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Transcript
3-9 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 3-9 Solving Decimal Equations Learn to solve equations involving decimals. 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 –$45.20 m = $24.75 Course 1 3-9 Solving Decimal Equations Remember! Use inverse operations to get the variable alone on one side of the equation. 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 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. 3-9 Solving Decimal Equations Additional Example 1B: Solving One-Step Equations with Decimals Solve the equation. Check your answer. 6k = 7.2 6k = 7.2 6k = 7.2 6 6 k = 1.2 k is multiplied by 6. Divide both sides by 6 to undo the multiplication. 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. 3-9 Solving Decimal Equations Additional Example 1C: Solving One-Step Equations with Decimals Solve the equation. Check your answer. m = 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. 3-9 Solving Decimal Equations Additional Example 2A: Measurement Application 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 3-9 Solving Decimal Equations Additional Example 2B: Measurement Application If carpet costs $23 per square meter, what is the total cost to carpet the floor? 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 3-9 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 Solving Fraction Equations: 5-10 Multiplication and Division Learn to solve equations by multiplying and dividing fractions. Course 1 Solving Fraction Equations: 5-10 Multiplication and Division Remember! Dividing by a number is the same as multiplying by its reciprocal. Course 1 Solving Fraction Equations: 5-10 Multiplication and Division Additional Example 1A: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. 3 __ j = 25 5 3 3 3 __ j ÷ __ = 25 ÷ __ 5 5 5 3 Divide both sides of the equation by __ . 5 3 __ j• 5 3 5 Multiply by __, the reciprocal of __. 5 3 5 5 __ __ = 25 • 3 3 5 j = 25 • __ 3 25 • 5 j = _____ 1•3 125 2 j = ___, or 41 __ 3 3 Course 1 Solving Fraction Equations: 5-10 Multiplication and Division Additional Example 1B: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. 2 7x = __ 5 1 2 7x 1 __ • __ = __ • __ 7 5 1 7 Multiply both sides by the reciprocal of 7. 2•1 x = ____ 5•7 2 __ x= 35 Course 1 The answer is in simplest form. Solving Fraction Equations: 5-10 Multiplication and Division Additional Example 1C: Solving Equations by Multiplying and Dividing Solve each equation. Write the answer in simplest form. 5y __ = 6 8 5 6 5y 5 __ __ ÷ __ __ = ÷ 8 1 8 8 5 __ Divide both sides by 8 . 8 6 5y 8 __ • __ = __ • __ 5 1 8 5 5 __ Multiply by the reciprocal of . 8 48 3 y = __ , or 9 __ 5 5 Course 1 Solving Fraction Equations: 5-10 Multiplication and Division Check It Out: Example 1A Solve each equation. Write the answer in simplest form. 3 __ j = 19 4 3 3 3 __ j ÷ __ = 19 ÷ __ 4 4 4 3 Divide both sides of the equation by __ . 4 3 __ j• 4 3 4 Multiply by __, the reciprocal of __. 4 3 4 4 __ __ = 19 • 3 3 4 j = 19 • __ 3 19 • 4 j = _____ 1•3 76 1 ___ j= , or 25 __ 3 3 Course 1 Solving Fraction Equations: 5-10 Multiplication and Division Check It Out: Example 1B Solve each equation. Write the answer in simplest form. 1 3x = __ 7 1 1 3x 1 __ • __ = __ • __ 3 7 1 3 Multiply both sides by the reciprocal of 3. 1•1 x = ____ 7•3 1 x = __ 21 Course 1 The answer is in simplest form. Solving Fraction Equations: 5-10 Multiplication and Division Lesson Quiz Solve each equation. Write the answer in simplest form. 1 1 1. 3x = __ x = __ 8 24 1 x=4 2. __ x = 16 4 3 x = 14 __ y =9 2 4. __ 3. __ x = 98 or 32 __ 7 7 3 3 y = 63 1 of the 5. Rebecca used 3 pt of paint to paint __ 4 trim in her bedroom. How many pints will Rebecca use for the trim in the entire bedroom? 12 Course 1