\\1,1
Ms. Martin has three different accounts with her stockbroker. Over a 4-month period the accounts showed significance changes. The first showed an increase of $22,859. The second showed a decrease of $16,099, and the third showed an increase of $5,690. What was the total change in the three accounts?

$22,859
the amount of money by which the first account increased

$16,099
the amount of money by which the second account decreased

 $5,690
the amount of money by which the third account increased

first* increase* second* decrease;* third* increase;* total change
three different accounts;* 4-month period;* total
accounts with* stockbroker;* total* in the three accounts

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

To find the total change in the three accounts, we ADD the two increases and SUBTRACT the decrease.
Y
Before solving, round the changes to the nearest $1,000.
$13,000 increase
$45,000 increase
        even
$15,800 decrease

Add to find the combined increase, then subtract.
Before rounding:   After rounding:
   $22,859             23,000
  +  5,690            + 6,000
  --------            -------
                       29,000
  - 16,099           - 16,000
                     --------
                      $13,000 increase
@
\\2,1
Soaring Balloons sells .4 of its balloons during the summer months. The company began the year with 10,000 balloons. If 8,930 balloons are sold during the year, how many are sold in the summer?

     .4
the number of balloons Soaring Balloons sells during the summer months

8,930
the number of balloons sold during the year

sells .4* balloons* summer;* 8,930* sold* year, how many* in* summer
began* with* balloons;* how many are sold
many are sold in the summer

Multiplication
Addition
Subtraction
Division

To find a decimal fraction of an amount we MULTIPLY the amount given by the decimal.
N
3,572 balloons
2,610 balloons
4,500 balloons
3,187 balloons

Multiply 8,930 balloons by the decimal .4.
This gives the number sold in the summer.

    8,930
     x .4
  -------
  3,572.0 balloons
@
\\3,1
Friendship Bank charges a fee of $.30 for each one hundred dollars in traveler's checks for depositors with a balance of $500.00 or more. What would the service fee be for a customer buying $9,500 in traveler's checks?

     $.30
how much money Friendship Bank charges for a given number of dollars in traveler's checks

  $100
the amount of money in traveler's checks for which the bank fee is charged

$9,500
how much money in traveler's checks the problem is asking about

$* for each one hundred dollars;* what would* fee be for* $
Friendship Bank* fee of $* in traveler's checks* balance of $
balance of $;* $* in traveler's checks

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

We would first find the number of 100-dollar units by DIVIDING 100 into the amount of money. We then MULTIPLY this by the service charge for each unit.
N
   $28.50
$2,850.00
    $2.85
   $58.50

$9,500 is divided by 100 to find the
number of $100 units. This amount is
then multiplied by .30.

9,500/100  =  95   $.95
                  x .30
                 ------
                  $28.50 service charge
@
\\4,1
Frank's Menswear sold $5,031 worth of pants during a "Two for the Price of One" special sale. More than 1,000 people entered the store during the sale period. If each special cost $117, how many specials were sold?

$5,031
how many dollars' worth of pants were sold during a "Two for the Price of One" sale

  $117
how much money each pants special cost

sold $* worth* each special cost $* how many* sold
special sale;* more than 1,000 people* during* sale period
many specials were sold

Division
Addition
Subtraction
Multiplication

To find the number of like amounts in a total, we DIVIDE.
N
43
40
53
32

The $5,031 in sales is divided by the price
of each special to find how many were sold.
        43 specials sold
    ------
117 ) 5031
      468
      ----
       351
       351
       ---
@
\\\5,1
A "Now" account at County Bank allows money on deposit to double every 7 years. The bank limits the number of "Now" accounts to one for each depositor. If someone deposits $500, how many years will he have to wait to have $2,000?

     2
the number used to double an amount

     7
the number of years it takes a "Now" account to double money on deposit

  $500
how much money someone deposits

$2,000
the amount of money the problem is asking about

money* double every 7 years;* deposits $*, how many years* to have $
bank allows* deposit* every 7 years;* limits* one for each;* how many
many years will he have to wait to have $

Multiplication
Addition
Subtraction
Division

This is a pattern in which money is growing by multiples of two every seven years. Use MULTIPLICATION.
N
14
 7 1/2
 7
 2

The pattern for each seven years is continued
until $2,000 is in the account.

Years:      0          7
Balance: $500   $500 x 2  =  $1,000

Years:          14
Balance: $1,000 x 2  =  $2,000

$2,000 is reached after 14 years.
@
\\6,1
Al's Fence Company fenced a rectangular school lot that is twice as long as it is wide. Al's charged $90 per meter of fencing. If the width is 26 meters, how much fencing was needed to entirely enclose the yard?

