Problem Solving With Fractions
Addition Patterns Putting things together Totaling Counting 
Subtraction Patterns Take away Compare Missing part = total – given part 
Examples:
1. Keith needs cubic yards of cement for a patio and cubic yards for a sidewalk. How much cement will he need altogether? 
Reminder of Addition Rules: 1. Find the LCD. 
2. A carpenter worked hours on
Monday, hours on Tuesday, and 6 hours on Wednesday. What was the total time the carpenter worked for those three days? 

3. A chemist has ml of solution in a beaker. If he pours out ml of the solution, how much is left? 
Reminder of Subtraction Rules: 1. Find the LCD. 
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Exercises 4  7 4. During her shift as a
nurse, Katie measured the liquid intake for one of her patients. The Turn Tape Back On For Solutions 

Multiplication Patterns
Given a _______ _______, find
distance over a certain time. 

Examples: 8. Joan can jog a mile in minutes. At this rate, how long will it take her to jog to the park, which is 5 miles from her house? 
Reminder of Multiplication Rules: 1. Change mixed numbers to improper fractions and write whole numbers with a denominator of 1. 2. Cancel common factors. 3. Multiply numerators; multiply denominators. 4. Change to mixed number if needed. 
9. A certain stock sells for dollars
per share. How much will 50 shares cost? 10. Elaine's house is worth two and threefourths times what she paid for it twelve years ago. If she paid $54,000 for it . . . a. How much is it worth now? 11. Jodi had,
yards of material. She used of it for some chair cushions. 

Multiplication Note:
Multiplying a given number by a fraction whose value
is less than one 

Example: 12. Adam had feet of lumber. He estimated that he would need to use about of that amount to build a playgym for his son. How much lumber will he use? 

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Exercises 13  16 13. If a cubic foot of
water weighs pounds, how much does 6 cubic feet of water weigh? 15. Judy earns $48,000 a year as a mathematician.
Lucy earns times that much as a Turn Tape Back On For Solutions 

Division Patterns
Given distance over time, find a
________. 

Examples: 17. Four football players are equally sharing pizzas. How much will each player get? 
Reminder of Division Rules: 1. Change mixed numbers to improper fractions and write whole numbers with a denominator of 1. 2. Invert the 2nd fraction and follow multiplication steps. 
18. Each lawn chair that George is
rewebbing needs feet of webbing. How many chairs can he reweb if he has 75 feet of webbing? 19. If you have lbs. of candy, how many boxes can you fill if each box holds lbs.? 

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Exercises 20  23 20. A car used gallons
of gasoline on a 400mile trip. How many miles per gallon did the Turn Tape Back On For Solutions 

Examples: 24. Sharon worked hours on Monday, hours on Tuesday, and 6 hours on Wednesday. What is the average number of hours Sharon worked for those three days? 25. A publisher needs pounds of paper for each edition of a certain book. How many books can be printed from 1200 pounds of paper? How much paper (if any) is left over? 

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Exercises 26  27 26. Juanita received a
$5000 inheritance and decided to invest some of it in the stock Turn Tape Back On For Solutions 

Problem Solving Strategies with
Fractions 1. Determine operation by
recognizing patterns: 

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Exercises 28  32 28. A chemist has some
liquid inside a container. When empty, the container weighs 30. Darlene bought lb. of oranges, lb. of apples,
and lb. of bananas. How many total Turn Tape Back On For Solutions 
Lesson 9: Problem Set
1. Ashley, John, and Beth are collecting cans for recycling. They collected
lbs.,
lbs., and 3 lbs. respectively. How many pounds of cans do they have altogether?
2. Mickey needs to sell 50 boxes of candy bars in order to win first prize. If
he has sold
boxes of candy bars already, how many more
boxes does he need to sell in order
to win first prize?
3. An industrial fan at high speed turns 640 revolutions per minute, how many
revolutions
per minute will the fan turn at
of the speed? How many
revolutions per minute at of
the speed?
4. A car travels 200 miles in hours. What is
the car’s average speed in (miles per
hour)? Round to the nearest whole.
5. Eric worked hours on Monday,
hours on Tuesday, 9 hours on Wednesday, and
hours on Thursday. If there are 40 hours in
a typical work week, how many hours
does Eric need to work on Friday?
6. Beth has 27 pounds of beans to make beanbags. How many
(whole) beanbags can she
fill if each beanbag takes lbs. of beans? How
many pounds of beans does she have
left over?
7. At Jefferson High Schoolof the freshman
class are on the honor roll. If the freshman
class has 320 students, how many are on the honor roll?
8. J. C. Limited’s stock on the New York Stock Exchange opened at
and at the end
of the day closed at . How much did the stock
gain for the day?
9. Kara ran miles on Monday,
miles on Wednesday, and
miles on Friday. Howmany miles did she average for those three days?
10. Viet’s car gets miles per gallon. If he
purchases 12 gallons of gas, how many miles
can he travel?