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

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. 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. 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. = 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 Additional Example 2A: Measurement Application 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 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 $

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

Course Solving Fraction Equations: Multiplication and Division Learn to solve equations by multiplying and dividing fractions.

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

Course 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 = __ j ÷ = 25 ÷ 3 5 __ j = __ j = j = _____ j = __ j =, or ___ 2 3 __ Divide both sides of the equation by. 3 5 __ Multiply by, the reciprocal of. 3 5 __ 5 3

Course 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 __ = x = ____ x = 2 35 __ Multiply both sides by the reciprocal of 7. The answer is in simplest form.

Course 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 __ ÷ = ÷ y =, or __ Divide both sides by. 5 8 __ 5y 8 __ = Multiply by the reciprocal of. __

Course Solving Fraction Equations: Multiplication and Division Check It Out: Example 1A Solve each equation. Write the answer in simplest form. j = __ j ÷ = 19 ÷ 3 4 __ j = 19 __ j = j = _____ 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

Course 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 __ = x = ____ x = 1 21 __ Multiply both sides by the reciprocal of 3. The answer is in simplest form.

Course Solving Fraction Equations: Multiplication and Division Lesson Quiz Solve each equation. Write the answer in simplest form. 1. 3x = 2. x = 4 3. x = = 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 __ y x = __ x = 98 3 __ 2 3 x = or 32 y = 63 12