\\1,1
Dan grew 1 bushel of tomatoes. 3/4 of the bushel were ripe tomatoes. He gave 1/2 bushel of ripe tomatoes to his Uncle Fred. What fraction of a bushel of ripe tomatoes does he have left?

3/4
how many bushels of ripe tomatoes there were

1/2
how many bushels Dan gave to his uncle

What fraction of a bushel* ripe tomatoes* left
3/4 of the bushel* ripe tomatoes;* 1/2 bushel
gave* to his uncle

Subtraction
Division
Addition
Multiplication

The words WHAT FRACTION...LEFT tell us we want to know the DIFFERENCE.
N
  1/4
  1/2
1
  3/4

We subtract:

 3     1       3     2       1
--- - ---  =  --- - ---  =  --- bushel
 4     2       4     4       4
@
\\2,1
Ray walks 3/4 of a mile to school. Robert walks 1/4 mile to school and Jim walks 1/8 mile. How many miles farther does Ray walk than Robert?

3/4
how many miles Ray walks to school

1/4
how many miles Robert walks to school

how many miles farther* Ray* than Robert
Robert walks* to school
how many miles* does Ray walk

Subtraction
Addition
Multiplication
Division

The words HOW MANY MILES FARTHER tell us we need the DIFFERENCE between Ray's distance and Robert's.
N
  1/2
1
3
  3/4

Subtracting:

 3     1       2       1
--- - ---  =  ---  =  --- mile
 4     4       4       2
@
\\3,1
Mary used 3 1/8 yards of material to make a dress. Mary bought 5/8 of a yard of ribbon to trim it. She used 3/8 of a yard of ribbon. How many yards of ribbon remained?

5/8
how many yards of ribbon Mary bought

3/8
how many yards of ribbon Mary used on her dress

how many yards of ribbon remained
bought 5/8 of a yard of ribbon
3/8 of a yard of ribbon* remained

Subtraction
Addition
Division
Multiplication

We want the DIFFERENCE between the original amount of ribbon and the amount that remained.
N
  1/4
1
  1/8
3

Subtracting:

 5     3       2       1
--- - ---  =  ---  =  ---
 8     8       8       4
@
\\4,1
Joe had 3/4 of an acre of land. He grew vegetables on 1/8 of it. He sold 3/8 of an acre to the city. How much of an acre does he have left?

3/4
how many acres Joe had

3/8
how many acres Joe sold

how much* left
had 3/4 of an acre of land
sold 3/8* to the city

Subtraction
Addition
Multiplication
Division

The words HOW MUCH...LEFT tell us we need the DIFFERENCE between the acreage Joe had and the acreage he sold.
N
3/8
3/4
1/4
1/5

Subtracting:

 3     3       6     3       3
--- - ---  =  --- - ---  =  ---
 4     8       8     8       8
@
\\5,1
A yard of fabric costs $3.60. Jane needs 5/8 of a yard and decides to buy a little extra. What will 3/4 of a yard cost?

$3.60
how much a yard of fabric costs

   3/4
the portion of a yard that is being asked about

yard of fabric costs;* 3/4 of a yard cost
fabric costs $3.60
a yard of fabric

Multiplication
Subtraction
Addition
Division

We MULTIPLY the cost of a yard by the number of yards.
N
$2.70
$0.90
$3.60
$4.80

Multiplying:

 3    $3.60      3    $.90
--- x -----  =  --- x -----  =  $2.70
 4      1        1      1 
@
\\6,1
There are two partly used bottles of catsup in the refrigerator. If you combine 1/5 of a bottle plus 1/3 of a bottle, how much catsup will there be?

1/5
how much of one bottle of catsup has been used

1/3
how much of the other bottle of catsup has been used

combine;* plus
two partly used bottles
how much

Addition
Subtraction
Multiplication
Division

The words COMBINE and PLUS tells us we have to ADD.
N
8/15
1/8
1/4
1/3

Add:

 1     1        5      3       8
--- + ---  =  ---- + ---- =  ---- bottle
 5     3       15     15      15
@
\\7,1
There are 250 trees in Central Park. If 2/7 are maples, what fraction of the trees in Central Park are not maples?

 2/7
how many of the trees in Central Park are maples

1
the whole

what fraction* are not maples
trees in Central Park are* maples
trees in Central Park are not maples

Subtraction
Division
Multiplication
Addition

We want the DIFFERENCE between the whole, one, and the fraction that are maples. The DIFFERENCE represents the fraction of trees that are not maples.
N
  5/7
1
  8/15
  7/2

Subtracting:

     2       7     2       5
1 - ---  =  --- - ---  =  ---
     7       7     7       7
@
\\8,1
A pint is 1/8 of a gallon. A quart is 2 pints. What part of a gallon is a pint plus a quart?

 1/8
what part of a gallon is a pint

2
the number of pints in a quart

what part of a gallon is a pint plus a quart
a pint is 1/8 of a gallon
what* is a pint plus a quart

Addition
Subtraction
Division
Multiplication

To get the answer we ADD the fraction of a gallon that a pint is to the fraction of a gallon that a quart is.
N
3/8
1/12
1/32
1/8

Adding:

 1     2       3
--- + ---  =  --- gallon
 8     8       8
@
\\9,1
Bill's neighbor, Anne, has 1/2 of an acre of land in her backyard. Bill has 3/8 of an acre in his backyard and 1/4 of an acre in his front yard. What is Bill's total acreage?