26
the length, in meters, of one side of a rectangular school lot

 2
the number used to compute what twice as long is

lot* twice as long as* wide;* width* 26 meters, how much fencing
Al's fence company fenced* school;* charged $* per meter;* how much
$90 per meter of fencing;* 26 meters;* how much

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

To find the length, we MULTIPLY the measure of the width by 2. We then ADD the four sides to find the fencing needed.
N
156 meters
 78 meters
l04 meters
 52 meters

The length equals twice the 26-meter width.
Adding the four sides gives the amount of
fencing needed.

         52
 26      52
x 2      26
---    + 26
 52    ----
        156 meters of fencing
@
\\7,1
The workers in General Steel Company were given a bonus equal to .45 of their yearly salary. The average annual salary earned was $26,000. How much in extra pay would a worker making $32,000 per year receive?

       .45
what proportion of their salary would workers receive as a bonus

$32,000
how much money the problem is asking about

bonus equal to .45* salary;* how much* extra pay*
workers in* steel company* given* yearly salary;* average* was $
earned* $;* how much* per year

Multiplication
Addition
Subtraction
Division

To find the part of a whole indicated by a decimal fraction, we MULTIPLY the amount by the decimal.
N
$14,400
 $3,200
 $9,400
$12,400

The product of $32,000 and .45
gives the amount of the bonus.

    $32,000
   x    .45
   --------
    160,000
  1,280,000
 ----------
 $14,400.00 bonus
@
\\8,1
The numeral engraved on the side of Columbus Avenue School reads, "Founded MCMLX." The school was renovated in the year MCMLXXXXV. In what year did the school start?

1000
what the numerical value of M is

 900
what the numerical value of CM is

  50
what the numerical value of L is

  10
what the numerical value of X is

founded MCMLX;* what year did* school start
numeral engraved* side of* school;* renovated in* MCMLXXXXV
school was renovated

Addition
Subtraction
Multiplication
Division

To find the value of a numeral in the Roman System we ADD the value of the symbols. We have to identify the special combinations first, so we can add them as a single amount.
N
1960
1970
1980
1990

We first identify "CM" as equal to 900.
We then add the other values.

   M +  CM +  L +  X

1000 + 900 + 50 + 10

=  1960
@
\\9,1
James received $500.00 in gifts. Of this, he deposited $213.77 into a savings account. A year later, the account had $240.59. How much interest had it earned?

$213.77
how much money James put into a savings account

$240.59
how much money was in the savings account a year later

deposited $;* year later* account had $;* how much interest* earned
deposited $;* year later;* how much
$* in gifts;* deposited $;* how much

Subtraction
Addition
Multiplication
Division

The DIFFERENCE between the money deposited and the bank balance represents interest on the account. SUBTRACTION is used to find it.
N
$26.82
$17.59
$17.49
$26.22

The difference between the deposit of $213.77 and
the balance of $240.59 is the interest received.

  240.59
- 213.77
--------
   26.82 interest on account
@
\\10,1
The Tots' Toy factory produced 10,875 wooden soldiers. Each wooden soldier cost $19.95. However, .16 of them had to be rejected after inspection. How many were rejected?

10,875
the number of wooden soldiers produced by the toy factory

      .16
the proportion of wooden soldiers rejected after inspection

produced* wooden soldiers;* .16* rejected;* how many* rejected
factory produced* wooden soldiers;* each* cost $;* how many
Each* soldier cost $*; many were rejected

Multiplication
Addition
Subtraction
Division

The rate of rejection TIMES the number of units produced is the number rejected.
N
1,740
  362
6,525
  740

The rejection rate of .16 is multiplied by
the 10,875 wooden soldiers.

         10,875
          x .16
         ------
         652 50
         10,875
       --------
       1,740.00 units
@
\\11,1
On each of Jane's birthdays her father gave her a silver dollar for each year of her age. Silver is valued at $7.50 per ounce. She has now collected 21 silver dollars. How old is Jane?

 1
the number of silver dollars given to Jane for each of the years on her birthday

21
the number of silver dollars already collected

silver dollar for each year of* age;* has* 21;* how old
Jane's birthdays* father gave* silver;* valued at $* per ounce
she has now collected 21 silver dollars

Addition
Subtraction
Multiplication
Division

The SUM of the years of each of Jane's birthdays will be equal to 21.
N
 6
36
 7
 3

We begin adding each of Jane's birthdays,
finding the partial sums. When we get 21,
the last amount added will tell us Jane's age.

Birthdays: 1 + 2 + 3 + 4 + 5 + 6

 Partial
    sums: =  3  =  6  =  10  =  15  =  21

Jane is 6 years old.
@
\\12,1
The On-The-Town Limo Service charges $16 an hour for its services. It is six miles from the airport to midtown. It takes 75 minutes to get to midtown during rush hour and 30 minutes during non-rush hours. How much less is the charge during non-rush hours?

