Download AC Math Name Unit 8: Operations with Rational Numbers Date

AC Math
Unit 8: Operations with Rational Numbers
Study Guide
Name ___________________________________
Date _______________ Period ______________
Integer Facts
1. Explain how to determine if the sum of two rational numbers will be positive or negative.
2. What does the absolute value of an integer describe?
Addition & Subtraction of Integers
2
5
3. ( )  ( )  _____
3
7
4. (8.7)  (4.2)  (4.9)  _____
5. (5)  (10.2)  _____
6. A submarine 250 feet below sea level descends an additional 175 feet before ascending 400 feet. Describe the
location of the submarine.
7. What expression can you make to represent the model below?
-6
-4
-2
0
2
4
6
Multiplication & Division of Integers
3
1
8. ( )(6)( )  _____
4
2
9. (60)  (5)  _____
10. (9)(4  10)  _____
11. What equation does this model represent?
KEY
= -1
= 1
Mixed Operations with Integers
12. Find two integers with a product of 20 and a sum of -9.
13. The temperature at 9 AM was 5F. The temperature dropped 4 degrees per hour for the next three hours. What is
the temperature at noon?
14. You want to buy a new video game but don’t have the money for it. You borrow $60 from your mother to buy the
game. Later that week, you mow three yards and earn $15 per yard. You also babysit for 8 hours and earn $4.50 per
hour plus a tip of $3. Do you have enough money to pay your mother back? If so, how much money do you have
left? If not, how much money do you still need? Justify your answer.
Decimal/Fraction Changes
15. Convert to a decimal:
3
13
16. Convert to a fraction: 0.11
17. Can you tell if a fraction is going to repeat just by looking at it? Explain.
18 – 20. The answer to the question is YES. You will have 20 questions on the test. I did not include some of them.
AC Math
Unit 8: Operations with Rational Numbers
Study Guide
Name ___________________________________
Date _______________ Period ______________
Integer Facts
1. Explain how to determine if the sum of two rational numbers will be positive or negative.
Adding two positive equals a positive/Adding two negatives equals a negative/Opposite signs – Subtract and take
the sign of the larger absolute value.
2. What does the absolute value of an integer describe?
Distance from zero
Addition & Subtraction of Integers
2
5
4. ( )  ( )  _____
3
7
1
21
4. (8.7)  (4.2)  (4.9)  _____
-8
5. (5)  (10.2)  _____ -15.2
7. A submarine 250 feet below sea level descends an additional 175 feet before ascending 465 feet. Describe the
location of the submarine.
40 feet above sea level (Yes, I know what you are going to say. I did this on purpose)
9. What expression can you make to represent the model below?
-6
-4
-2
0
2
4
6
-5 + 12 = 7
Multiplication & Division of Integers
3
1
6. ( )(6)( )  _____
4
2
9
4
9. (60)  (5)  _____
-12
10. (9)(4  10)  _____ -54
11. What equation does this model represent?
KEY
= -1
= 1
2 x -3 = -6 -3 x 2 = -6
-6 ÷ -3 = 2
-6 ÷ 2 = -3
Mixed Operations with Integers
12. Find two integers with a product of 20 and a sum of -9.
- 4, - 5
13. The temperature at 9 AM was 5F. The temperature dropped 4 degrees per hour for the next three hours. What is
the temperature at noon?
-7
14. You want to buy a new video game but don’t have the money for it. You borrow $60 from your mother to buy the
game. Later that week, you mow three yards and earn $15 per yard. You also babysit for 8 hours and earn $4.50 per
hour plus a tip of $3. Do you have enough money to pay your mother back? If so, how much money do you have
left? If not, how much money do you still need? Justify your answer.
- 60 + (3 x 15) + (8 x 4.5) + 3
Yes, $24
Decimal/Fraction Changes
15. Convert to a decimal:
3
13
16. Convert to a fraction: 0.11
.23 (rounded to the hundredths)
1
(simplified)
9
17. Can you tell if a fraction is going to repeat just by looking at it? Explain.
Yes, if the prime factorization of the denominators are only 2’s, only 5’s, or only 2’s and 5’s.
18 – 20. The answer to the question is YES. You will have 20 questions on the test. I did not include some of them.