3/8
how many acres Bill has in his backyard

1/4
how many acres Bill has in his front yard

total acreage
land in her backyard
1/4 of an acre in his front yard

Addition
Division
Subtraction
Multiplication

The word TOTAL tells us we must ADD the two figures that represent Bill's land in order to obtain Bill's TOTAL ACREAGE.
N
  5/8
  3/32
1
  1/8

Adding:

 3     1       3     2       5
--- + ---  =  --- + ---  =  ---
 8     4       8     8       8
@
\\10,1
Steve runs between 7:30 a.m. and 8:30 a.m. He ran 1/4 of a mile on Wednesday, 3/4 of a mile on Thursday and 1 1/2 miles on Friday. How many miles did he run in the three days?

  1/4
how many miles Steve ran on Wednesday

  3/4
how many miles Steve ran on Thursday

1 1/2
how many miles Steve ran on Friday

how many miles* in the three days
on Wednesday,* on Thursday and* on Friday
1 1/2 miles on Friday

Addition
Subtraction
Multiplication
Division

The words HOW MANY MILES tell us we want the SUM of the three days' mileage.
N
2 1/2
1 3/4
  1/2
  9/32

We add:

 1     3       1       1     3     3
--- + --- + 1 ---  =  --- + --- + ---
 4     4       2       4     4     2


    1     3     6       10       5         1
=  --- + --- + ---  =  ----  =  ---  =  2 ---
    4     4     4        4       2         2
@
\\11,1
Mr. Jones bought a 12-yard ball of string. He gave Tim 3/4 of a yard of string but Tim only used 1/3 of a yard. How many yards did Tim have left?

3/4
how many yards of string Tim was given

1/3
how many yards of string Tim used

how many yards* left
Mr. Jones bought
Tim only used

Subtraction
Addition
Multiplication
Division

What is LEFT is the DIFFERENCE between the amount Tim was given and what was used.
N
  5/12
  4/7
  1/4
2 2/5

Subtract:

 3     1        9      4        5
--- - ---  =  ---- - ----  =  ----
 4     3       12     12       12
@
\\12,1
School is 2 miles from the center of town. Jimmy lives 2/3 of a mile from school and Patrick lives 3/4 of a mile from school. How many miles farther from school does Patrick live?

2/3
how many miles Jimmy lives from school

3/4
how many miles Patrick lives from school

how many miles farther
Jimmy lives* and Patrick
how many miles* from school

Subtraction
Multiplication
Division
Addition

The words HOW MANY MILES FARTHER tell us we want the DIFFERENCE between Patrick's distance from school and Jimmy's.
N
  1/12
1
  1/6
  5/12

Subtract:

 3     2        9      8        1
--- - ---  =  ---- - ----  =  ----
 4     3       12     12       12
@
\\13,1
Tom often reads more than 1/2 of an hour a day. Tom spent 3/4 of an hour yesterday and 3/4 of an hour today reading his new book. How many hours did he spend in the two days reading his new book?

3/4
how many hours yesterday Tom spent reading

3/4
how many hours today Tom spent reading

how many hours* in* two days
Tom spent* reading his new book
3/4 of an hour today

Addition
Division
Multiplication
Subtraction

We want the TOTAL time spent reading the book. Therefore, we ADD.
N
1 1/2
  5/8
1 3/4
2 7/8

We add:

 3     3       6         2         1
--- + ---  =  ---  =  1 ---  =  1 ---
 4     4       4         4         2
@
\\14,1
A storekeeper had 4 pounds of nuts. He sold a quarter pound plus 3/8 of a pound of nuts. How many pounds of nuts did he sell?

1/4
how many pounds of nuts are sold

3/8
how many pounds of nuts are sold

quarter pound* plus 3/8* pound;* how many
sold a quarter pound
plus

Addition
Subtraction
Multiplication
Division

The word PLUS tells us we have to ADD.
N
  5/8
  3/8
1 1/4
  2/3

Add:

 1     3       2     3       5
--- + ---  =  --- + ---  =  ---
 4     8       8     8       8
@
\\15,1
Phil got over 70% on his math test. He missed 5 problems out of 20. What fraction of the problems did he miss?

 5
the number of problems Phil missed on the math test

20
the number of problems there were on the math test

what fraction of the problems did he miss
missed 5 problems out of 20
what* problems did he miss

Division
Subtraction
Multiplication
Addition

The fraction of PROBLEMS MISSED to TOTAL PROBLEMS is found through DIVISION.
N
1/4
1/3
1/2
1/5

Divide:

  5       1
----  =  ---
 20       4
@
\\16,2
Guy bought a 1/8 carat diamond ring for his girlfriend at $1,600 a carat. Before he bought the ring, he had $250. How much did he have after buying it?

       1/8
the number of carats in the diamond ring Guy bought

$1,600
how much money a carat cost

  $250
how much money Guy had before he bought the ring

before* he had $;* how much* after
diamond ring* at $1,600 a carat
bought the ring;* had $250

Multiplication/Subtraction
Addition/Multiplication
Subtraction/Division
Not given

We find the COST of the ring by MULTIPLICATION and the AMOUNT LEFT by SUBTRACTION.
N
    $50
   $150
$12,800
$13,050

The ring costs:

   1/8 x $1,600  =  $200.

Thus, Guy has:

   $250 - $200  =  $50 left.
@
\\17,2
Charles had saved $15.00. He spent 1/3 of it on a shirt that was 45% cotton and 55% polyester. How much did he have left?

$15.00
how much money Charles had saved

   1/3
how much of his savings Charles spent on a shirt

saved;* spent;* how much* left
spent* it on a shirt
how much did he have

Multiplication/Subtraction
Division/Multiplication
Addition/Subtraction
Not given

We MULTIPLY to get the COST of the shirt. Then, we SUBTRACT the amount spent on the shirt from the original savings to find HOW MUCH he had LEFT.
N
$10
$30
$20
 $5

Charles spent $15 x 1/3
=  $5 on the shirt.

Thus, he had:
   $15 - $5  =  $10 left.
@
\\18,2
Merle needed a total of 3/8 of a yard of fabric. She bought 1/8 yard of silk at $3.28 a yard, and 1/4 yard of satin at $4.24 a yard. What was the total cost?

