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9.5: Homework

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• Page ID 70336

• Julie Harland
• MiraCosta College
• Submit homework separately from this workbook and staple all pages together. (One staple for the entire submission of all the unit homework)
• Start a new module on the front side of a new page and write the module number on the top center of the page.
• Answers without supporting work will receive no credit.
• Some solutions are given in the solutions manual.
• You may work with classmates but do your own work.

Do each of the following steps using your C-strips.

• State how many C-strips (each an equal part of the whole) make up one unit.
• State which C-strip makes up one part of the whole.
• State the fraction that the C-strip in part b represents.
• State how many of the C-strips in part b you need to make into a train.
• State which C-strip is the length of the train you made in part c

a. If S represents 1 unit, then which C-strip represents \(\frac{7}{11}\)?

b. If H represents 1 unit, then which C-strip represents \(\frac{2}{3}\)?

c. If P represents 1 unit, then which C-strip represents \(\frac{3}{2}\)?

d. If L represents 1 unit, then which C-strip represents 3 ?

e. If Y represents 1 unit, then which C-strip represents \(\frac{6}{5}\)?

f. If O represents 1 unit, then which C-strip represents \(\frac{1}{2}\)?

g. If B represents 1 unit, then which C-strip represents \(\frac{4}{3}\)?

Do each step using your C-strips.

• State how many C-strips will make up the named C-strip stated in the problem.
• Which C-strip makes up one equal part?
• State how many of the C-strips in part b will make up one unit.
• Form the unit by making a train from the equal parts (C-strip in part b) and state which C-strip has the same length as that train.

a. If O represents \(\frac{5}{6}\), then which C-strip is 1 unit?

b. If W represents \(\frac{1}{7}\), then which C-strip is 1 unit?

c. If D represents \(\frac{3}{2}\), then which C-strip is 1 unit?

d. If N represents \(\frac{4}{3}\), then which C-strip is 1 unit?

e. If D represents 3, then which C-strip is 1 unit?

f. If K represents \(\frac{7}{9}\), then which C-strip is 1 unit?

• State which C-strip is one unit.
• State which C-strip is the answer.

a. If N represents \(\frac{2}{3}\), then which C-strip represents \(\frac{1}{4}\)?

b. If D represents \(\frac{3}{4}\), then which C-strip represents \(\frac{3}{2}\)?

c. If B represents \(\frac{3}{2}\), this which C-strip represents \(\frac{4}{3}\)?

Use your fraction arrays to determine all fractions on the fraction array that are equivalent to 3/4. Do this by finding 3/4 on the array, and seeing what other numbers are the same length. Include a diagram.

Use your multiple strips to write 6 fractions equivalent to 5/6. Draw the strips.

Use your multiple strips to write 6 fractions equivalent to 3/8 Draw the strips.

Compare 3/8 and 1/3 using models. Show all of the steps, and explain the procedure as shown in this module.

Add 3/8 and 1/3 using models. Show all of the steps, and explain the procedure as shown in this module.

Do the following subtraction using models: 3/5 – 1/4. Show all of the steps, and explain the procedure as shown in this module.

Do the following multiplications using models. Show all of the steps, and explain the procedure as shown in this module.

a. 3/8 \(\cdot\) 2/5

b. 4/7 \(\cdot\) 2/3

By looking at the final drawing someone made to model a multiplication of two fractions, determine which multiplication was performed, and then state the answer.

a. 5/6 \(\cdot\) 2/3 OR 2/3 \(\cdot\) 5/6

b. 1/2 \(\cdot\) 7/8 OR 7/8 \(\cdot\) 1/2

If all of the dots shown for each problem represent 1 unit, determine the multiplication problem that someone did to get the answer, and state the answer.

Fill in the chart showing how to do the following multiplications using C-strips. The multiplication is in the first column. State an appropriate choice for the unit (name a C-strip, or sum of two C-strips) in the second column. Write the C-strip obtained after the first part of the multiplication (which is the second fraction as a part of the unit) in the third column. Then, do the final multiplication, and write the C-strip obtained in the fourth column. In the fifth column, write a fraction using C-strips putting the final unit obtained in the fourth column as the numerator, and the unit in the denominator. Then, in the last column, write the answer as a fraction. Do not simplify.