$16
how much money On-The-Town Limo Service charges for an hour of its services

 75
how many minutes it takes to get to midtown during rush hour

 30
how many minutes it takes to get to midtown during non-rush hours

$* hour;* 75 minutes* rush hour* 30* non-rush;* how much less* non-rush
charges $* for* services;* six miles from* airport to midtown
$16 an hour;* 75 minutes* 30 minutes;* how much

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

The amount of time saved is found by SUBTRACTING the times given. That part of an hour is then MULTIPLIED by the hourly charge.
N
$12.00
 $4.75
 $7.50
 $5.00

The difference between 75 and 30 minutes will yield
what part of an hour should be multiplied by the $16.00
hourly rate.
    75           3     16       3     4
  - 30          --- x ----  =  --- x ---
  ----           4      1       1     1

45 minutes or 3/4 hour      12
                        =  ----  =  $12
                             1
@
\\13,1
In l995, delicatessens in the United States sold $62,050,217,000 worth of foods and services. Of this, 45% was for frankfurters. On average, how much business, in dollars, did delicatessens do each day?

$62,050,217,000
how many dollars' worth of foods and services delicatessens in the United States sold in 1995

            365
how many days there are in one year

sold $* worth;* how much* each day
on average, how much business
United States sold $* worth of food;* % was* frankfurters;* how much

Division
Addition
Subtraction
Multiplication

Total sales are being broken into 365 even parts. DIVISION is used to do this.
Y
Before solving, round total sales to the nearest million.
170 million dollars
 17 million dollars
170 billion dollars
759 thousand dollars

Divide the amount of food and services
by the 365 days in a year.

         $170,000,000
    -----------------
365 ) $62,050,000,000
       36 5
       -----
       25 55
       25 55
       -----
@
\\14,1
The Oakville City school volleyball team was allotted $880 for uniforms and equipment by the athletic committee. There were 18 players on the team. If nine uniforms were bought for $59.90 each, how much was left for equipment?

$880
how much money was allotted to the volleyball team for uniforms and equipment

   9
the number of uniforms that were bought

 $59.90
how much money each uniform cost

$* for uniforms* equipment;* nine uniforms* $* each;* how much* left
volleyball team* allotted $;* 18 players;* how much
nine uniforms* $* each* how much

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

MULTIPLICATION is used to find the total of the nine similar amounts. SUBTRACTION finds what was left for purchase of other equipment.
N
$340.90
$100.00
$259.90
$340.10

$59.90 is multiplied by 9 to find
the cost of uniforms. This product
is then subtracted from $880.

 $59.90      $880.00
x     9     - 539.10
-------     --------
$539.10      $340.90  left for equipment
@
\\15,1
On January 10, 1956, the price of gold was $111.50 per ounce. An ounce of silver was $7.50. How much would an 18-ounce set of gold tableware be worth for its value in gold?

$111.50
how much money, per ounce, the price of gold was on the date given

  18
how many ounces of gold are in the set of gold tableware

gold* $* per ounce;* how much* 18-ounce* be worth
price of gold* $* per ounce;* ounce of silver* $;* how much
how much would* gold tableware be worth

Multiplication
Addition
Subtraction
Division

MULTIPLICATION is used to find the total of a like amount taken a given number of times.
N
$2.007.00
$1,503.25
  $200.39
$2,277.39

The product of $111.50 and 18 is how much
the tableware is worth.

    $111.50
   x     18
   --------
     892 00
    1115 0
  ---------
  $2,007.00
@
\\16,2
Tasty Cake charges 5 cents per square inch for sheet cake. The company takes in about $750.00 each day. What would be the cost of a rectangular cake measuring 15 inches by 20 inches?

 5
how many cents per square inch Tasty Cake charges for sheet cake

15
the length, in inches, of one side of a rectangular cake

20
the length, in inches, of another side of a rectangular cake

5 cents per square inch;* what* cost of* 15 inches by 20 inches
charges* cents* for sheet cake;* takes in* $* each day;* cost
the cost of a rectangular cake

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

The number of square inches in a rectangle is the PRODUCT of length and width. This is then MULTIPLIED by the cost per square inch.
N
 $15.00
$120.00
  $6.00
  $1.20

The product of 15 x 20 equals the number of
square inches. This is then multiplied by $.05.

  15       300
x 20     x .05
----    ------
 300    $15.00 cost of cake
@
\\17,2
Arnold bought a dozen erasers and a dozen brushes for art class. He had $25.00 to spend. If erasers cost $.29 each and brushes cost $.89 each, how much in all did he spend for these supplies?

12
the number of erasers Arnold bought for art class

 $.29
how much money each eraser costs

12
the number of brushes Arnold bought for art class

 $.89
how much money each brush costs

dozen erasers* brushes;* $* each, how much in all
Arnold bought* erasers and* brushes;* had $* to spend
$25.00 to spend;* for these supplies

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

Since each item was bought the same number of times, we are able to COMBINE the prices of the two and MULTIPLY the SUM cost by a dozen.
N
$14.16
 $5.80
 $6.69
$18.96

We are applying the distributive
property to find the answer:

(12 x $.29) + (12 x $.89)    $1.18
                            x   12
=  12 x ($.29 + $.89)       ------
                              2 36
=  12 x $1.18                11 8
                            ------
                            $14.16
@
\\18,2
Ace Audio Store gave away radios to new customers during a drive for new accounts. Each radio cost the store $3.25. The retail price of the radio was $5.95 If the store gave away $123.50 worth of radios at cost, how many accounts were opened during this drive?