  1/8
how many yards of silk Merle bought

$3.28
how much money a yard of silk cost

  1/4
how many yards of satin Merle bought

$4.24
how much money a yard of satin cost

silk at;* satin at;* total cost
1/8 yard* and 1/4 yard;* total
$3.28 a yard, and* $4.24 a yard

Multiplication/Addition
Subtraction/Multiplication
Division/Multiplication
Not given

We must MULTIPLY to find the cost of each piece of fabric and then ADD these products together to find the total cost.
N
$1.47
$7.52
$0.96
$1.06

Merle spent 1/8 x $3.28  =  $.41 on silk
        and 1/4 x $4.24  =  $1.06 on satin

Thus, the total cost was:

   $.41 + $1.06  =  $1.47.
@
\\19,2
Raoul bought a half-gallon of milk at $2.98 per gallon and a quart (1/4 gallon) of orange juice at $5.28 a gallon. How much did he spend?

  1/2
how many gallons of milk Raoul bought

$2.98
how much money a gallon of milk cost

  1/4
how many gallons of orange juice Raoul bought

$5.28
how much money a gallon of orange juice cost

milk at;* juice at;* how much did he spend
half-gallon of milk* and a quart* of orange juice
$2.98* and* $5.28;* how much

Multiplication/Addition
Division/Addition
Addition/Division
Multiplication/Subtraction

We MULTIPLY the price per gallon by the fraction to find EACH PRICE and ADD the results to find HOW MUCH Raoul spent.
N
$2.81
$1.49
$1.32
$4.26
The milk cost 1/2 x $2.98 = $1.49 and the
orange juice cost 1/4 x $5.28 = $1.32.

Thus, the total cost was:

   $1.49 + $1.32  =  $2.81.
@
\\20,2
If a town is 3/5 female, what fraction of the town's population is male?

 3/5
what portion of the town's population is female

1
the whole

what fraction of* population is male
a town is 3/5 female
what* population is male

Subtraction
Addition
Multiplication
Division

To find out WHAT FRACTION of the whole town is male, we SUBTRACT the 3/5 from 1.
N
2/5
2/3
1/2
1/3

Subtracting:

     3       5     3       2
1 - ---  =  --- - ---  =  ---
     5       5     5       5
@
\\21,2
In the town of Sunray a city block equals 1/20 of a mile and a country block equals 1/15 of a mile. If the school is a city block and a country block away from town, what fraction of a mile is that?

1/20
what portion of a mile a city blck equals

1/15
what portion of a mile a country block equals

a city block and a country block;* what fraction of a mile
city block equals;* country block equals
school is a city block and a country block away from town

Addition
Multiplication
Division
Subtraction

To find out WHAT FRACTION OF A MILE is the answer, we need to ADD the two distances.
N
7/60
1/35
2/35
7/12

Adding:

  1      1        3      4        7
---- + ----  =  ---- + ----  =  ----
 20     15       60     60       60
@
\\22,2
Henry and Fred went fishing and caught a total of 7 fish. Henry's longest fish was 12 3/4 inches long and Fred's longest fish was 10 2/3 inches long. How many inches longer was Henry's fish?

12 3/4
how many inches Henry's longest fish was

10 2/3
how many inches Fred's longest fish was

how many inches longer
Fred's longest fish* 10 2/3 inches long
how many inches* was Henry's fish

Subtraction
Addition
Multiplication
Division

The words HOW MANY INCHES LONGER indicate that we want the DIFFERENCE between the two lengths given.
N
 2 1/12
 2 3/5
22 5/7
 2 1/3
Subtract the smaller from the larger:

    3        2       51     32
12 --- - 10 ---  =  ---- - ----
    4        3        4      3


    153     128       25          1
=  ----- - -----  =  ----  =  2 ----
     12      12       12         12
@
\\23,2
To decorate for a Fourth of July party, Jenny has 1/5 yard of red cloth, 1/10 yard of blue cloth, and 1/8 yard of white cloth. How many yards of cloth does she have in all?

1/5
how many yards of red cloth Jenny has

1/10
how many yards of blue cloth Jenny has

1/8
how many yards of white cloth Jenny has

how many yards* in all
red cloth,* blue cloth* and* white cloth
yards of cloth

Addition
Division
Subtraction
Multiplication

The words HOW MANY YARDS...IN ALL tell us we want the SUM of the three quantities.
N
17/40
 1/34
 3/34
 3/40

Adding:

 1      1     1        8      4      5
--- + ---- + ---  =  ---- + ---- + ----
 5     10     8       40     40     40


    17
=  ----
    40
@
\\24,2
In New York City, it is 3/20 of a mile from 96th Street to 99th Street. It is 1/10 of a mile from 99th Street to 101st Street. How far is it (in miles) from 96th to 101st Street?

3/20
how many miles it is from 96th Street to 99th Street

1/10
how many miles it is from 99th Street to 101st Street

how far* (in miles) from 96th to 101st Street
from 96th Street to 99th Street
1/10 of a mile* to 101st Street

Addition
Division
Subtraction
Multiplication

We must ADD the two distances to find the total distance between the two streets.
N
1/4
1/20
1/2
1/5

Adding:

  3      1        3      2        5
---- + ----  =  ---- + ----  =  ----
 20     10       20     20       20

    1
=  ---
    4
@
\\25,2
If 16 out of 24 children passed a 20-question quiz, what fraction of the class passed?