Perform the following division using the box and dot methods. First define the unit. Then explain and show all of the steps. Include diagrams.

a. 5 \(\div\) 1/3

b. 3/4 \(\div\) 1/3

Determine if the following statements are true or false by comparing cross products.

a. 19/23 = 57/69

b. 24/37 = 68/91

Write each fraction in simplest form using each of the two methods:

(1) prime factorization and

(2) finding GCF.

a. \(\frac{216}{420}\)

b. \(\frac{195}{286}\)

Use cross products to compare each of the following fractions. Use < or >.

a. 18/23 and 5/8

b. 11/18 and 121/250

Find 3 rational numbers, written with a common denominator, between 3/8 and 5/8.

Find 3 rational numbers, written with a common denominator, between 1/2 and 4/7.

a. 21 of John's students have cats at home. This represents 7/10 of John's students. How many students are in John's class? Solve the problem using models. Explain how the model works.

b. At an elementary school, 38 teachers drive alone to work. This represents 2/3 of the teachers. How many teachers work at the school? Solve the problem using models. Explain how the model works.

Write in words how to read each of the following decimals.

Multiply the following decimals mentally then do it again by showing the same steps as shown in this module..

a. (0.3)(0.8)

b. (1.2)(0.4)

c. (1.22)(2.3)

d. (3.2)(2.41)

For each fraction, determine if it can be written as an equivalent fraction with a power of ten in the denominator. If a fraction cannot be written as a terminal decimal, explain why not. Otherwise, show ALL of the steps to write it as a terminal decimal.

a. \(\frac{11}{16}\)

b. \(\frac{3}{125}\)

c. \(\frac{1}{12}\)

d. \(\frac{9}{40}\)

e. \(\frac{21}{56}\)

Rewrite each of the following decimals as simplified fractions. For repeating decimals, use the techniques shown in this module. Then, check your answer using a calculator by dividing the numerator by the denominator to see if the result matches the original problem.

a. \(0.\bar{7}\)

b. \(0.\overline{72}\)

c. \(0.\overline{235}\)

d. \(0.2\bar{5}\)

e. \(0.3\overline{42}\)

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Eureka Math Grade 8 Module 4 Lesson 9 Answer Key

Engage ny eureka math 8th grade module 4 lesson 9 answer key, eureka math grade 8 module 4 lesson 9 exercise answer key.

Exercise 1. Write the equation for the 15 th step. Answer: S 15 -7+7∙5 15 =5S 15

Exercise 2. How many people would see the photo after 15 steps? Use a calculator if needed. Answer: S 15 -7+7∙5 15 =5S 15 S 15 -5S 15 -7++7∙5 15 =5S 15 -5S 15 S 15 (1-5)-7+7∙5 15 =0 S 15 (1-5)-7+7+7∙5 15 -7∙5 15 =7-7∙5 15 S 15 (1-5)=7(1-5 15 ) S 15 =\(\frac{7\left(1-5^{15}\right)}{(1-5)}\) S 15 =53 405 761 717

Exercises 3–11 as an Alternative to Discussion Students should be able to complete the following problems independently as they are an application of skills learned to this point, namely, transcription and solving linear equations in one variable. Have students work on the problems one at a time and share their work with the whole class, or assign the entire set and allow students to work at their own pace. Provide correct solutions at the end of the lesson.

Exercise 3. Marvin paid an entrance fee of $5 plus an additional $1.25 per game at a local arcade. Altogether, he spent $26.25. Write and solve an equation to determine how many games Marvin played. Let x represent the number of games he played. 5+1.25x=26.25 1.25x=21.25 x=\(\frac{21.25}{1.25}\) x=17 Marvin played 17 games.

Exercise 4. The sum of four consecutive integers is -26. What are the integers? Answer: Let x be the first integer. x+(x+1)+(x+2)+(x+3)=-26 4x+6=-26 4x=-32 x=-8 The integers are -8, -7, -6, and -5.