  $3.25
how much money each radio cost the store

$123.50
how many dollars' worth of radios the store gave away

each radio cost the store* $;* gave away $* worth* how many accounts
radios;* each* $;* retail price* $;* gave away $
many accounts were opened during this drive

Division
Addition
Subtraction
Multiplication

The total cost of the radios is DIVIDED by the unit cost to find how many radios were given away.
N
38
83
63
17

$123.50 is divided by the cost of $3.25
for each radio.
          38 new accounts
    --------
325 ) 123 50
       97 5
       ----
       2600
       2600
       ----
@
\\19,2
The floor of the Early Bird Restaurant is built in the shape of an octagon. Inlaid metal strips correspond to the diagonals of the octagon. The metal strips cost $50 per meter. If one of the strips measures 11.5 meters, what is the total length of metal strips?

11.5
the length, in meters, of one strip, or diagonal, of the octagon floor

 4
the number of diagonals in an octagon

strips* diagonals of* octagon;* one* measures* meters* total length
metal strips* octagon;* cost $* per meter;* total
metal strips correspond to the diagonals of the octagon

Multiplication
Addition
Subtraction
Division

The length of each strip is MULTIPLIED by the number of diagonals in an octagon.
N
46.0 meters
36.0 meters
92.5 meters
73.5 meters

An octagon has four diagonals of equal length. The
11.5 meter length given for one diagonal is multiplied
by 4 to find the total length of the strips.

   11.5
    x 4
  -----
   46.0 meters of metal stripping
@
\\20,2
Verna collected 100 old stamps. The stamps varied in denomination from 1 cent to $1. The ones from before 1850 are worth $4 each, and those from after 1850 are worth $2. How much is Verna's collection worth if 25% are from before 1850.

100
the number of stamps Verna collected

 $4
how much money the stamps before 1850 are worth

 $2
how much money the stamps after 1850 are worth

 25%
what percentage of Verna's stamps are before 1850

100;* before 1850* worth $* each* after* $;* how much* 25%* from before
100 old stamps;* denomination from 1 cent to $1;* how much
Verna's collection* 25% are from before 1850

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

25% or 25 of the 100 stamps are worth $4 each. The remaining 75 are each worth $2. We MULTIPLY to find their dollar value and then ADD to find the total value.
N
$250
$100
$180
$150

The 25 older stamps are worth $4 each. The 75 other
stamps are worth $2 each. We multiply to find the
value for each and then add.

 $ 4     $  2      $100
x 25     x 75     + 150
----     ----     -----
$100     $150      $250 total value
@
\\21,2
Atlas Music Store paid $6,400 for 8 thirty-second radio commercials. Atlas' radio budget was $15,000 per year. How much did each minute of air time cost?

$6,400
how much money the store paid for radio commercials

     8
the number of radio commercials the store paid for

    30
how many seconds each radio commercial lasted

    60
how many seconds there are in a minute

$* for 8 thirty-second* commercials;* how much* each minute
store paid* for* radio commercials;* budget was $* per year
radio budget was $* per year

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

To find the total time in seconds, we MULTIPLY. This product is DIVIDED by 60 to change seconds to minutes. We then DIVIDE the number of minutes into the total cost to find the rate for each minute.
N
$1,600
$1,400
$1,500
$1,800

30 seconds times 8 equals the number of seconds of air
time. We then divide this by 60 to convert to minutes.
The cost is then divided by the number of minutes.

 30                4 minutes       $1600 per minute
x 8             -----            -------
---         60 ) 240           4 ) $6400
240 sec.                            4
                                    -
                                    24
                                    24
@
\\22,2
The Happy Pancake Shop sells 2.6 times as many pancakes as it does waffles. Pancakes and waffles cost 50 cents each. If it sold 630 waffles, how many pancakes did it sell?

  2.6
how many times more pancakes were sold as waffles

630
the number of waffles sold by the Happy Pancake Shop

2.6 times* pancakes as* waffles;* 630 waffles* how many pancakes
pancakes and waffles* 50 cents each;* 630 waffles;* how many
happy pancake shop;* sold 630 waffles

Multiplication
Addition
Subtraction
Division

To find a higher multiple of a given amount we MULTIPLY the amount by the multiple or factor.
N
 1,638
   164
16,380
   638

630 is multiplied by 2.6 to find
the number of pancakes sold.

   630
 x 2.6
 -----
 378 0
1260
------
1638.0 or 1,638 pancakes
@
\\23,2
A farmer cleared a rectangular field with an area of 600 square feet. It had a width of 20 feet. He expected a yield of 200 bushels of corn. What was the length of the field?

