y 8 __ 6 1 5 8 5 8 ÷ = ÷ y =, or 9 48 5 __ Divide both sides by. 5 8 __ 5y 8 __ 6 1 8 5 8 5 = 3 5 5 8 Multiply by the reciprocal of. __

16. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Check It Out: Example 1A Solve each equation. Write the answer in simplest form. j = 19 3 4 __ j ÷ = 19 ÷ 3 4 __ 3 4 3 4 j = 19 __ 3 4 4 3 4 3 j = j = 19 4 1 3 _____ 4 j = 19 3 __ 76 ___ 1 3 j =, or 25 3 __ Divide both sides of the equation by. 3 4 __ Multiply by, the reciprocal of. 3 4 __ 4 3

17. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Check It Out: Example 1B Solve each equation. Write the answer in simplest form. 3x = 1 7 __ 3x 1 __ 1 7 1 3 1 3 = x = 1 7 3 ____ x = 1 21 __ Multiply both sides by the reciprocal of 3. The answer is in simplest form.

18. Course 1 5-10 Solving Fraction Equations: Multiplication and Division Lesson Quiz Solve each equation. Write the answer in simplest form. 1. 3x = 2. x = 4 3. x = 14 4. = 9 5. Rebecca used 3 pt of paint to paint of the trim in her bedroom. How many pints will Rebecca use for the trim in the entire bedroom? 1 8 __ 1 4 3 7 y 7 1 4 x = 16 1 24 __ x = 98 3 __ 2 3 x = or 32 y = 63 12