Presentation on theme: "Learn to solve equations using multiplication and division."— Presentation transcript:
1Learn to solve equations using multiplication and division.
2Vocabulary Division Property of Equality Multiplication Property of Equality
3DIVISION PROPERTY OF EQUALITY You can solve a multiplication equation using the Division Property of Equality.DIVISION PROPERTY OF EQUALITYWordsNumbersAlgebraYou can divide both sides of an equation by the same nonzero number, and the equation will still be true.4 • 3 = 12x = y4 • 3 = 12x = y22zz12 = 62
4Additional Example 1: Solving Equations Using Division Solve 8x = 32.8x = 328x = 32Divide both sides by 8.881x = 41 • x = xx = 4Check8x = 328(4) = 32?Substitute 4 for x.32 = 32?
5Try This: Example 1 Solve 9x = 36. 9x = 36 9x = 36 Divide both sides by 9.991x = 41 • x = xx = 4Check9x = 369(4) = 36?Substitute 4 for x.36 = 36?
6MULTIPLICATION PROPERTY OF EQUALITY You can solve a division equation using the Multiplication Property of Equality.MULTIPLICATION PROPERTY OF EQUALITYWordsNumbersAlgebraYou can multiply both sides of an equation by the same number, and the statement will still be true.2 • 3 = 6x = y4 •2 • 3 =zx = y8 • 3 = 24
7Additional Example 2: Solving Equations Using Multiplication 7Solve = 7.n7=7 •7 •Multiply both sides by 7.n = 49Checkn7= 7497= 7?Substitute 49 for n.7 = 7?
8Try This: Example 2 n 4 Solve = 16 n 4 = 16 4 • 4 • =4 •4 •Multiply both sides by 4.n = 64Checkn4= 16644= 16?Substitute 64 for n.16 = 16?
9Additional Example 3: Food Application Joe has enough flour to bake one sheet cake but would rather make cookies. How many dozen cookies can he make?DessertApple crispBread puddingCookies (1 doz.)Pumpkin pieSheet cakeTiramisuCups of Flour1.542183
10= = • Additional Example 3 Continued cups of flour for 1 dozen cookiesnumber of dozen cookiescups of flour in 1 cake=•=2c82c = 8Write the equation.2c = 8Divide both sides by 2.22c = 4Joe can make 4 dozen cookies with the same amount of flour that he would need for 1 sheet cake.
11= = • Try This: Example 3 cups of flour for bread pudding number of bread pudding dessertscups of flour in 1 cake=•=4b84b = 8Write the equation.4b = 8Divide both sides by 4.44c = 2Joe can make 2 bread pudding desserts with the same amount of flour that he would need for 1 sheet cake.
12= = • Additional Example 4: Money Application 1 4 x 50 x = 50 1 4 Meg has saved $50, which is one-fourth of the amount she needs for a school trip. What is the total amount she needs?fraction of amount raised so fartotal amount needed=amount raised so far14•=x50x = 5014Write the equation.x =14Multiply both sides by 4.4 •4 •x = 200Meg needs $200 total.
13= = • Try This: Example 4 1 x 750 8 1 x = 750 8 1 8 • x = 750 8 • 8 The school library needs money to complete a new collection. So far, the library has raised $750, which is only one-eighth of what they need. What is the total amount needed?fraction of total amount raised so fartotal amount needed=amount raised so far18•=x750x = 75018Write the equation.x =188 •8 •Multiply both sides by 8.x = 6000The library needs to raise a total of $6000.
14Sometimes it is necessary to solve equations by using two inverse operations. For instance, the equation 6x 2 = 10 has multiplication and subtraction.Variable term6x 2 = 10MultiplicationSubtractionTo solve this equation, add to isolate the term with the variable in it. Then divide to solve.
15Additional Example 5: Solving a Simple Two-Step Equation Solve 3y – 7 = 20.Step 1:3y – 7 = 20Add 7 to both sides to isolate the term with y in it.+ 7+ 73y = 27Step 2:3y = 27Divide both sides by 3.33y = 9
16Try This: Example 5Solve 4y + 5 = 29.Step 1:4y + 5 = 29Subtract 5 from both sides to isolate the term with y in it.– 5– 54y = 24Step 2:4y = 24Divide both sides by 4.44y = 6