16
how many children passed the quiz

24
how many children there were in the class

what fraction of the class passed
16 out of 24 children passed
24 children;* 20-question quiz

Division
Subtraction
Addition
Multiplication

To find out WHAT FRACTION PASSED, we DIVIDE 16 by 24.
N
  2/3
1 1/2
  1/3
  7/8

Dividing:

 16        8       4       2
----  =  ----  =  ---  =  ---
 24       12       6       3
@
\\26,2
While waiting for her bus, Janice noticed that on the average she would see 3 express buses pass her before her local bus arrived. What fraction of buses are locals (out of the whole)?

3
how many express buses passed before a local arrived

1
the number of local buses

what fraction of buses are locals
on the average
3 express buses* before her local

Addition/Division
Multiplication
Subtraction/Division
Addition

We DIVIDE the number of local buses by the TOTAL NUMBER of buses.
N
1/4
1/3
1/2
3/4

We know there is a total of
3 express + 1 local
=  4 buses in a group.

We divide 1 by 4:

1/4 of the buses are local.
@
\\27,2
The cooking class usually used 2 1/3 dozen eggs in three days, but this week was different. On Monday, the class used 1/3 of a dozen eggs, on Tuesday 1/6 of a dozen eggs and on Thursday 1/4 of a dozen eggs. How many dozens of eggs were used in the three days?

1/3
what portion of a dozen eggs the cooking class used on Monday

1/6
what portion of a dozen eggs the cooking class used on Tuesday

1/4
what portion of a dozen eggs the cooking class used on Thursday

how many dozens of eggs* used in* three days
the cooking class* used* eggs
how many* eggs were used

Addition
Multiplication
Division
Subtraction

In this problem, HOW MANY tells us to ADD all the eggs used in 3 days.
N
  3/4
  1/12
1 1/4
  1/4

Add:

 1     1     1        4      2      3
--- + --- + ---  =  ---- + ---- + ----
 3     6     4       12     12     12

     9       3
=  ----  =  ---
    12       4
@
\\28,2
A recipe for dessert called for 1/4 cup of sugar in the first layer, 1/2 cup in the second layer and 2/3 cup in the icing. How many cups of sugar were needed?

1/4
how many cups of sugar were needed for the first layer of dessert

1/2
how many cups of sugar were needed for the second layer of dessert

2/3
how many cups of sugar were needed for the icing

how many cups of sugar* needed
1/4 cup* first layer;* second layer
2/3 cup in the icing

Addition
Multiplication
Subtraction
Division

In this problem, HOW MUCH tells us to ADD all the amounts of sugar used in the recipe.
N
1 5/12
2 1/6
  4/9
  5/12

Add:

 1     1     2        3      6      8
--- + --- + ---  =  ---- + ---- + ----
 4     2     3       12     12     12


    17          5
=  ----  =  1 ----
    12         12
@
\\29,2
Mr. Mark had 3/4 of a bushel of corn when he started feeding his 14 chickens. When he was finished he had 3/5 of a bushel left. What fraction of a bushel did he use?

3/4
how many bushels of corn Mr. Mark had when he started feeding his chickens

3/5
how many bushels of corn Mr. Mark had left when he finished feeding his chickens

when he started;* had* left;* what fraction* did he use
corn* when he started feeding his* chickens
when he was finished he had* left

Subtraction
Addition
Multiplication
Division

To find the AMOUNT USED, we want the DIFFERENCE between the original and the final amounts of feed.
N
   3/20
   1/2
 1 5/12
11 5/6

Subtract:

 3     3       15     12        3
--- - ---  =  ---- - ----  =  ----
 4     5       20     20       20
@
\\30,2
If Lou spends 1 3/4 hours doing his homework, how many minutes does it take him?

 1 3/4
how many hours Lou spends doing his homework

60
how many minutes there are in an hour

1 3/4 hours;* how many minutes
Lou spends 1 3/4 hours
doing his homework

Multiplication
Addition
Subtraction
Division

To find HOW MANY MINUTES it takes him, we MULTIPLY the number of hours by the number of minutes per hour.
N
105
 85
120
125

Multiply:

   3     60       7     60
1 --- x ----  =  --- x ----
   4      1       4      1

    7     15
=  --- x ----  =  105 min.
    1      1
@
\\31,3
Laura is 10 years old. She spends 48 days of her summer vacation with her grandmother, who is 51 years old. Laura's vacation totals 72 days. What part of her vacation does she spend with her grandmother?

48
how many days of vacation Laura spends with her grandmother

72
the total number of vacation days Laura has

what part* with* grandmother
48 days of* vacation
vacation totals 72 days

Division
Addition
Subtraction
Multiplication

In this problem, WHAT PART means WHAT FRACTION of 72 is 48.
N
2/3
3/4
1/2
2/5

Divide, and reduce:

 48       24       12       6       2
----  =  ----  =  ----  =  ---  =  ---
 72       36       18       9       3
@
\\32,3
There are 468 pupils in Dorothy's school. Her class has 40 pupils. 1/8 of her class was absent because of illness. How many in Dorothy's class were present?

40
the number of pupils in Dorothy's class

  1/8
what part of the class was absent

40 pupils;* 1/8* absent;* how many in Dorothy's class were present
pupils in Dorothy's* class
absent because of illness

Multiplication/Subtraction
Addition/Multiplication
Addition/Division
Multiplication/Division

We MULTIPLY to find how many in Dorothy's class were absent. Then we SUBTRACT this number from the total number of students in the class to find HOW MANY WERE PRESENT.
N
35
 8
 4
 5

1/8 x 40  =  5 students were ill.

Thus,

  40 - 5  = 35 students were in school.
@
\\33,3
For a small patch in his driveway, Miguel bought sand at the rate of $15 per 100-pound bag and cement at $40 per 100-pound bag. He bought 1/4 of a bag of sand and 3/8 of a bag of cement mix. How much did he pay?

