Pre-Algebra 1-4 Solving Multiplication and Division Equations

Warm Up Solve. x = 12 n = 7 k = 1 t = 66 x = = x = t  k = = n x  3 = 9

Problem of the Day Jackie went shopping for a new wardrobe. She bought seven new shirts and four new pairs of pants. She made sure that they can all be worn together in combinations. How many outfits can she put together? 28

Learn to solve equations using multiplication and division.

Division Property of Equality Multiplication Property of Equality Vocabulary

You can solve a multiplication equation using the Division Property of Equality. You can divide both sides of an equation by the same nonzero number, and the equation will still be true. 4 3 = x = y DIVISION PROPERTY OF EQUALITY WordsNumbersAlgebra z 4 3 = = 6 2 z

Solve 8x = 32. 8x = 32 1x = 4 Divide both sides by 8.  Check 8x = x = 4 8x = 32 8(4) = 32 ? 32 = 32 ? Substitute 4 for x. 1 x = x Solving Equations Using Division

Solve 9x = 36. 9x = 36 1x = 4 Divide both sides by 9.  Check 9x = x = 4 9x = 36 9(4) = 36 ? 36 = 36 ? Substitute 4 for x. 1 x = x Try This

You can multiply both sides of an equation by the same number, and the statement will still be true. 2 3 = 6 x = y z z MULTIPLICATION PROPERTY OF EQUALITY WordsNumbersAlgebra 2 3 = = 24 You can solve a division equation using the Multiplication Property of Equality.

Solve = 7. n 7 n 7 = Multiply both sides by 7. n = 49 Check n 7 = 7 Substitute 49 for n = 7 ?  7 = 7 ? Solving Equations Using Multiplication

Solve = 16 n 4 n 4 = Multiply both sides by 4. n = 64 Check n 4 = 16 Substitute 64 for n = 16 ?  16 = 16 ? Example 2

Joe has enough flour to bake one sheet cake but would rather make cookies. How many dozen cookies can he make? Dessert Apple crisp Bread pudding Cookies (1 doz.) Pumpkin pie Sheet cake Tiramisu Cups of Flour Food Application

cups of flour for 1 dozen cookies cups of flour in 1 cake  = number of dozen cookies 2 = c8 2c = c = 4 Joe can make 4 dozen cookies with the same amount of flour that he would need for 1 sheet cake. Write the equation. Divide both sides by 2. 2c = 8 Example Continued

amount raised so far  = = x x = 6000 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? Write the equation. Multiply both sides by 8. total amount needed 1 8 x = The library needs to raise a total of $6000. fraction of total amount raised so far Another Example

Sometimes it is necessary to solve equations by using two inverse operations. For instance, the equation 6x  2 = 10 has multiplication and subtraction. 6x  2 = 10 Variable term Subtraction Multiplication To solve this equation, add to isolate the term with the variable in it. Then divide to solve.

Solve 3y – 7 = 20. 3y – 7 = 20Step 1: Add 7 to both sides to isolate the term with y in it y = 27 Step 2:3y = y = 9 Divide both sides by 3. Solving a Simple Two-Step Equation

Solve 4y + 5 = 29. 4y + 5 = 29Step 1: Subtract 5 from both sides to isolate the term with y in it. – 5 4y = 24 Step 2:4y = y = 6 Divide both sides by 4. Try This

Solve. 1. = t = = n + 17 = Joan is making a scrapbook of her pictures. She wants to put three pictures on each page. She has 63 photos. Write and solve an equation to find how many pages she will need for all of the photos. k = 18 n = 4 21 pages t = 7 b = 126 k 6 b 9 Lesson Quiz