Multiplying And Dividing Rational Numbers (MDR) STUDY GUIDE
1. I can explain the rules for multiplying integers.
1.) When multiplying 2 things with the same signs, the answer is ____________________.
2.) When multiplying 2 things with different signs, the answer is _____________________.
2. I can use the rules for multiplying integers to solve problems involving rational numbers.
1.) 8 X -4 = __________
2.) -10 x (-6) = __________
3.) -5 X -7 = __________
4.) -3 X 9 = ______________
5.) -1.4 x (0.2) = __________
6.) 4 ½ X -3 = __________
7.) -5.4 X -1.2= __________
8.) -2 ¾ X -5 ½ = _______________
Write and solve a multiplication sentence with integers for each word problem. Make sure the product is
in simplest form.
1.) Mrs. Lyons is playing Jeopardy against Mr. Bowen. Mr. Bowen incorrectly answers questions with 40
points five times in a row. What is his score so far?
2.) In Alaska, the temperature can get cold really quickly. Yesterday, the temperature dropped 3 degrees
for 9 hours straight. What is the total temperature change during the 9 hours?
3.) Mr. Crouch bought 4 new guitars to hand out at school for prizes. Each guitar cost $125.50. What
was the total cost of his purchase?
4.) Today, the 6th graders had 5 students absent, the 7th graders had 8 students absent, and the 8th graders
had 9 students absent. If the attendance follows the same trend for the month (assume 20 days), how
many times will a 7th grade student be absent during the month?
5.) Mrs. Barnett’s recipe for zucchini bread calls for 3 ¼ cups of sugar and 4 eggs. She wants to make 6
batches so that she has enough for everyone. How much sugar will she need?
3. I can explain the rules for dividing integers.
1.) When dividing 2 things with the same signs, the answer is ____________________.
2.) When dividing 2 things with different signs, the answer is _____________________.
4. I can use the rules for dividing integers to solve problems involving rational numbers.
1.) 8 / -4 = __________
2.) -60 / (-6) = __________
3.) -35 / -7 = __________
4.) -9 / 3 = ______________
5.) -1.4 / (0.2) = __________
6.) 4 ½ / -3 = __________
7.) -5.4 / -1.2= __________
8.) -2 ¾ / -5 ½ = _______________
Write and solve a division sentence with integers for each word problem. Make sure the answer is in
simplest form.
1.) Mr. Slone said that his car was worth $30,000 when it was purchased. However, over the last 3 years it
has decreased in value $5400. What integer represents the average decrease in value per year?
2.) The cafeteria purchased French bread pizza for lunch next week. If they would have purchased the
pizza last week while it was on sale, it would only have cost $2.00 per pizza. Now, 7 days later, the price
is $3.78 per pizza. What integer represents the average increase in the price of the pizza per day?
3.) Over the last 40 weeks, Mr. Neace has lost $2400 playing the lottery. What is his average loss per
week?
4.) Meyrick and his Aunt Angie (Mrs. Goodlett, 5th grade teacher from OES) like to pick black berries.
Together they have picked 8 ¾ pounds of blackberries. They want to divide them evenly between
themselves and a few family members (Meyrick, Aunt Angie, Jennilee, Grandma, Uncle Mike, and Uncle
Barney). How many pounds should they put in each person’s container?
5.) After searching for buried treasure, a group of pirates decide to quit for the night. They had found
treasure worth $540.52 so far. The 4 pirates each get to take the same amount of treasure home for the
night. How much treasure did each pirate get to take?
5. I can solve complex fractions.
Calculate the following complex fractions. Make sure your answer is in simplest form.
1.) 4 1/3
-3/4
2.) -1 ¾
-7 4/5
3.) -5/6
2/3
4.) The amount of salt in the Bath County’s storage unit to use on icy roads decreased by 12 ¾ feet over a
4 ¼ week time period. Set up a complex fraction to find the average rate at which the amount of salt has
decreased per week. Then, simplify it to find the answer.
5.) Mr. Bowen’s wife gives him a weekly allowance. Because of bad behavior his allowance has been
shrinking at a rate of 2 3/10 dollars every 3 ½ days. Set up a complex fraction to find the average rate at
which his weekly allowance has been decreased each day. Then, simplify to find the answer.
6.) A submarine descends at a rate of 4000 ft in 8 2/5 minutes. Set up a complex fraction to find the
average rate at which the submarine descends per minute. Then, simplify to find the answer.