Name Class Date. Multiplication Equations
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1 Name Class Date 2-7 Multiplication Equations Modeling Essential question: How do you solve whole-number equations that contain multiplication video tutor CC.6.EE.7 EXPLORE Multiplication Equations Deanna has a cookie recipe that requires 2 eggs to make 3 batches of cookies. How many eggs are needed per batch of cookies Let represent the number of eggs needed. Number of batches Number of eggs per batch = Total eggs 3 = 2 To answer this question, you can use algebra tiles to solve 3 = 2. A Model 3 = B There are 3 variable tiles, so draw circles to separate the tiles into 3 equal groups. One group has been circled for you. C How many unit tiles are in each group This is the solution of the equation. TRY THIS! eggs are needed per batch of cookies.. Caroline ran 5 miles in 5 days. She ran the same distance each day. Write and solve an equation to determine the number of miles she ran each day. Chapter 2 79 Lesson 7
2 Separating the tiles on both sides of an equation mat into an equal number of groups models dividing both sides of an equation by the same number. When an equation contains multiplication, solve by dividing both sides of the equation by the same number. 2 Division Property of Equality You can divide both sides of an equation by the same nonzero number, and the two sides will remain equal. CC.6.EE.7 EXAMPLE Solve each equation. A 9a = 54 What number is multiplied by a Using the Division Property of Equality Divide both sides of the equation by this number. 9a = 54 a = Divide. Check: 9a = 54 9 ( ) = 54 Substitute for a. = 54 Multiply on the left side. B 72 = 3d What number is multiplied by d Divide both sides of the equation by this number. 72 = 3d = d Divide. Check: 72 = 3d 72 = 3 ( ) Substitute for d. 72 = Multiply on the right side. TRY THIS! Solve each equation. 2a. 3 = 2 2b. 8h = 26 2c. 43 = y = h = y = Chapter 2 80 Lesson 7
3 3 CC.6.EE.6 EXAMPLE Solving Problems with Multiplication Equations Mr. Nguyen is planting a new rectangular garden. The garden will be 8 feet wide and he needs 200 square feet for the vegetables he wants to plant. How long should he make the garden Draw a diagram. Area = square feet ft ft Now write and solve an equation. Let represent the length of the garden. Area of new garden = Width of new garden. Length of new garden 200 = = 8 is multiplied by. = both sides by 8. Mr. Nyugen should make his new garden feet long. REFLECT 3a. Eplain how to check your answer in 3. 3b. Describe how solving an addition equation is different than solving a multiplication equation. TRY THIS! 3c. At a garden center, 80 containers of small bushes are separated into groups of 2. Write and solve an equation to find how many groups of containers there will be. Chapter 2 8 Lesson 7
4 practice Solve each equation.. 6c = 8 c = 4. 9y = 8 y = = 24f f = 2. 2a = 4 a = 5. 7h = 805 h = = 6k k = = 5 = 6. 25d = 350 d = 9. 32v = 672 v = For 0 5, write and solve an equation to answer each question. 0. Carmen participated in a read-a-thon. Mr. Cole pledged $4 per book and gave Carmen $44. How many books did Carmen read. Last week, Tina worked 35 hours in 5 days. She worked the same number of hours each day. How many hours did she work each day 2. Lee drove his car 476 miles and used 7 gallons of gasoline. How many miles did Lee s car travel per gallon of gasoline 3. A large rectangular area rug for a living room covers an area of 35 square feet. If the length of the rug is 5 feet, how wide is it Area: 35 square feet 4. On some days, Mercedes commutes 4 hours per day to the city for business meetings. Last month she commuted for a total of 36 hours. How many days did she commute to the city last month 5 ft ft 5. A volunteer group collected 384 cans of food. The food will be divided evenly among 6 local charities. How many cans of food will each charity receive Chapter 2 82 Lesson 7
5 Name Class Date Additional Practice 2-7 Solve each equation. Check your answers.. 8s v q 4. 2m n t p v Solve each equation. Check your answers m. 20r p d 5. n q f w 9. A hot-air balloon flew at 0 miles per hour. Using the variable h, write and solve a multiplication equation to find how many hours the balloon traveled if it covered a distance of 70 miles. 20. A passenger helicopter can travel 300 miles in the same time it takes a hot-air balloon to travel 20 miles. Using the variable s, write and solve a multiplication equation to find how many times faster the helicopter can travel than the hot air balloon. Chapter 2 83 Practice and Problem Solving
6 Problem Solving Write and solve a multiplication equation to answer each question.. In 975, a person earning minimum wage made $80 for a 40-hour work week. What was the minimum wage per hour in If an ostrich could maintain its maimum speed for 5 hours, it could run 225 miles. How fast can an ostrich run 3. About 2,000,000 people live in Paris, the capital of France. That is 80 times larger than the population of Paris, Teas. How many people live in Paris, Teas 4. The average person in China goes to the movies 2 times per year. That is 3 times more than the average American goes to the movies. How many times per year does the average American go to the movies Circle the letter of the correct answer. 5. Recycling just ton of paper saves 7 trees! If a city recycled enough paper to save 36 trees, how many tons of paper did it recycle A 7 tons B 8 tons C 9 tons D 9 tons 7. The distance between Atlanta, Georgia, and Denver, Colorado, is,398 miles. That is twice the distance between Atlanta and Detroit, Michigan. How many miles would you have to drive to get from Atlanta to Detroit A 2,796 miles B miles C 699 miles D,400 miles 6. Seaweed found along the coast of California, called giant kelp, grows up to 8 inches per day. If a giant kelp plant has grown 62 inches at this rate, for how many days has it been growing F 80 days H 9 days G 44 days J 8 days 8. Jupiter has 2 times more moons than Neptune has, and 8 times more moons than Mars has. Jupiter has 6 moons. How many moons do Neptune and Mars each have F 8 moons, 2 moons G 2 moons, 8 moons H 28 moons, 32 moons J 32 moons, 28 moons Chapter 2 84 Practice and Problem Solving
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1 y = Recitation Worksheet 1A. 1. Simplify the following: b. ( ) a. ( x ) Solve for y : 3. Plot these points in the xy plane:
Math 13 Recitation Worksheet 1A 1 Simplify the following: a ( ) 7 b ( ) 3 4 9 3 5 3 c 15 3 d 3 15 Solve for y : 8 y y 5= 6 3 3 Plot these points in the y plane: A ( 0,0 ) B ( 5,0 ) C ( 0, 4) D ( 3,5) 4
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Different: Arrow go different directions, circles are different, one answer is whole the other real
a) 1.) Fatima enrolled in a traveler rewards program. She begins with 7,500 bonus points. For ever trip she takes, she collects 500 bonus points. D) When Fatima has collected 30,000 bonus points, she gets
Name: Class: Date: ID: A
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