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1 Study Island Copyright 2015 Edmentum All rights reserved. Generation Date: 05/25/2015 Generated By: Matthew Beyranevand Students Entering Grade 7 Part 1 Explanations Explanations On the number line, opposite numbers are the same distance from zero. The opposite of any number can also be written by changing the sign. Since is to the right of zero on the number line, the opposite of is to the left of zero on the number line. The number is represented by the letter T on the number line Write Laura's running rate as the following ratio in fraction form. Laura ran 99 miles in 11 weeks. To find how many miles she ran in 1 week, divide the numerator and the denominator by 11. So, Laura has been running at a rate of 9 miles per week. 6. Since the ratio of feet to yards is always the same, set up a proportion. Now, cross multiply and divide. file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_e 1/18

2 So, 15 is the missing value. 7. Order of Operations: 1. Parentheses or Brackets from the inside out. 2. Exponents 3. Multiplication and Division from left to right. 4. Addition and Subtraction from left to right Recall that 30% = ( ) 4 = So, to determine the answer, set up an equation where n is the number n = 7.5 n = n = 25 = = = Recall that 35% =. So, to find 35% of 45, multiply 45 by Order of Operations: 1. Parentheses or Brackets from the inside out. 2. Exponents file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_e 2/18

3 3. Multiplication and Division from left to right. 4. Addition and Subtraction from left to right Recall that 70% = ( ) = = = = = = 53.1 So, to determine the answer, set up an equation where n is the number. 0.7 n = 31.5 n = n = After 2 hours, Tom and Juanita will be Tom's distance plus Juanita's distance apart because they are traveling in opposite directions. Calculate Tom's distance below. Calculate Juanita's distance below. 20 mph 2 hours = 40 miles 14 mph 2 hours = 28 miles The total distance is the sum of Tom's and Juanita's distances, shown below. 40 miles + 28 miles = 68 miles 17. On a number line, smaller numbers are to the left of larger numbers. Both numbers have a negative value. The number that is farther to the left of zero is less than the number that is closer to zero. So, the following is true. Rachel's elevation < Ferdinand's elevation 18. On this number line, each tick mark is a whole number. Moving to the right, the numbers increase. Moving to the left, the numbers decrease. The red dot is 2 tick marks to the left of 86,836. So, the red dot is on 86,834, because the following is true. 86,836 2 = 86,834 file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_e 3/18

4 The numbers given on this number line are consecutive whole numbers. Notice there are three tick marks between the numbers on the number line. This means that the tick marks between the numbers represent fractions of whole numbers. The fact that there are three tick marks between the numbers indicates that the number line is divided into fourths (or 0.25). To figure out where the red dot is located, if it is not located at a whole number value, find the nearest whole number. Then, either add (if the red dot is to the right) or subtract (if the red dot is to the left) by 0.25 at each tick mark. The red dot is located at 3.5 on this number line. 24. To determine which hot dog stand has the best deal, calculate the unit price for each hot dog. Benny's Hot Dogs charges $2 for 4 hot dogs. ABC Hot Dogs charges $4.50 for 6 hot dogs. Hot Dog Hut charges $2.00 per hot dog, but it has a buy one get one free deal. At $0.50 per hot dog, Benny's Hot Dogs has the best deal. 25. After 3 hours, Maria and Ming will be Maria's distance plus Ming's distance apart because they are traveling in opposite directions. Calculate Maria's distance below. Calculate Ming's distance below. 45 mph 3 hours = 135 miles 51 mph 3 hours = 153 miles The total distance is Maria's distance plus Ming's distance, which shown below. 26. A gain is a positive quantity. 135 miles miles = 288 miles file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_e 4/18

5 Since the gain is $7.59, the correct answer is Write Jaime's typing rate as the following ratio in fraction form. Jaime typed 315 words in 7 minutes. To find how many words she typed in 1 minute, divide the numerator and the denominator by 7. So, Jaime's typing rate is 45 words per minute. 28. The numbers given on this number line are consecutive whole numbers. Notice there are nine tick marks between the numbers on the number line. This means that the tick marks between the numbers represent fractions of whole numbers. The fact that there are nine tick marks between the numbers indicates that the number line is divided into tenths (or 0.10). To figure out where the red dot is located, if it is not located at a whole number value, find the nearest whole number. Then, either add (if the red dot is to the right) or subtract (if the red dot is to the left) by 0.10 for each tick mark. The red dot is located at 8.2 on this number line. 29. Since the ratio of grams to kilograms is always the same, set up a proportion. Now, cross multiply and divide. So, 7,000 is the missing value. 30. When finding ratios, make sure the ratio is in the correct order. The question asks for the ratio of tomato plants to tomatoes. So, the number of tomato plants is on the left and the number of tomatoes is on the right. The ratio can be simplified. 4:44 file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_e 5/18