$15
how much money a 100-pound bag of sand cost

$40
how much money a 100-pound bag of cement cost

   1/4
how many bags of sand Miguel bought

   3/8
how many bags of cement Miguel bought

bought sand at* and cement at;* how much did he pay
$15 per 100-pound bag and* $40 per 100-pound bag
1/4 of a bag of sand;* 3/8 of a bag of cement mix

Multiplication/Addition
Multiplication/Subtraction
Addition/Division
Not given

To find the costs of each we MULTIPLY. Then we ADD the results to find HOW MUCH he paid.
N
$18.75
$14.24
$15.00
$38.38

The sand cost 1/4 x $15  =  $3.75.

The cement mix cost 3/8 x $40  =  $15.

Adding:

       $15.00 + $3.75  =  $18.75
@
\\34,3
Steve and Stanley are painting a barn red. They bought 20 gallons of paint. Steve has painted 1/4 of the barn. Stanley has completed 3/8 of it. What part of the barn has been painted so far?

1/4
what portion of the barn Steve has painted

3/8
what portion of the barn Stanley has painted

what part of the barn has been painted
Steve and Stanley are painting a barn
Stanley has completed 3/8

Addition
Multiplication
Subtraction
Division

The part of the barn painted so far can be determined by finding the SUM of the parts each man has painted.
N
5/8
3/32
1/2
3/5

Adding:

 1     3       2     3       5
--- + ---  =  --- + ---  =  ---
 4     8       8     8       8
@
\\35,3
Maggie has 83 silver coins that weigh 3/4 of an ounce each. She has 3 gold coins that weigh 1/4 of an ounce each. How many ounces of silver does Maggie have?

83
how many silver coins Maggie has

  3/4
how many ounces each coin weighs

83 silver coins;* 3/4* ounce each;* how many ounces of silver
Maggie has* silver coins
3 gold coins;* 1/4* ounce each;* how many ounces

Multiplication
Addition
Subtraction
Not given

To find HOW MANY ounces of silver Maggie has, which is the sum of like addends, MULTIPLICATION is most easily used.
Y
Before solving, round 83 to the nearest ten.
 60
240
 41
110
83 is rounded to 80.

To multiply, we rename 80 as 80/1.

We then proceed:

 80     3       20     3
---- x ---  =  ---- x ---  =  60 ounces
  1     4        1     1
@
\\36,3
Carol and Jan were building a cabinet. Carol built 2/5 of the cabinet. Jan built 1/5 of the same cabinet. How much of the cabinet remained to be completed?

 2/5
what portion of the cabinet Carol built

 1/5
what portion of the cabinet Jan built

1
the whole

Carol built;* Jan built;* how much* remained
1/5 of the same cabinet
how much of the cabinet* completed

Addition/Subtraction
Subtraction/Multiplication
Multiplication/Division
Not given

ADDITION is used to find the portion of the cabinet that had been completed. This amount is then SUBTRACTED from 1.
N
2/5
1/5
3/5
3/10

The portion of the cabinet completed
is:
 2     1       3
--- + ---  =  ---
 5     5       5

We then subtract from one to get:

     3       5     3        2
1 - ---  =  --- - ----  =  ---
     5       5     5        5
@
\\37,3
Eva bought 32 boxes of pretzels. Each box weighed 6 1/2 ounces. In seven days she ate 8 of the boxes of pretzels. What fraction of the boxes of pretzels did Eva eat?

32
how many boxes of pretzels Eva bought

 8
how many boxes of pretzels Eva ate

bought;* ate;* what fraction* did Eva eat
Eva bought 32 boxes of pretzels
she ate 8;* what fraction

Division
Addition
Subtraction
Multiplication

The RATIO of PRETZELS EATEN to PRETZELS BOUGHT is 8/32. DIVIDING gives us the answer.
N
  1/4
  3/8
  1/2
4

The ratio of 8 to 32 reduces:

  8        4       2       1
----  =  ----  =  ---  =  ---
 32       16       8       4
@
\\38,3
Harriet and Susan bought 2 1/4 pounds of licorice and 1 3/4 pounds of India nuts. They are sharing the nuts. What amount will each of the women receive if the nuts are divided equally?

1 3/4
how many pounds of nuts Harriet and Susan are sharing

2
the number used to create equal shares

divided equally
1 3/4 pounds of India nuts
each of the women

Division
Addition
Multiplication
Not given

DIVISION is used to find the amount of any quantity DIVIDED EQUALLY.
N
  7/8 pounds
1     pound
  2/7 pounds
3 1/2 pounds

Dividing:

   3           7     2       7     1
1 --- / 2  =  --- / ---  =  --- x ---
   4           4     1       4     2

    7
=  ---
    8
@
\\39,3
The face of a rectangular-shaped watch measures 7/8 of an inch long by 5/8 of an inch wide. The watchband measures 5 1/8 inches long by 1/4 of an inch wide. What is the area of the face?

7/8
how many inches long the face of the watch is

5/8
how many inches wide the face of the watch is

long* by* wide;* what is the area
a rectangular-shaped watch
measures 7/8 of an inch long

Multiplication
Addition
Subtraction
Not given

The AREA of a rectangular object equals its length TIMES its width.
N
  35/64 square inch
3       square inches
2  3/16 square inches
   5/64 square inch

Multiplying length times width, we get:

 7     5       35
--- x ---  =  ---- square inch.
 8     8       64
@
\\40,3
Amy and Jerome both have a 45-minute study period at school. Amy did 1/3 of her homework at school. Jerome did 1/5 of his at school. How much more homework did Amy complete than Jerome?

1/3
how much of her homework Amy did at school

1/5
how much of his homework Jerome did at school

how much more* than
Amy did 1/3* homework at school
Jerome did 1/5 of his

Subtraction
Addition
Multiplication
Not given

To determine HOW MUCH MORE one measure is than another, we use SUBTRACTION.
N
2/15
1/3
1/2
8/15

 1     1        5      3        2
--- - ---  =  ---- - ----  =  ----
 3     5       15     15       15

Amy did 2/15 more work than Jerome.
@
\\41,3
One-third of what Susan earned babysitting last week was used for a new purse. If she made $12.30, how much did she have left?