600
the number of square feet in a rectangular field cleared by a farmer

 20
the width, in feet, of the rectangular field

rectangular* area of* square feet;* width* feet;* what was* length
farmer* field* area of* square feet;* 200 bushels of corn
600 square feet;*  yield of 200 bushels

Division
Addition
Subtraction
Multiplication

The product of length and width determines the area. To find the length, being given the width and area, we DIVIDE the area by the width.
N
 30 feet
620 feet
155 feet
 40 feet

To find what number times 20
equals 600, we divide 600 by 20.

length x 20  =  600

            600
length  =  -----  =  30 feet
             20
@
\\24,2
The salaries of three clerks are (1) $16,820 (2) $14,250 and (3) $20,430. The starting salaries for each was $1,000 less. What is the average salary for these clerks?

      3
the number of clerks the problem is asking about

$16,820
how much money the first clerk makes

$14,250
how much money the second clerk makes

$20,430
how much money the third clerk makes

salaries* three clerks* $* $* and* $;* what is* average
salaries* $* $* and* $;* each was $* less
salary;* for these clerks

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

To find the average of a given number of salaries we first ADD the amounts and then DIVIDE by the number of salaries.
Y
Before solving, round each of the salaries to the nearest thousand.
$17,000
$14,500
$42,000
$42,500

The sum of the rounded-off salaries is divided by 3.

Salaries:   After rounding:
   $16,820     $17,000           $17000
    14,250      14,000          -------
    20,430    + 20,000        3 ) 51000
   -------    --------            3
                51,000            -
                                  21
                                  21
                                  --
@
\\25,2
Bill collected newspapers to raise money for his school. He filled 3/7 of a box with newspaper. A full box was worth $22.00. However, he could only get refunds for 7/10 of it. What part of the box was used to help his school?

3/7
the fraction of a box Bill filled with newspapers

7/10
the fraction of what Bill had in the box for which he got refunds

filled 3/7* box;* refunds for 7/10;* what part* was used
collected newspapers;* filled* a box;* full box* worth $
part of the box* used to help his school

Multiplication
Addition
Subtraction
Division

To find a fractional part of a given amount, we MULTIPLY that fraction by the amount stated.
N
 3/10
10/17
 1/7
 3/7

To find what the fraction of the box is,
we multiply.

  7     3        1     3        3
---- x ---  =  ---- x ---  =  ----
 10     7       10     1       10
@
\\26,2
In 1880, the U.S. population was 50,155,783. By 1970 it had risen to 203,235,298. Immigration accounted for approximately 25% of the increase. How many times greater was the population in 1970?

 50,155,783
how much the population was in the U.S. in 1880

203,235,298
how much the population had risen to by 1970

1880* population was;* 1970* risen to;* how many times greater* in 1970
U.S. population was;* immigration accounted for* % of* increase
many times greater was the population in 1970

Division
Addition
Subtraction
Multiplication

To find how many times greater one amount is than a lesser one, we DIVIDE the smaller into the greater of the two. (This can be done by simplifying rational form).
Y
Before solving, round the population for each year to the nearest million.
 4
 3
 2
30

50,155,783 is rounded to 50 million.
203,235,298 is rounded to 200 million.

 200
-----  =  4 times
  50
@
\\27,2
A cashier serviced 32 customers in 8 hours. The cashier worked 40 hours each week. On the average, how many minutes did he take for each customer?

32
the number of customers a cashier serviced

 8
the number of hours the cashier spent with the customers

60
how many minutes there are in one hour

32 customers in 8 hours;* how many minutes* each
cashier serviced 32 customers;* worked 40 hours each week;* average
customers;* hours;* worked* each week

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

Hours are converted to minutes by MULTIPLYING them by 60. The number of customers handled is then DIVIDED into the number of minutes to find the average time spent.
N
15 minutes
14 minutes
10 minutes
 8 minutes

Multiply 8 by 60 to convert hours to minutes. The
minutes are divided by 32 to find the average time
for each customer.
             15 minutes average time
          -----
 60    32 ) 480
x 8         32
---         ---
480         160
            160
            ---
@
\\28,2
A decorator placed a frame around a mirror shaped like a septagon. The mirror was hung eight feet off the floor. If 39.9 inches of border were used around this mirror, what is the length of each edge?

39.9
how many inches of border were used around the mirror

 7
how many sides a septagon has

septagon;* inches of border* what is* length of each edge
frame around* mirror;* hung eight feet off* floor
border* around* mirror;* what is* length

Division
Addition
Subtraction
Multiplication

The length of an edge of a septagon is one-seventh its perimeter, so we DIVIDE.
N
5.7 inches
4   inches
4.3 inches
8.6 inches

Dividing 39.9 inches by the number of
edges gives the length of each edge.