6 Dividing both sides by 4 gives the following ratio. 31. (4 4):(44 4) = 1: When finding ratios, make sure the ratio is in the correct order. The question asks for the ratio of daisies to roses. So, the number of daisies is on the left and the number of roses is on the right. The ratio can be simplified. Dividing both sides by 2 gives the following ratio. 2:10 (2 2):(10 2) = 1:5 33. When finding ratios, make sure the ratio is in the correct order. The question asks for the ratio of lights to tiles. So, the number of lights is on the left and the number of tiles is on the right. The ratio can be simplified. Dividing both sides by 10 gives the following ratio. 34. There are 3 feet in 1 yard. 10:120 (10 10):(120 10) = 1:12 Therefore, 7 yards is equal to 21 feet Order of Operations: 1. Parentheses or Brackets from the inside out. 2. Exponents 3. Multiplication and Division from left to right. 4. Addition and Subtraction from left to right = = = = Substitute 5 in for x in the expression, and use order of operations to evaluate. file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_e 6/18

7 38. When finding ratios, make sure the ratio is in the correct order. The question asks for the ratio of pieces of chocolate without nuts to pieces of chocolate with nuts. So, the number of pieces of chocolate without nuts is on the left and the number of pieces of chocolate with nuts is on the right. The ratio can be simplified. Dividing both sides by 4 gives the following ratio. 20:12 (20 4):(12 4) = 5:3 39. Recall that 90% =. So, to find 90% of 50, multiply 50 by. 40. The distance (90 miles) and the time (3 hours) are provided. From these two numbers, calculate the rate ("how fast"), using the formula d = rt. 41. Recall that 25% = d = rt 90 miles = (r)(3 hours) 90 miles 3 hours = r 30 mph = r So, to determine the answer, set up an equation where n is the number n = 8.75 n = file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_e 7/18

8 n = The opposite of a number is the number that is the same distance from 0 on the number line, but in the opposite direction. First, graph 0.3 on the number line. Since 0.3 is 0.3 of a unit to the right of 0, the only number that is the same distance from 0 is the number that is 0.3 of a unit to the left of 0. So, the opposite of 0.3 is The rate (4 mph) and the time (3 hours) are provided. From these two numbers, calculate the distance ("how many miles"), using the formula d = rt. d = rt = (4 mph)(3 hours) = 12 miles 46. Recall that 50% =. So, to find 50% of 25, multiply 25 by. 47. Recall that 15% = So, to determine the answer, set up an equation where n is the number n = 6.75 n = n = 45 file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_e 8/18

9 50. A ratio represents a comparison between two values. The ratio of apple trees to orange trees can be expressed in three ways to : Order of Operations: 1. Parentheses or Brackets from the inside out. 2. Exponents 3. Multiplication and Division from left to right. 4. Addition and Subtraction from left to right = = = = When finding ratios, make sure the ratio is in the correct order. The question asks for the ratio of tomatoes to onions. So, the number of tomatoes is on the left and the number of onions is on the right. The ratio can be simplified. Dividing both sides by 2 gives the following ratio :4 (14 2):(4 2) = 7:2 54. The opposite of a number is the number that is the same distance from 0 on the number line, but in the opposite direction. First, graph 0.3 on the number line. Since 0.3 is 0.3 of a unit to the left of 0, the only number that is the same distance from 0 is the number that is 0.3 of a unit to the right of 0. So, the opposite of 0.3 is 0.3. file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_e 9/18

10 Since the ratio of centimeters to meters is always the same, set up a proportion. Now, cross multiply and divide. So, 500 is the missing value. 57. Order of Operations: 1. Parentheses or Brackets from the inside out. 2. Exponents 3. Multiplication and Division from left to right. 4. Addition and Subtraction from left to right = = = = An account balance below zero is a negative quantity, so and are incorrect. Since the account balance is $ below zero, is the correct answer. 59. Since the ratio of pints to quarts is always the same, set up a proportion. Now, cross multiply and divide. file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_ 10/18

11 So, 12 is the missing value. 60. The distance (56 miles) and the rate (8 mph) are provided. From these two numbers, calculate the time ("how long"), using the formula d = rt. d = rt 56 miles = (8 mph)(t) 56 miles 8 mph = t 7 hours = t 61. A ratio represents a comparison between two values. The ratio of chocolate cones sold to strawberry cones sold can be expressed in three ways to : First, convert quarts to pints. There are 2 pints in 1 quart. Next, convert pints to cups. There are 2 cups in 1 pint. So, 7 quarts is equal to 28 cups. 64. Recall that 60% = 0.6. So, to determine the answer, set up an equation where n is the number. 0.6 n = 21 n = file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_ 11/18