   1/3
what portion of the money Susan earned was used to buy a new purse

$12.30
how much money Susan earned

how much* left
what Susan earned* last week
one-third* used for a new purse

Multiplication/Subtraction
Subtraction/Addition
Addition/Multiplication
Multiplication/Division

MULTIPLY to find the cost of the purse and SUBTRACT that from the original to find HOW MUCH she had left.
N
 $8.20
$12.30
 $4.10
 $3.00

She spent:

  1/3 x $12.30  =  $12.30 / 3
  =  $4.10.

She has:

  $12.30 - $4.10  =  $8.20 left.
@
\\42,3
Mrs. Sturdy bought 3/4 of a dozen doughnuts for $1.80. How much did each doughnut cost?

  3/4
what part of a dozen doughnuts Mrs. Sturdy bought

$1.80
how much money Mrs. Sturdy paid for the doughnuts

12
the number of doughnuts in a dozen

3/4 of a dozen* for $;* how much* each
Mrs. Sturdy bought* a dozen doughnuts
doughnuts for $1.80

Multiplication/Division
Multiplication/Addition
Multiplication/Subtraction
Not given

We MULTIPLY to find the number of doughnuts and DIVIDE to find the price per doughnut.
N
20 cents
$1.35
80 cents
$1.98

3/4 of a dozen doughnuts is:
   3/4 x 12  =  9 doughnuts.

Dividing to find the cost
per doughnut, we get:

   $1.80 / 9  =  $.20
   =  20 cents per doughnut.
@
\\43,3
Marilyn bought 1/2 dozen roses for her mother on Mother's Day. She paid $5.40. At this price, what was the cost of one rose?

  1/2
the fraction of a dozen roses Marilyn bought

$5.40
how much money Marilyn paid for the roses

12
the number of roses in a dozen

1/2 dozen;* paid $;* cost of one rose
1/2 dozen roses* on Mother's Day
she paid $5.40

Multiplication/Division
Addition
Subtraction
Multiplication

We MULTIPLY to find the number of roses and DIVIDE to find the cost of one rose.
N
90 cents
$1.60
$2.70
60 cents

1/2 dozen roses is 1/2 x 12  =  6 roses.

Thus, the cost of one rose equals 

   $5.40 / 6  =  $.90  =  90 cents.

Note: There are 12 in 1 dozen.
@
\\44,3
Tom's friends bought him a birthday cake for $4.80. Joe paid for 1/8 of the total cost. Sam paid 1/4 of the total cost, and Pete paid the rest. How much did Joe pay?

$4.80
how much money Tom's friends spent for the birthday cake

  1/8
what portion of the cost of the cake Joe paid

1/8 of* total;* how much did Joe pay
birthday cake for $4.80
Joe paid for 1/8 of the total cost

Multiplication
Addition
Subtraction
Division

We MULTIPLY the cost of the cake by the fraction that represents the amount Joe paid.
N
60 cents
95 cents
$4.80
$1.20

Multiply:

 1              $4.80
--- x $4.80  =  -----  =  $.60
 8                8
                       =  60 cents
@
\\45,3
The new baby weighed 6 7/8 pounds when he was born. He gained 3 3/4 pounds in 3 months. What was the average monthly gain?

3 3/4
how many pounds the baby gained

3
the number of months in which the baby gained the pounds

average monthly gain
he gained* pounds
3 months

Division
Addition
Multiplication
Subtraction

The AVERAGE GAIN equals the TOTAL GAIN DIVIDED by the NUMBER OF MONTHS.
N
 1 1/4
 1 3/4
   1/4
11 1/4

Divide:

   3           15           15     1
3 --- / 3  =  ---- / 3  =  ---- x ---
   4            4            4     3


    15       5         1
=  ----  =  ---  =  1 --- pounds
    12       4         4
@
\\46,4
Bill built a box 8 2/3 feet by 6 1/3 feet by 9 5/6 feet. He sawed 4 5/6 feet off a board that was 13 1/2 feet long. What was the length of the board that remained?

 4 5/6
how many feet Bill sawed off the board

13 1/2
how many feet long the board was to start with

what* length of* board* remained
sawed 4 5/6 feet off
board* was 13 1/2 feet long

Subtraction
Addition
Division
Multiplication

The words WHAT...LENGTH...REMAINED tell us we must find the DIFFERENCE between the original length and the part that was cut off.
N
 8 2/3
 6 1/3
 9 5/6
18 1/3

Subtracting:

    1       5       27     29       81 - 29
13 --- - 4 ---  =  ---- - ----  =  ---------
    2       6        2      6          6


    52       26         2
=  ----  =  ----  =  8 ---
     6        3         3
@
\\47,4
From a piece of dress goods that was 60 inches wide and 13 1/4 yards long, Mae cut a piece 4 7/8 yards long. How many yards remained?

13 1/4
how many yards long the piece of dress goods was

 4 7/8
how many yards Mae cut from the piece of dress goods

how many yards remained
piece of dress goods* 13 1/4 yards long
Mae cut a piece;* how many yards

Subtraction
Division
Multiplication
Addition

The words HOW MANY...REMAINED tell us we want the DIFFERENCE between the original length and the length of the piece that was cut off.
N
 8 3/8
 7 7/8
21 5/8
 9 1/8

Subtracting:

    1       7       53     39       106 - 39
13 --- - 4 ---  =  ---- - ----  =  ----------
    4       8        4      8           8


    67         3
=  ----  =  8 ---
     8         8
@
\\48,4
At at an athletic field there is a section of bleachers containing a dozen rows of seats. If each row is 45 feet long, and 1 1/2 feet is allowed for each person, how many people can sit in the section at once?