          5.7 inches
       ------
     7 ) 39.9
         35
         --
          4 9
          4 9
          ---
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\\29,2
Jan's Jewelry Shop charges $6 an inch for a gold chain. Gold is valued at $380.00 per ounce. If a chain is 7 1/4 inches long, what would be its price?

$6
how much money, per inch, the jewelry shop charges for a gold chain

 7 1/4
how many inches the chain is

$* an inch;* 7 1/4 inches long* what would be* price
Jewelry Shop charges $* for* gold chain;* $* per ounce;* price
chain is* inches long

Multiplication
Addition
Subtraction
Division

The price per inch is MULTIPLIED by the number of inches of gold chain.
N
 $43.50
 $42.00
 $24.00
$174.40

The length 7 1/4 inches is multiplied by $6.

   1           29     6       174 
7 --- x 6  =  ---- x ---  =  -----
   4            4     1        4

       2          1
=  43 ---  =  43 ---
       4          2

or $43.50 for the chain
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\\30,2
Mike's wardrobe consisted of 2 pairs of sneakers, 4 differently colored shirts, 2 differently colored jeans, 1 hat, and 1 jacket. How many ways can he wear his shirts and jeans without repeating the same two items?

4
the number of differently colored shirts Mike owns

2
the number of differently colored jeans Mike owns

4* shirts, 2* jeans;* how many ways* wear* without repeating
2* sneakers, 4* shirts, 2* jeans, 1* hat* jacket;* how many
Mike's wardrobe* differently colored;* how many* same two items

Multiplication
Addition
Subtraction
Division

The number of arrangements of two independent sets is the PRODUCT of samples in each of the two sets.
N
8
6
5
4

The number of arrangements is the product
of the number of colored shirts and the
number of colored jeans.

4 x 2  =  8 arrangements
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\\31,3
The Pells had a family income of $40,000 per year. They worked out a monthly budget. It included $695 for rent, $275 for utilities, $575 for food and clothing, and $320 for transportation and other expenses. How much do the Pells intend to spend for the entire year?

$695
how much money the Pells are spending monthly for rent

$275
how much money the Pells are spending monthly for utilities

$575
how much money the Pells are spending monthly for food and clothing

$320
how much money the Pells are spending monthly for transportation

  12
the number of months in a year

monthly;* $* rent, $* utilities, $* food* $* expenses. how much* year
income of $* per year;* monthly budget;* how much* spend
the Pells intend to spend for the entire year

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

The total budget for the month is found by ADDING all the categories together. The monthly total is then MULTIPLIED by 12 to find the year's budget.
Y
Before solving, round each monthly expense to the nearest hundred.
$22,800
$22,480
$24,000
$21,600

Each monthly expense is rounded and added. The total
is multiplied by 12.
Expenses: Rounded:
$695      $700        $1900
 275       300       x   12
 575       600       ------
 320     + 300        3 800
 ---     -----       19 000
        $1,900      -------
                    $22,800 to be spent for the year
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\\32,3
The Do-All Construction Company is split into five divisions. The average weekly salary in the plumbing division is $450.00. It has a total payroll of $28,500 per week. If 14% is paid out to workers in that division what amount of money is paid?

$28,500
how much money, per week, the Do-All Construction company has in payroll

     14%
what percent of the payroll is paid out to workers in the plumbing division

total payroll* $* per week;* %* paid* in that division* amount of money
do-all construction company* five divisions;* average* salary
average weekly salary

Multiplication
Addition
Subtraction
Division

To find a percent of an amount, we MULTIPLY the amount by the decimal form of the percent.
N
 $3,990
 $2,964
$14,000
   $399

The payroll of $28,500 is multiplied by the
decimal form of 14%.
  $28,500
 x    .14
 --------
  1140 00
  2850 00
---------
$3,990.00 paid to workers in the plumbing division
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\\33,3
There are 25 quarters and 25 nickels in a roll. On the average, bank customers request 2.4 rolls of quarters for each roll of nickels. If 840 rolls of quarters are asked for by customers, what is the likely number of nickel rolls requested?

  2.4
how many rolls of quarters are requested by bank customers for each roll of nickels

840
the number of rolls of quarters asked for by customers

quarters* for* nickels;* 840 rolls of quarters* number of nickel rolls
25 quarters* 25 nickels in* roll;* average* each roll
likely number of nickel rolls

Division
Addition
Subtraction
Multiplication

To find what number is 2.4 times smaller than 840, we DIVIDE 840 by 2.4.
N
350
325
240
280

840 is divided by 2.4

                      350 rolls of nickels
     -------       ------
2.4 ) 840.0  =  24 ) 8400
                     72
                     ---
                     120
                     120
                     ---
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\\34,3
The Friendly Savings Bank will loan a customer up to 75% of the net market value of his home at 9% interest. What is the largest amount they would loan a customer whose home has a net market value of $127,500?