12 n = When finding ratios, make sure the ratio is in the correct order. The question asks for the ratio of screws to pieces of wood. So, the number of screws is on the left and the number of pieces of wood is on the right. The ratio can be simplified. Dividing both sides by 2 gives the following ratio. 14:8 (14 2):(8 2) = 7:4 66. When finding ratios, make sure the ratio is in the correct order. The question asks for the ratio of country songs to rock songs. So, the number of country songs is on the left and the number of rock songs is on the right. The ratio can be simplified. Dividing both sides by 3 gives the following ratio. 21:30 (21 3):(30 3) = 7: On a number line, smaller numbers are to the left of larger numbers. Negative values are always less than positive values. So, the following is true. Holly's account balance < Emily's account balance 68. When finding ratios, make sure the ratio is in the correct order. The question asks for the ratio of students planning on going to an in state college to students planning on going to an out of state college. So, the number of students planning on going to an in state college is on the left and the number of students planning on going to an out of state college is on the right. The ratio can be simplified. Dividing both sides by 10 gives the following ratio. 120:70 (120 10):(70 10) = 12:7 69. Since the ratio of inches to yards is always the same, set up a proportion. file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_ 12/18

13 Now, cross multiply and divide. So, 252 is the missing value. 70. Order of Operations: 1. Parentheses or Brackets from the inside out. 2. Exponents 3. Multiplication and Division from left to right. 4. Addition and Subtraction from left to right ( ) 2 = = = = Substitute 3 in for x in the expression, and use order of operations to evaluate There are 12 inches in 1 foot. file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_ 13/18

14 Therefore, 48 inches is equal to 4 feet A temperature below zero is a negative quantity, so and are incorrect. Since the temperature is twenty five and two thirds degrees below zero, is the correct answer. 77. An account balance below zero is a negative quantity, so 52 and 520 are incorrect. Since the account balance is $52 below zero, 52 is the correct answer. 78. The red dot is between 0 and 1. There are five tick marks between 0 and 1. These tick marks divide the space between 0 and 1 into six equal parts. Therefore, each tick mark between the numbers represents. The red dot is four marks to the right of 0, so the red dot is at point. This reduces to. 79. On a number line, smaller numbers are to the left of larger numbers. Both numbers have a positive value. The number that is closer to zero is less than the number that is farther to the right of zero. So, the following is true Richard's distance < Kyle's distance 82. The opposite of a number is the number that is the same distance from 0 on the number line, but in the opposite direction. First, graph on the number line. file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_ 14/18

15 Since is of a unit to the left of 0, the only number that is the same distance from 0 is the number that is of a unit to the right of 0. So, the opposite of is. 83. A debt is a negative quantity, so 1, and 1, are incorrect. Since the debt is one thousand dollars and eight cents, 1, is the correct answer The opposite of a number is the number that is the same distance from 0 on the number line, but in the opposite direction. First, graph on the number line. Since is of a unit to the right of 0, the only number that is the same distance from 0 is the number that is of a unit to the left of 0. So, the opposite of is. 86. The numbers given on this number line are consecutive whole numbers. Notice there are four tick marks between the numbers on the number line. This means that the tick marks between the numbers represent fractions of whole numbers. The fact that there are four tick marks between the numbers indicates that the number line is divided into fifths (or 0.2). To figure out where the red dot is located, if it is not located at a whole number value, find the nearest whole number. Then, either add (if the red dot is to the right) or subtract (if the red dot is to the left) by 0.2 for each tick mark. The red dot is located at 10.8 on this number line Order of Operations: 1. Parentheses or Brackets from the inside out. 2. Exponents 3. Multiplication and Division from left to right. 4. Addition and Subtraction from left to right. file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_ 15/18

16 89. Order of Operations: 1. Parentheses or Brackets from the inside out. 2. Exponents 3. Multiplication and Division from left to right. 4. Addition and Subtraction from left to right ( ) 2 = = = = ( ) = = = = = = Since the ratio of millimeters to centimeters is always the same, set up a proportion. Now, cross multiply and divide. So, 50 is the missing value. 91. First, convert pints to cups. There are 2 cups in 1 pint. Next, convert cups to fluid ounces. There are 8 fluid ounces in 1 cup. So, 6 pints is equal to 96 fluid ounces. file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_ 16/18

17 92. Recall that 95% = So, to determine the answer, set up an equation where n is the number n = n = n = The total distance that Mishka covers on her road trip will be the sum of highway distance and side road distance. Her open highway distance is shown below. Her side road distance is shown below. 75 mph 3 hours = 225 miles 35 mph 1 hour = 35 miles So, the total distance that Mishka covers on her road trip is shown below miles + 35 miles = 260 miles 95. When finding ratios, make sure the ratio is in the correct order. The question asks for the ratio of small bones to large bones. So, the number of small bones is on the left and the number of large bones is on the right. The ratio can be simplified. Dividing both sides by 3 gives the following ratio. 9:6 (9 3):(6 3) = 3:2 96. The red dot is between 0 and 1. There are four tick marks between 0 and 1. These tick marks divide the space between 0 and 1 into five equal parts. Therefore, each tick mark between the numbers represents. The red dot is two marks to the right of 0, so the red dot is at point file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_ 17/18

18 100. A temperature above zero is a positive quantity. Since the temperature is degrees above zero, the correct answer is. file:///c:/users/beyranevandm.district/appdata/local/temp/temp1_entering%20grade%207%20summer%20math%20hard%20copy.zip/study_island_ 18/18