12
how many rows there are in a section of bleachers at the athletic field

45
how many feet long each row in the section of bleachers is

 1 1/2
the number of feet allowed for each person sitting in a seat

rows;* feet long;* feet* for each person, how many people can sit
a dozen rows;* each row is 45 feet long
1 1/2 feet* for each person;* in the section

Division/Multiplication
Addition/Multiplication
Subtraction/Division
Subtraction/Multiplication

We use DIVISION to find the number of people per row and MULTIPLICATION to find the total number of people who can sit in the stands.
N
360
540
120
720

First, we find that:

        1       45     3       45     2       90
45 / 1 ---  =  ---- / ---  =  ---- x ---  =  ----
        2        1     2        1     3        3

=  30 people can sit per row.

Then, 30 x 12  =  360 people can sit
in this section of bleachers.
@
\\49,4
The store bought 4 1/2 dozen men's hats at $42 a dozen and 3 dozen women's hats at the same price. What was the total cost of the men's hats?

  4 1/2
how many dozen men's hats the store bought

$42
how much money the dozen men's hats cost

total cost;* men's hats
store bought 4 1/2 dozen men's hats
$42 a dozen

Multiplication
Addition
Subtraction
Division

We find the TOTAL COST of the men's hats through MULTIPLICATION.
N
$189.00
$264.00
$168.00
$162.50

We multiply:

         1       42     9       21     9
$42 x 4 ---  =  ---- x ---  =  ---- x ---
         2        1     2        1     1

=  189

Thus, the cost is $189.
@
\\50,4
Gail has a gallon of paint in her closet. She wants to paint an area of 9 square yards. A pint of paint covers an area of 1 1/2 square yards. How many pints of paint will it take to cover the 9 square yards?

9
the number of square yards to be covered by paint

1 1/2
how many square yards a pint of paint covers

how many pints of paint* to cover
a pint of paint covers an area
paint covers* 1 1/2 square yards

Division
Addition
Subtraction
Multiplication

To find HOW MANY pints of paint will be needed, we must DIVIDE the total area to be covered by the area each can of paint will cover.
N
 6
 9
 3
13 1/2

Dividing as well as converting the mixed fraction
to an improper fraction, we get:

       1       9     3       9     2       3     2
9 / 1 ---  =  --- / ---  =  --- x ---  =  --- x ---
       2       1     2       1     3       1     1

=  6 pints of paint
@
\\51,4
Half of the workers arrived at the office before 9 o'clock. One quarter more arrived by 9:30. What fraction of the workers were at the office by 9:30?

1/2
what portion of the workers arrived at the office before 9:00

1/4
what portion of the workers arrived by 9:30

what fraction* were at the office by 9:30
workers arrived at the office before 9 o'clock
what* workers were at the office by 9:30

Addition
Multiplication
Division
Subtraction

In this problem, WHAT FRACTION means how many. Therefore, we want the SUM.
N
3/4
1/4
1/6
1/2

The sum is:

 1     1       2     1       3
--- + ---  =  --- + ---  =  ---
 2     4       4     4       4
@
\\52,4
Frank worked 2 1/2 hours in a grocery store on Monday, 1 3/4 hours on Tuesday, and 3 1/2 hours on Wednesday. How much time (in hours) did he work over the first two days?

2 1/2
how many hours Frank worked on Monday

1 3/4
how many hours Frank worked on Tuesday

how much time* did he work* first two days
Frank worked* in a grocery store
worked* on Monday,* on Tuesday, and* on Wednesday

Addition
Subtraction
Division
Multiplication

The words HOW MUCH...DID HE WORK...FIRST TWO DAYS tell us we want the total time for the days specified. Therefore, we ADD.
N
4 1/4
3 1/4
2 3/4
8 1/4

We add:

   1       3       5     7       10 + 7
2 --- + 1 ---  =  --- + ---  =  --------
   2       4       2     4          4

    17         1
=  ----  =  4 ---
     4         4

Frank worked 4 1/4 hours in the two days.
@
\\53,4
There are 24 people in swimming class: 1/4 are blond, 1/3 are redheads and the others are brunettes. How many brunettes are in the class?

24
how many people are in the swimming class

  1/4
what portion of people in the swimming class are blond

  1/3
what portion of people in the swimming class are redheads

 1
the whole

blond;* redheads;* others are brunettes;* how many brunettes
in swimming class;* how many
blond;* redheads and* brunettes

Addition/Subtraction/Multiplication
Addition/Multiplication
Division/Addition/Multiplication
Division/Multiplication/Subtraction

We ADD the figures for the non-brunettes. This SUBTRACTED from 1 gives the portion of brunettes in the class. MULTIPLICATION by the number of students in the class gives us the number of brunettes in the class.
N
10
16
 4
32

Portion of non-brunettes:
 1     1        3      4        7
--- + ---  =  ---- + ----  =  ----
 4     3       12     12       12

The remainder are brunettes.
This comes to 1 - 7/12 =  12/12 - 7/12  =  5/12.

Multiply to get the number of brunettes:
  5     24
---- x ----  =  5 x 2  =  10 brunettes
 12      1
@
\\54,4
18 pounds of candy are put into 4-inch long bags containing 1/8 pound each. How many bags will it take to bag all the candy?

18
how many pounds of candy are to be put into bags

  1/8
how many pounds of candy fit into each bag

how many bags* to bag all the candy
18 pounds of candy* put into* bags
bags containing 1/8 pound each

Division
Addition
Subtraction
Multiplication

To find HOW MANY, we DIVIDE the total amount of candy by the amount each bag holds.
N
144
  2 1/4
 84
 10

We divide:

      1
18 / ---  =  18 x 8  =  144 bags
      8
@
\\55,4
Mr. and Mrs. Cummings both work. They spend 1/4 of their combined salaries for their mortgage payment. If their monthly income is $1,080, how much do they pay annually for their mortgage?