      75%
the part of the net market value of a home that the Friendly Savings Bank will loan a customer

$127,500
how much money the net market value of a home is

75% of* net market value;* what is* largest amount* value of $
% of* value* at 9% interest
9% interest;* of $127,500

Multiplication
Addition
Subtraction
Division

To find a percent of a given amount, we MULTIPLY the amount by the decimal form of the percent.
N
$95,625
$15,300
$95,525
$75,000

$127,500 is multiplied by .75 to find
the largest loan.

  $127,500
 x     .75
 ---------
  6,375 00
 89,250 00
----------
$95,625.00 largest amount of a loan
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\\35,3
A garage attendant gets paid $6 per hour plus time and a half for overtime. The garage attendant's weekly salary is $240.00 for a 40-hour week. How much extra money would he get if he worked 8 extra hours during the week? (Time and a half is 1 1/2 times regular salary.)

$6
how much money a garage attendant gets paid per hour

 1 1/2
how many times his hourly wage a garage attendant would get paid if he worked overtime

 8
the number of extra hours the problem is asking about

$* per hour* time and a half* overtime;* how much extra* 8 extra hours
$* per hour plus;* weekly salary* $;* how much* money
garage attendant* paid* overtime;* weekly;* extra hours

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

The hourly wage is MULTIPLIED by 1 1/2 to find the overtime wage, which is then MULTIPLIED by the number of hours.
N
$72
$96
$60
$48

The overtime wage is the product of 1 1/2 and 6.
This is then multiplied by 8 hours.

   1           3     6       18
1 --- x 6  =  --- x ---  =  ----
   2           2     1        2

=  $9 per hour       8 x $9  =  $72 in overtime
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\\36,3
The "Banking Olympics" is held every four years. This year the record for counting out money was broken by 1 3/5 seconds when Maxwell counted out $862.49 in 5 1/2 seconds. What was the time of the former record holder?

1 3/5
by how much time Maxwell broke the record for counting out money

5 1/2
the number of seconds it took Maxwell to break the record for counting out money

broken by* seconds* counted* in* seconds;* time of* former record
banking olympics* every four years;* record* counted out $
$* in* second;* time

Addition
Subtraction
Multiplication
Division

The amount by which a time record is broken PLUS the new record equals the former best time.
N
7 1/10 seconds
3 9/10 seconds
6 4/7  seconds
7 1/5  seconds

1 3/5 seconds and 5 1/2 seconds are
added to find the former record.

  1 + 3/5      6/10
+ 5 + 1/2      5/10
---------     -----
  6 +         11/10  =  6 + 1 1/10
                     =  7 1/10 seconds
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\\37,3
Webster bought a guitar for $85. He owned it for a year and a half. He sold it for $72.25. What percent did Webster lose on the sale of the guitar?

$85
how much money Webster paid for the guitar

$72.25
how much money Webster sold the guitar for

bought* for $;* sold* for $;* what percent* lose on the sale
guitar for $;* owned* year and a half;* sold* $;* sale of* guitar
what* did Webster lose

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

The selling price is SUBTRACTED from the buying price to find the amount of Webster's loss. The loss is DIVIDED by Webster's purchase price to find the percent lost on the sale.
N
15%
10%
12%
20%

$72.25 is subtracted from $85 to find the amount lost.
The loss is then divided by the $85 cost of the guitar.

   $85.00            .15 or 15% lost on the sale
  - 72.25        -------
  -------     85 ) 12.75
   $12.75           8 5
                   -----
                    4 25
                    4 25
                    ----
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\\38,3
Ms. Harlow began her vacation on July 21. She hoped to be away for two weeks. She spent an average of $82.40 each day of her vacation. She started with $1,000 and came home with $11.20. How many days was she away?

   $82.40
how much money Ms. Harlow spent on average each day of her vacation

$1,000
how much money Ms. Harlow started with

   $11.20
how much money Ms. Harlow came home with

$* each day;* started with $* came home with $;* how many days
vacation;* for two weeks;* how many days
two weeks;* average of $82.40 each day

Division
Addition
Subtraction
Multiplication

To find a number of even amounts in a larger total, we DIVIDE. The remainder will be the amount she came back with.
N
12
 8
11
10

$1,000 divided by $82.40 yields the number of days away.
                          12 days
       ------        -------
82.40 ) 1000  =  824 ) 10000
                        824
                        ----
                        1760
                        1648
                        ----
                         112
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\\39,3
The Owens Gas Company has 150 employees. Each may be reached by phone by requesting a three-digit extension number. How many different phone extensions are possible using this system?

 3
the number of digits in each extension number

10
the number of possible digits to be used in the extension number

three-digit extension number;* how many different* extensions
Owens Gas Company* 150 employees;* reached by phone* extension
different phone extensions are possible using this system

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

The probability of independent events is the PRODUCT of the number of possible digits in each of the three places. This indicates the number of extensions possible.
N
1,000
  120
  720
    3

The probability of each of the digits is one
in ten. The three probabilities are multiplied
to find the number of phone extensions.

