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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. Find equivalent fractions
using the LCD.
3. Add the numerator; keep
the common denominator.
4. Simplify.
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.
2. Find equivalent fractions using
the LCD.
3. Subtract the numerators; keep
the common denominator.
*If needed borrow 1 from the
whole number in the form of
the common denominator.
4. Simplify.
Turn Tape Off And Work Practice Exercises 4 - 7

4. During her shift as a nurse, Katie measured the liquid intake for one of her patients. The
patient took in ounces in the morning and ounces in the afternoon.

a. How much liquid did the patient take in altogether?

b. For the same patient, how much more liquid did the patient take in during the
afternoon than in the morning?

5. Susan is hemming slacks that measure 36 inches. The measurement needs to be
inches. How much will she need to remove?

6. Adam's fuel tank in his truck holds gallons of gas. If he started with a full tank and
used gallons, how much gas remains in the tank?

7. Jan sold cases of baby formula on Monday, cases on Tuesday, and cases on
Wednesday. How much was sold altogether?

Turn Tape Back On For Solutions
Multiplication Patterns

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

Given a _______ _______, find the cost of more than one.

Taking a __________ of a number (double, triple, etc.)

Take a ____________ _______ of a number (1/2 of, 1/3 of, etc.)
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 three-fourths 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.

a. How much fabric did she use?

b. How much is left?
Multiplication Note:

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

results in an answer that is ________ than the original number.
Example:

12. Adam had feet of lumber. He estimated that he would need to use about of that
amount to build a play-gym for his son. How much lumber will he use?
Turn Tape Off And Work Practice Exercises 13 - 16

13. If a cubic foot of water weighs pounds, how much does 6 cubic feet of water weigh?

14. A quantity of medicine weighs grams. How much will of the quantity of medicine
weigh?

15. Judy earns $48,000 a year as a mathematician. Lucy earns times that much as a
computer specialist. How much does Lucy earn?

16. A stock costs $ per share. How much will 25 shares cost? (Convert answer to dollars
and cents).

Turn Tape Back On For Solutions
Division Patterns

Given distance over time, find a ________.
Given a total of several items, find the amount for _____ item.
Find an __________.
Split something into ________ pieces or parts.
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 re-webbing needs feet of webbing. How many chairs
can he re-web 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.?
Turn Tape Off And Work Practice Exercises 20 - 23

20. A car used gallons of gasoline on a 400-mile trip. How many miles per gallon did the
car get on this trip?

21. A caterer has pounds of turkey. How many pound servings can he get from this
amount?

22. How many -cup size servings of juice can be poured from a pitcher containing 12
cups?

23. Jim has ounces of gold that is worth $1000. How much is one ounce worth?

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?
Turn Tape Off And Work Practice Exercises 26 - 27

26. Juanita received a $5000 inheritance and decided to invest some of it in the stock
market. If she buys 20 shares of stock A for $ per share and 32 shares of stock B at
$per share, how much will she have left from the $5000?

27. A chemist needs to separate 123 grams of a substance into three portions. The first
portion will equal one third of the total substance. The second portion will be of the
remaining amount. How many grams are in each of the three portions?

Turn Tape Back On For Solutions
Problem Solving Strategies with Fractions

1. Determine operation by recognizing patterns:
____________ – finds a total
____________ – compares (how much?)
____________ – from a given rate or unit amount, find the total
____________ – from a total, find a rate or unit amount

2. Estimate by using ____________ whole numbers or fractions.

3. Always check to determine if the answer is reasonable.
Turn Tape Off And Work Practice Exercises 28 - 32

28. A chemist has some liquid inside a container. When empty, the container weighs
grams. When the liquid is put into the container, it weighs grams. How much does the
liquid weigh?

29. Megan received a check for $1500. After paying of this amount for school tuition,
she paid of the remaining amount for textbooks. After these expenses, how much
does she have left?

30. Darlene bought lb. of oranges, lb. of apples, and lb. of bananas. How many total
pounds of fruit did she buy?

31. A manufacturer promotes their detergent as “concentrated”, and only ounces are
needed per load. If measured each time, how many loads could be washed from an
88-ounce box?

32. Forty-eight centerpieces are needed for a wedding reception. If each piece needs yard
of ribbon, how much ribbon do we need to buy?

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?

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