7th Grade Number System Unit Review Packet

(A bank of 42 questions reviewing 6th grade material)

Fractions

  1. Samantha is thinking of a number that can factor into both 70 and 110. What is the greatest possible number that she could be thinking of?
  1. Timothy can catch a fish in 5 minutes on a lake. Rayna can catch one in 9 minutes. If they both start catching fish at the same time, then in how many minutes will they have caught the same amount of fish? How many fish will the two have to take home with them at that time?
  1. The baseball team is getting ready to go on the field. There are 9 players on the team. Each player has 1 bat and 5 balls with them for the game. How much gear do they have altogether. Write the problem in two different ways and then solve.
  1. Jose purchasedpound of peanuts and pound of raisons. Find the total weight of his purchases.
  1. Linda spent of an hour talking to her friends Sara and Mary on her cell phone Saturday night. If she talked to Sara for of the hour, how long did she talk to Mary?
  1. The total amount of soda, water, and lemonade bought for the party is 12 L. The soda contains 3L. The water contains 1L less liquid than the soda. How much liquid does the lemonade contain?
  1. William has 300 Pokemon cards. He hasmore Pokemon cards than Jonathan. How many Pokemon cards does Jonathan have?
  1. Joanna trains every day for an upcoming marathon. Today she ran of a 20mile course. How many miles did she run?

Decimal Computation

  1. A carpenter needs to glue different sizes of wood pieces together. What length will the new piece of wood be when the wood sizes are 0.008cm, 0.125cm, 0.15cm, 0.185cm, and 0.005cm long?
  1. Susan purchased $39.46 in groceries at a store. She then gave the cashier a $50 bill to pay with. What should be the amount of change Susan receives back?
  1. School lunches cost Sally’s mom $14.50 per week. About how much would 15.5 weeks of lunches cost her mom?
  1. A director replayed 231 of the 1,000 scenes filmed for a movie. Write a decimal for the part of the movie the director replayed.
  1. What is the average speed in miles per hour of a car that travels 965.4 miles in 15.7 hours? Round your answer to the nearest tenth.

Statistics

2, 35, 6, 4, 11, 10, 19, 13, 21, 2, 11, 16, 11, 5, 7

  1. Find the mean, median, and mode for the data set above.
  1. Create a bow and whisker plot for the data set above.
  1. Find the range, any outliers, and first and third quartiles for the data set above.
  1. Find the mean absolute deviation for the data set above.

Number System

  1. Mt. Everest is 8.8 km above sea level while the Mariana Trench is 10.9km below sea level. If a vacationer was to visit both, what integers could she write in her journal to represent the amount of km for each location?
  1. Thomas was driving over the speed limit by 15 miles/hour. He then passed a car that was driving the complete opposite of that. A cop on the side of the road saw both drivers and was prepared to give both a ticket. Represent the two different speeds of the two drivers using integers.
  1. Janet left the store with $.67 to put in her piggy bank at home for change. Margo left with 7/9 of a dollar. Who had more money leaving the store?
  1. The quadrant where the x and y coordinates of a point are both negative is quadrant _____?
  1. The point (-1, 5) is located in quadrant _____?

Expressions, Equations, and Inequalities

  1. Solve the following problems using the correct order of operations.

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  1. Translate the following into algebraic expressions and evaluate for when a number = 2.

the difference of 5 and a number

 nine less than the product of a number and two

 half the sum of fourteen and a number added to 30

sixteen more than the quotient of 20 and a number

  1. Write the following equations and solve for the number.

the product of 3 and a number is equal to twenty one.

 the difference between 16 and a number is 5.

 A number divided by 7 is equal to eight.

The sum of nine and twenty-three is a number.

  1. Write and graph the following inequalities.

a number is at most 30

 a number is at least more than 2

 a number cannot exceed the value of 96

a number must be more thanthan 5

Geometry

  1. What is the area of a desk with a width of 4 feet and a length of 6 feet? Will a square computer with a side of 1 ft be able to fit on the desk?
  1. The height of a parallelogram is 5 feet more than its base. If the area of the parallelogram is 204 square feet, find its base and height.
  1. A trapezoid has base lengths of 19.5 and 24.5 centimeters with an area of 154. What is the height of the trapezoid?
  1. Ricardo is surveying a plot of land in the shape of a right triangle. The area of the land is 45,000 square meters. If one leg of the triangular plot is 180 meters long, what is the other leg of the triangle?
  1. A basketball court is 19 feet by 12 feet. The owner of the court wants to add a safety zone around one end of it to surround one of the baskets. The safety zone will create a perfect semicircle. What is the area of the whole new court?
  1. A 20 foot by 12 foot pool is to be surrounded by a deck 6 feet in width. How many square feet of decking is needed to do this?
  1. A small square city park has a total area of 324 square feet. A border of flowers surrounds the park and has a width of 2 feet. How many feet is the area of the park with the flower border?
  1. What is the name of a solid figure that has a four triangular sides and a square bottom? How many edged does this figure have? Vertices? Faces?
  1. A birthday gift is 55cm long, 40 cm wide, and 5 cm high. The sheet of paper you want to use to wrap it measures 75cm by 100cm. Is the paper large enough to wrap the gift? Explain.
  1. How much cat food would fit into a can that has a height of 14.5cm and a diameter of 9cm? How much paper (in ) would you need to make the label?
  1. A cubic tank with 4.6 M edges is filled with water. How much water will be left in the tank if some is drained off to fill a cylindrical tank with a radius of 2.2 M and a height of 4.6 M?

Ratios and Proportions

  1. At a swim meet, there is one coach for every three swimmers in the pool. What is the ratio of coaches to swimmers?
  1. There are 2 pieces of pie for each guest at Thanksgiving dinner. There are also 8 spoonfuls of whipped cream for every 4 guests. What are the two ratios that represent the situations? Are these equivalent ratios?
  1. There are 36 cookies in a package at the store. 9 of them are chocolate chip, 6 of them are oatmeal raison, and 20 of them are sugar. What is the ratio of total cookies to oatmeal raison? What is the ratio of oatmeal raison to sugar?
  1. Allana’s car can travel 102.5 miles on 3 gallons of gas. How many miles per gallon can the car travel?
  1. Four friends are eating out at a restaurant. The bill at the end of dinner comes out to be $52. There is also an additional $4 in tax and a 7% tip that needs to be added on. What is the cost per person?

Answer Key

NJ Center for Teaching and Learning ~ 1 ~

  1. 10
  2. 45 minutes, 14 fish
  3. 9(1+5) = 9 + 45 = 54 balls and bats
  4. 225 cards
  5. 15 miles
  6. 0.473 cm
  7. $10.54
  8. $224.75
  9. 0.231
  10. 61.5 miles/hour
  11. mean = 11.53

median= 11

mode = 11

  1. range = 33

outliers = 35

1st quartile = 5

3rd quartile = 16

  1. 6
  2. +8.8, -10.9
  3. +15, -15
  4. Margo
  5. quadrant III
  6. quadrant II
  7. 14









  1. 



  1. 





  1. 24, yes bc the computer has an area of 2
  2. base = 12ft, height = 17ft
  3. height = 7cm
  4. 500 meters
  5. 284.52
  6. 528
  7. 484
  8. square pyramid, 8 edges, 5 vertices, 5 faces
  9. yes because the surface area of the present = 5350 and the paper can cover 7500
  10. 473.56 of food, 921.98 of paper
  11. 27.43of water
  12. 1:3
  13. 6:1, 3:10
  14. 34.17 miles/gallon
  15. $14.98

NJ Center for Teaching and Learning ~ 1 ~