10 x 10 x 10  =  1,000 extensions
@
\\40,3
The Photo Eye Store bought 36 cameras for $60 each. They marked up the price by $24. What percent of the purchase price is this mark-up?

$60
how much money the store spent for each camera

$24
the amount of money by which the store marked up the price of each camera

$* each;* marked up* by $;* what percent of* price is* mark-up
store bought* cameras for $;* price by;* what* price
percent of the purchase price

Division
Addition
Subtraction
Multiplication

The mark-up DIVIDED by the price of the camera indicates the percentage increase.
N
40%
35%
24%
36%

$24 is divided by $60.
The quotient is converted to a percent.

       .40  =  40% mark-up
   -------
60 ) 24.00
     24 0
     ----
        0
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\\41,3
The Shirt Stop sold 4 3/4 dozen shirts on a busy day. Each shirt sold for $26.00. How many shirts did they sell?

 4 3/4
the number of shirts sold on a busy day at the Shirt Stop

12
the number a dozen is equal to

sold 4 3/4 dozen;* how many shirts
dozen shirts;* each* for $;* how many
shirt stop sold* busy day;* many shirts

Multiplication
Addition
Subtraction
Division

To find the total of a given number of like measures, we MULTIPLY.
N
57
54
75
48

4 3/4 is multiplied by 12 to find the
number of shirts sold.

   3            19     12
4 --- x 12  =  ---- x ----
   4             4      1

    19     3       57
=  ---- x ---  =  ----
     1     1        1

=  57 shirts sold
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\\42,3
70% of the coins produced at the Philadelphia Mint are pennies and 10% are dimes. If 13,500,000 coins were produced in one day, which expression describes the likely number of pennies?

        70%
the percentage of the coins produced at the Philadelphia Mint that are pennies

13,500,000
the number of coins produced in one day

70%* are pennies;* 13,500,000 coins* number of pennies
coins* at* philadelphia mint are pennies* dimes;* produced* likely
pennies and* dimes;* likely number of pennies

Multiplication
Addition
Subtraction
Division

The PRODUCT of the number of coins produced and the decimal form for 70% is the number of pennies produced.
N
9.45 x 10 to the sixth power
9.45 x 10 to the eighth power
9.45 x 10 to the seventh power
9.45 x 10 to the ninth power

13,500,000 is multiplied by .70
to find the number of pennies.

  13,500,000
       x .70
------------
9,450,000.00

or 9.45 x 10 to the sixth power
@
\\43,3
Walter sold $48,000 worth of cars from his father's used car lot one month. The lot had an average of 150 cars at any one time. If he was paid a 3% commission on these sales, how much did Walter earn that month?

$48,000
how many dollars' worth of cars Walter sold from his father's used car lot one month

      3%
the percentage Walter was paid as commission on these sales

sold $* worth;* paid* % commission* how much* earn
used car lot one month;* average* 150 cars;* how much
150 cars;* paid* commission on these sales

Multiplication
Addition
Subtraction
Division

To find a commission paid as a percent of sales, we MULTIPLY that percent by the amount of sales.
N
$1,440
  $144
$1,240
$4,800

To multiply $48,000 by a percent, we first
convert the percent to its decimal form.

  $48,000
 x    .03
---------
$1,440.00 paid to Walter
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\\44,3
Patsy's Department Store had sales of $42,385 on opening day. 900 customers bought merchandise that day. If $19,763 were credit card sales, how much was paid in cash?

$42,385
how much money Patsy's had in sales on opening day

$19,763
how much money was in credit card sales

sales of $*;* $* were credit card sales* how much was* cash
$* on opening day;* 900;* credit card sales
sales* 900 customers bought;* how much

Subtraction
Addition
Multiplication
Division

Cash sales is the DIFFERENCE between the total sales for the day and sales made on credit.
N
$22,622
$37,422
$23,622
$62,148

The credit card sales of $19,763 is subtracted
from the total daily sales of $42,385.

 $42,385
- 19,763
--------
 $22,622 sales paid in cash
@
\\45,3
The Donut Lovers company found it was able to sell the pastry from the holes it punched in donuts for 7 cents each. The full donut cost 25 cents. How much money was made by their selling the centers from 13,342 donuts?

     7
how much, in cents, the donut company sold the punched-out donut centers for

13,342
the number of donut centers that were sold

donut* holes* 7 cents each;* how much money* from 13,342 donuts
donut* holes* for 7 cents;* full* cost 25 cents;* how much
full donut* 25 cents;* how much money* from 13,342 donuts

Multiplication
Addition
Subtraction
Division

The PRODUCT of the number of donuts and the price of a donut center is the amount made from selling donut centers.
N
  $933.94
$9,339.40
  $723.39
   $93.39

The product of 13,342 and the decimal form
for 7 cents (.07) is the answer.

 13,342
 x $.07
-------
$933.94 from sales of donut centers
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