Exercise 5. A book has x pages. How many pages are in the book if Maria read 45 pages of a book on Monday, \(\frac{1}{2}\) the book on Tuesday, and the remaining 72 pages on Wednesday? Answer: Let x be the number of pages in the book. x=45+\(\frac{1}{2}\) x+72 x=117+\(\frac{1}{2}\) x \(\frac{1}{2}\) x=117 x=234 The book has 234 pages.

Exercise 6. A number increased by 5 and divided by 2 is equal to 75. What is the number? Answer: Let x be the number. \(\frac{x+5}{2}\)=75 x+5=150 x=145 The number is 145.

Exercise 7. The sum of thirteen and twice a number is seven less than six times a number. What is the number? Answer: Let x be the number. 13+2x=6x-7 20+2x=6x 20=4x 5=x The number is 5.

Exercise 8. The width of a rectangle is 7 less than twice the length. If the perimeter of the rectangle is 43.6 inches, what is the area of the rectangle? Answer: Let x represent the length of the rectangle. 2x+2(2x-7)=43.6 2x+4x-14=43.6 6x-14=43.6 6x=57.6 x=\(\frac{57.6}{6}\) x=9.6 The length of the rectangle is 9.6 inches, and the width is 12.2 inches, so the area is 117.12 in 2 .

Exercise 9. Two hundred and fifty tickets for the school dance were sold. On Monday, 35 tickets were sold. An equal number of tickets were sold each day for the next five days. How many tickets were sold on one of those days? Answer: Let x be the number of tickets sold on one of those days. 250=35+5x 215=5x 43=x 43 tickets were sold on each of the five days.

Exercise 10. Shonna skateboarded for some number of minutes on Monday. On Tuesday, she skateboarded for twice as many minutes as she did on Monday, and on Wednesday, she skateboarded for half the sum of minutes from Monday and Tuesday. Altogether, she skateboarded for a total of three hours. How many minutes did she skateboard each day? Answer: Let x be the number of minutes she skateboarded on Monday. x+2x+\(\frac{2 x+x}{2}\)=180 \(\frac{2 x}{2}\)+\(\frac{4 x}{2}\)+\(\frac{2 x+x}{2}\)=180 \(\frac{9 x}{2}\)=180 9x=360 x=40 Shonna skateboarded 40 minutes on Monday, 80 minutes on Tuesday, and 60 minutes on Wednesday.

Eureka Math Grade 8 Module 4 Lesson 9 Exit Ticket Answer Key

Question 1. Rewrite the equation that would represent the sum in the fifth step of the Facebook problem: S 5 =7+7∙5+7∙5 2 +7∙5 3 +7∙5 4 S 5 =7+7∙5+7∙5 2 +7∙5 3 +7∙5 4 S 5 -7=7∙5+7∙5 2 +7∙5 3 +7∙5 4 S 5 -7+7∙5 5 =7∙5+7∙5 2 +7∙5 3 +7∙5 4 +7∙5 5 S 5 -7+7∙5 5 =5(7+7∙5+7∙5 2 +7∙5 3 +7∙5 4 ) S 5 -7+7∙5 5 =5(S 5 ) S 5 -5S 5 -7+7∙5 5 =0 S 5 -5S 5 =7-(7∙5 5 ) (1-5) S 5 =7-(7∙5 5 ) (1-5) S 5 =7(1-5 5 ) S 5 =\(\frac{7\left(1-5^{5}\right)}{1-5}\)

Question 2. The sum of four consecutive integers is 74. Write an equation, and solve to find the numbers. Answer: Let x be the first number. x+(x+1)+(x+2)+(x+3)=74 4x+6=74 4x=68 x=17 The numbers are 17, 18, 19, and 20.

Eureka Math Grade 8 Module 4 Lesson 9 Problem Set Answer Key

Assign the problems that relate to the elements of the lesson that were used with students.