   1/4
what portion of their combined salaries Mr. and Mrs. Cummings spend for their mortgage payment

$1,080
the amount of money Mr. and Mrs. Cummings earn monthly

12
the number of months in a year

spend 1/4;* monthly income;* how much* annually for their mortgage
1/4 of* combined salaries for* mortgage
monthly income is $;* how much* annually

Multiplication
Addition
Division
Subtraction

We must MULTIPLY twice: first, to find the amount of the monthly mortgage; second, to find the annual mortgage.
N
$3,240
$1,080
$2,240
  $270

The monthly mortgage is:

   1/4 x $1,080  =  $1,080 / 4
   =  $270.

Thus, the annual mortgage is:

   12 x $270  =  $3,240.
@
\\56,4
It costs 3/4 of a cent per hour to run an electric sewing machine. How long (in hours) can the machine run for 1/2 cent?

3/4
how many cents per hour it costs to run an electric sewing machine

1/2
how many cents the problem is asking about

costs* per hour;* how long* can the machine run for 1/2 cent
costs* per hour to run an electric sewing machine
3/4 of a cent* to run an electric sewing machine;* how long

Division
Multiplication
Addition
Subtraction

Cost per hour x No. of hours = Total cost. Therefore, No. of hours = Total cost / Cost per hour.
N
2/3
1/2
3/8
3/7

Dividing:

 1     3       1     4       4       2
--- / ---  =  --- x ---  =  ---  =  ---
 2     4       2     3       6       3

Therefore, for 1/2 cent the machine
will run 2/3 hour.
@
\\57,4
Timothy bought a 10-speed bicycle. The original price was $72. However, the bike was on sale at 1/4 off. How much did Timothy pay for the bike?

$72
the original price of Timothy's bicycle

  1/4
by what fraction off the original price the bicycle was reduced

1/4 off;* how much did Timothy pay
bicycle;* price was $72
bike was on sale at 1/4 off

Multiplication/Subtraction
Addition/Multiplication
Division/Multiplication
Addition/Subtraction

First, the markdown must be found by MULTIPLYING the original price by 1/4. Then, the sale price is found by SUBTRACTING the markdown from the original price.
N
$54.00
$72.00
$90.00
$18.00

The markdown was:

   1/4 x $72  =  $72 / 4  =  $18.

Thus, Timothy spent:

   $72 - $18  =  $54.
@
\\58,4
The Teasdales own a small 100-acre farm. They grew 1,350 bushels of wheat. The average production in the U.S. was 16 1/4 bushels per acre. How much more or less per acre was the Teasdales' production?

  100
how many acres the Teasdales own

1,350
how many bushels of wheat the Teasdales grew

   16 1/4
how many bushels per acre were produced in the U.S. on average

average* how much* less per acre was the Teasdales' production
100-acre farm;* how much* per acre
grew 1,350 bushels;* average production* 16 1/4 bushels

Division/Subtraction
Addition
Subtraction
Multiplication

We DIVIDE the bushels by the number of acres to find the Teasdales' PRODUCTION. Then, this is SUBTRACTED from the U.S. production to give us the DIFFERENCE.
N
 2 3/4 fewer bushels per acre
13 1/2 fewer bushels per acre
 2 3/4 more bushels per acre
13 1/2 more bushels per acre

The Teasdales' production is:
1350 / 100  =  13 1/2 bushels per acre.

    1        1       65     27       65     54
16 --- - 13 ---  =  ---- - ----  =  ---- - ----
    4        2        4      2        4      4

    11       54         3
=  ----  =  ----  =  2 ---
     4        4         4
That is 2 3/4 fewer bushels per acre.
@
\\59,4
A piece of calico material is 24 3/4 yards long. If each student in sewing class needs 3/4 of a yard, how many pieces, each 3/4 of a yard long, can be cut from the piece of material?

24 3/4
how many yards long the piece of material is

   3/4
how many yards of material each student needs

yards long;* how many pieces* can be cut
piece of calico material* 24 3/4 yards long
sewing class needs 3/4 of a yard

Division
Addition/Multiplication
Division/Subtraction
Addition/Subtraction

To find HOW MANY PIECES of the same length can be cut from the whole, we need to DIVIDE.
N
33
22
44
55

Divide:

    3     3       99     3       99     4
24 --- / ---  =  ---- / ---  =  ---- x ---
    4     4        4     4        4     3

    99
=  ----  =  33 pieces
     3
@
\\60,4
Bob has a newsstand at the corner of 4th Street and 3rd Avenue. Yesterday he sold 118 newspapers and 42 magazines. If he makes a 3 1/2-cent profit on each newspaper and 24 cents on each magazine, what was his profit?

118
how many newspapers Bob sold

 42
how many magazines Bob sold

  3 1/2
how many cents profit Bob makes on each newspaper

24
how many cents profit Bob makes on each magazine

newspapers;* magazines;* profit on each;* what was his profit
sold 118 newspapers;* what* profit
4th Street and 3rd Avenue;* 118 newspapers and 42 magazines

Multiplication/Addition
Addition
Multiplication
Not given

We MULTIPLY to find the profits from papers and from magazines, and then ADD the two amounts.
N
$14.21
$26.71
 $5.81
$12.41

Bob's profit in newspapers is:
         1             118     7
118 x 3 --- cents  =  ----- x ---
         2              1      2

=  59 x 7  =  413  =  $4.13

His profit on magazines is:
   42 x 24 cents  =  $10.08.
The total is $4.13 + $10.08  =  $14.21.
@

