7th Grade Math Review

Simplifying Fractions

100

4/8

1/2

200

33/99

1/3

300

3/39

1/13

400

180/240

3/4

500

-35/25

improper fraction: -7/5
mixed number: -1   2/5

Order of Operations

100

30/5 + 2

8

200

(5*3)2 + 8 / 2

34

300

(3 - 4) + 2 * 4

7

400

(4^2 - 1) * 3

45

500

8 / 4 + (4 / 2^2 - 2)

1

Ratios

100

If there are 6 dogs and 3 cats, what is the ratio of dogs to cats (reduced!)?

2 : 1 

200

If there are 6 dogs and 3 cats, what is the ratio of cats to dogs (reduced!)? 

1 : 2

300

Simplify 16:4

4:1

400

Simplify 144:60

12:5

500

What should x be so that these are equivalent?

10:12 and x : 36

30

Integer Calculations

100

742 - 375 = ?

367

200

200 - 348 = ?

-148

300

-83 - 59 = ? 

-142

400

-49 + 102 = ?

53

500

-33 * -6

198

Fundamental Counting Principle

100

You are going to lunch and can choose between 3 entrees (spaghetti, chicken, and salad) and 5 drinks (water, sports drink, soda, juice, and lemonade). How many possible choices could you make? Draw a tree diagram.

3 * 5 = 15 possible choices

spaghetti - water (1)
              - sports drink (2)
              - soda (3)
              - juice (4)
              - lemonade (5)
chicken   - water (6)
              - sports drink (7)
              - soda (8)
              - juice (9)
              - lemonade (10)
salad      - water (11)
             - sports drink (12)
             - soda (13)
             - juice (14)
             - lemonade (15) 

200

You are going camping and can choose 3 activities to do in the day. In the morning, you can go hiking or bird watching. In the afternoon, you can go kayaking, swimming, or fishing. In the evening, you can sit by the campfire, play card games, or go to sleep early.

Draw a tree diagram and say how many possible schedules you could have.

2 * 3 * 3 = 18 possible schedules

hiking - kayaking   -  campfire (1)
                            -  card games (2)
                            -  sleep (3)
         - swimming  - campfire (4)
                           - card games (5)
                            - sleep (6)
         - fishing      - campfire (7)
                           - card games (8)
                           - sleep (9)
birding - kayaking  - campfire (10)
                            - card games (11)
                            - sleep (12)
           - swimming - campfire (13)
                             - card games (14)
                             - sleep (15)
           - fishing      - campfire (16)
                            - card games (17)
                            - sleep (18)

300

Define the fundamental counting principle.

If there are n ways to do one thing and m ways to do another thing, then there are n x m ways to do both things.

400

You take a survey with five yes or no questions. How may different ways could you complete the survey?

2 * 2 * 2 * 2 * 2 = 2 ^ 5 = 32

500

Your math final exam has a multiple choice section that consists of 5 questions with options A, B, C, and D followed by a true and false section that is 10 questions long. How many possible ways could you fill out your test? (You may use a calculator on this problem, but you must explain your reasoning.)

4 ^ 5 * 2 ^ 10 = 1024 * 1024 = 1048576