Question 1. You forward an e-card that you found online to three of your friends. They liked it so much that they forwarded it on to four of their friends, who then forwarded it on to four of their friends, and so on. The number of people who saw the e-card is shown below. Let S 5 represent the number of people who saw the e-card after one step, let S 2 represent the number of people who saw the e-card after two steps, and so on. S 5 =3 S 2 =3+3∙4 S 3 =3+3∙4+3∙4 2 S 4 =3+3∙4+3∙4 2 +3∙4 3

a. Find the pattern in the equations. Answer: S 2 =3+3∙4 S 2 -3=3∙4 S 2 -3+3∙4 2 =3∙4+3∙4 2 S 2 -3+3∙4 2 =4(3+3∙4) S 2 -3+3∙4 2 =4S 2

S 3 =3+3∙4+3∙4 2 S 3 -3=3∙4+3∙4 2 S 3 -3+3∙4 3 =3∙4+3∙4 2 +3∙4 3 S 3 -3+3∙4 3 =4(3+3∙4+3∙4 2 ) S 3 -3+3∙4 3 =4S 3

S 4 =3+3∙4+3∙4 2 +3∙4 3 S 4 -3=3∙4+3∙4 2 +3∙4 3 S 4 -3+3∙4 4 =3∙4+3∙4 2 +3∙4 3 +3∙4 4 S 4 -3+3∙4 4 =4(3+3∙4+3∙4 2 +3∙4 3 ) S 4 -3+3∙4 4 =4S 4

b. Assuming the trend continues, how many people will have seen the e-card after 10 steps? Answer: S 5 0-3+3∙4 10 =4S 10 S 10 -4S 10 -3+3∙4 10 =0 S 10 (1-4)=3-3∙4 10 S 10 (1-4)=3(1-4 10 ) S 10 =\(\frac{3\left(1-4^{10}\right)}{(1-4)}\) S 10 =1 048 575 After 10 steps, 1,048,575 people will have seen the e-card.

c. How many people will have seen the e-card after n steps? Answer: S n =\(\frac{3\left(1-4^{n}\right)}{(1-4)}\)

For each of the following questions, write an equation, and solve to find each answer.

Question 2. Lisa has a certain amount of money. She spent $39 and has \(\frac{3}{4}\) of the original amount left. How much money did she have originally? Answer: Let x be the amount of money Lisa had originally. x-39=\(\frac{3}{4}\) x -39=-\(\frac{1}{4}\) x 156=x Lisa had $156 originally.

Question 3. The length of a rectangle is 4 more than 3 times the width. If the perimeter of the rectangle is 18.4 cm, what is the area of the rectangle? Answer: Let x represent the width of the rectangle. 2(4+3x)+2x=18.4 8+6x+2x=18.4 8+8x=18.4 8x=10.4 x=\(\frac{10.4}{8}\) x=1.3 The width of the rectangle is 1.3 cm, and the length is 7.9 cm, so the area is 10.27 cm 2 .

Question 4. Eight times the result of subtracting 3 from a number is equal to the number increased by 25. What is the number? Answer: Let x be the number. 8(x-3)=x+25 8x-24=x+25 7x-24=25 7x=49 x=7 The number is 7.

Question 5. Three consecutive odd integers have a sum of 3. What are the numbers? Answer: Let x be the first odd number. x+(x+2)+(x+4)=3 3x+6=3 3x=-3 x=-1 The three consecutive odd integers are -1, 1, and 3.

Question 6. Each month, Liz pays $35 to her phone company just to use the phone. Each text she sends costs her an additional $0.05. In March, her phone bill was $72.60. In April, her phone bill was $65.85. How many texts did she send each month? Answer: Let x be the number of texts she sent in March. 35+0.05x=72.60 0.05x=37.6 x=\(\frac{37.6}{0.05}\) x=752 She sent 752 texts in March. Let y be the number of texts she sent in April. 35+0.05y=65.85 0.05y=30.85 y=\(\frac{30.85}{0.05}\) y=617 She sent 617 texts in April.

Question 7. Claudia is reading a book that has 360 pages. She read some of the book last week. She plans to read 46 pages today. When she does, she will be \(\frac{4}{5}\) of the way through the book. How many pages did she read last week? Answer: Let x be the number of pages she read last week. x+46=\(\frac{4}{5}\) (360) x+46=288 x=242 Claudia read 242 pages last week.

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Home > INT2 > Chapter 9 > Lesson 9.1.1 > Problem 9-8

Solve the inequalities below. Show your solutions on a number line.  

Solve as an equation to find the boundary point. Then check points in each region to determine which region is the solution.

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