ARITHMETIC CONCEPTS STUDY GUIDE (with answers)
(Note: calculators are not allowed when taking Accuplacer)
Add, subtract, multiply, and divide whole numbers (#’s like 2, 58, 39, etc.), fractions (#’s like ⅖, ⅙, ⅜, ⅓, etc.),
decimals (#’s like 2.6, 54.453, 68.7939, etc.), and percents (#’s like 3% or 0.03, 37% or 0.37, 52% or 0.52)
Examples:
2) 5 + 2 =
1) 59 + 34=
3) 123 + 2.6 + 9.04 =
4) 63 – 49 =
6) 96 – 0.3992=
7) 37 x 42 =
8) 4 x 9 =
10) 623 ÷ 7 =
11) ¼ ÷ ½ =
12) 3 ÷ 5 =
5) 9
– 2 ½=
9) 1.89 x 5.03=
Change a mixed number (#’s like 4⅓, 9⅖, etc.) to an improper fraction (#’s like
13) 7.055 ÷ 0.83=
, ,
etc.) and vice versa.
Examples:
15) Change 4 to an improper fraction
14) Change to a mixed number
Calculate an average (average means a “central” value for a set of numbers) given integers (#’s like 4, 26, 83, etc.)
Example:
16) Calculate the average of 35, 42, 33, 45, and 40.
Solve simple word problems
Example:
17) What is the cost of 6 CD’s at $14 each and 7 DVD’s at $25 each?
18) A truck traveled 371 miles on 26.5 gallons of gas. How many miles per gallon did it get?
Understand simple graphs to answer questions
Example:
19) This circle graph shows how each tuition dollar is spent by the Oaks School.
Administration,
$0.09
Maintenance,
$0.14
Books/Supplies,
$0.17
Wages,
$0.40
Benefits,
$0.20
How much of each dollar is left after expenses for wages have been paid?
Make conversions between fractions, decimals, and percents (meaning you can go from a fraction and give the
equivalent (equivalent means same) decimal of that fraction and the equivalent percent of that fraction; along with
that, you can go from a decimal and give the equivalent fraction of that decimal and the equivalent percent of that
decimal and the same for percents)
Examples:
20) Find an equivalent fraction to ⅜
21) Find an equivalent fraction to 0.6
22) Find an equivalent fraction to 45%
23) Find an equivalent decimal to 24) Find an equivalent decimal to 47%
25) Find an equivalent percent to 2/8
26) Find an equivalent percent to 0.09
Estimate (estimate means NOT the exact answer) products (products are the answers to a multiplication problem)
and squares (examples: 3 x 3= 32 or 9, 6 x 6 = 62 or 36) of decimals.
Examples:
27) Choose the range the estimated product of 4.5 and 3.7 will be in:
a) 12 - 20
b) 1 -10
c) 12 - 16
d) 25 - 35
28) Choose the range of the best estimate of the square of 6.7:
a) 12-14
b) 36-49
c) 85-94
d) 21-32
Estimate square roots (3 x 3=9…3 is the square root of 9, 4 x 4=16…4 is the square root of 16) of whole numbers and
decimals
Example:
29) Estimate √15 to three decimal places.
Divide whole numbers by decimals and fractions.
Examples:
30) 0.2601 ÷ 9 =
31) 4
27.36
32) 4.374 ÷ 0.03 =
33) 27 ÷ 4 ½ =
34) 34 ÷ 5 =
Solve simple percent problems of the form p% of w = ? and ?% of w = r (p% means percent, w means the whole, r
means the part of the whole, ? is the unknown) HINTS: is means = , of means multiply
Examples:
35) What is 11% of 3,000?
36) 60 is what percent of 12, 000?
Solve word problems involving fractions, ratio, percent increase and decrease, and area (length times width)
Examples:
37) In one year, the population of Cleveland increased from 900 to 981. What was the percent increase?
38) A Student’s college tuition is $6300. A loan was obtained for of the tuition. How much was the loan?
39) On a recent day the stock of LTC Inc. opened at $45⅖ and rose $2⅘ in the course of the day. What was the
closing price?
40) Allie ran the 50 meter relay in 11.5 seconds, and later ran the same distance in 9.7 seconds. By how much
did she improve her time?
41) The regular price of a suit is $120. It is on sale at 19% off. What is the discount?
All of these concepts need to be understood (without the use of a calculator) to begin to be
successful in Math with Business Apps, College Mathematics, and Math & Logic (Please note:
knowing just these problems will not guarantee success in the courses):
Equivalent (equivalent means same) forms of fractions
Example:
42) Find an equivalent fraction to .
Estimate computations involving fractions
Example:
43) A wheel on a bicycle makes 71 revolutions per minute. If it rotates for 40 minutes, how many revolutions
does it make?
Solve simple percent problems in the form of p% of ? = r (p% means percent, r means the part of the whole, ? is the
unknown) HINTS: is means = , of means multiply
Examples:
44) 28 is 40% of what number?
45) 36 is 80% of what number?
Solve word problems involving the manipulation of units of measurement
46) A pharmacist has 100 mL of a solution of alcohol and water; 5% is alcohol. How many milliliters of the
solution are alcohol?
Solve complex word problems involving percent, average, and proportional reasoning
47) The regular price of a suit is $120. It is on sale at 19% off. What is the discount?
48) A student took the Accuplacer-Arithmetic Test 3 times. The scores were 78, 43, and 92. What was the
average of the scores this student got on the Accuplacer-Arithmetic Test?
Solve simple number sentences involving a variable (a variable an unknown value represented by a letter)
Examples:
49) Solve for p: 12.2 = p – 8.6
50) Solve for x:
x
=½
51) When 10 is subtracted from two times a certain number, the result is twenty-eight (28). What is the
number?
Answers to Accuplacer-Arithmetic Score Guide
1) 93
2) 8 3) 134.64
4) 14
5) 7
6) 95.6008
7) 1554
8) 42 9) 9.5067
10) 89
11)
12)
13) 8.5
14) 2
15)
16)
17)
18)
19)
39
$259
14 miles per gallon
$0.60
answer: answer:
20) Answer may vary. Example answer:
21) Answer may vary. Example
22) Answer may vary. Example
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
0.8
0.47
25%
9%
a
b
3.873
0.0289
6.84
145.8
6
34) 6
35)
36)
37)
38)
330
0.5%
9%
$5,400
39) $48
40) 1.8 seconds
41) $22.80
42)
43)
44)
45)
46)
47)
48)
49)
2850 revolutions
70
450
5mL
$1820
71
20.8
50)
51) 19