# NUMBER THEORY AND THE REAL NUMBERS

1 . Find a rational number with a denominator
of 28 and equal to 3/4 .

2 . Find the reciprocal of :

3 . Perform the indicated operations:

4 . Write as decimals:

5 . Write in simplest form as the quotient of two
Integers:

6 . Write:

a . 50.0601 in expanded form .
b . in
decimal form.

7 . Do the following calculation and write the

8 . Which of the following numbers is (are)
irrational?

9 . a. Find a rational number between and 0.25.
b. Find an irrational number between and 0.25.

1 0 . The diameter of a circle is 4 inches . To the
nearest tenth of an inch what is the circumference
of this circle? (Use π ≈ 3.14.)

1 1 . Tell whether the underlined item is used as a
cardinal number, an ordinal number, or for
identification.

a. Joe came third in the election.
b. Susan's lottery ticket won five dollars.
c. Bill's auto license number was 272-864.

12. What properties of the system of natural
numbers are used in the following equations

a. (7 + 6) + 3 = (7 + 3) + 6
b. 9(10 + 3) = 90 + 27
c. (2 × 39) × 5 = (2 × 5) × 39

13. Write 286 as a product of primes .

14. Write the prime numbers between 40 and 50.

1 5 . Is 123 prime or composite?

1 6 . Consider the numbers 6345, 718, 849, 1650
Identify the numbers divisible by :

a . 2
b . 3
c . 5

1 7 . Find the GCF of 135, and 225 and reduce the
fraction to lowest terms .

1 8 . Find the LCM of 90, 135 and 225 and perform
the indicated operations:

1 9 . What fractional part of Julian's budget goes
for entertainment if 3/5 of his budget is for
school expenses, 1/5 is for gasoline,1/20 is
for savings and the remainder is for entertainment?

20. Evaluate: 6 × 12 ÷ 4 × 104 - 2(-8 + 4) × 103

2 1 . Perform the indicated operations:

a. 4.35 + 5.7
b. 8.32 - 4.73
c. 0.39 × 5.6
d. 16.74 ÷ 5.4

2 2 . The three sides of a triangle are measured as
18.4, 6.68, and 19.66 cm, respectively. What
is the perimeter of this triangle? (Give the
answer to the correct number of places.)

2 3 . The dimensions of a rectangular court are
measured as 83.6 by 50.5 feet. What is the
area of this court? (Give the answer to the
correct number of places.)

2 4 . The circumference of a ball is measured as
11.5 inches. What is the diameter of this ball?
(Use π ≈ 3.14 and give the answer to the
correct number of places.)

2 5 . Write as a decimal:

a. 23%
b. 5.75%
c. 0.34%

2 6 . Write as a percent:

a. 0.54
b. 2.43
c. 3/5
d. 5/9 (Answer to one decimal place.)

2 7 . A 2-liter bottle of soda sells for 69 cents and
costs the store 49 cents. Find the percent of
profit, correct to two decimal places.

2 8 . 50 of the employees of Company A make
between \$25,000 and \$50,000 annually. If
this represents 20% of the company's employees,
how many employees does Company A
have?

2 9 . Simplify as much as possible:

3 0 . Perform the indicated operations and simplify :

3 1 . For a right triangle with sides of length a, b
and hypotenuse c, c2 = a2 + b2. If the sides
of a right triangle are 6 and 9 inches long,
what is the length of the hypotenuse?

3 2 . Classify the given numbers by making a
check mark in the appropriate row:

3 3 . Classify as an arithmetic or a geometric
sequence:

a. 3, 6, 12, 24, . . .
b. 4, 7, 10, 13, . . .

3 4 . For the sequence 6, 9, 12, 15, . . ., find:

a. The first term
b. The common difference
c. The sum of the first ten terms
d. The sum of the first n terms

3 5 . For the sequence 4, -2, 1, -1/2 , . . . , find:

a. a1
b. r
c. The sum of the first five terms.
d. The sum of the first n terms

3 6 . Use the sum of an infinite geometric sequence
to write the following repeating decimals as
fractions in lowest terms:

a. 0.888 . . .
b. 1.121212 . . .
c. 2.777 . . .

TEST B CHAPTER 5, NUMBER THEORY AND THE REAL NUMBERS

1 . A rational number between and 0.25 is

a. 0.222 . . .
b. 0.232332333 . . .
c. 0.24567 . . .
d. 0.22333 . . .
e. 0.24999 . . .

2 . The diameter of a circle is 4 inches. To the nearest tenth of an inch,
what is the circumference of this circle? (Use π ≈ 3.14.)

a. 12.6 in.
b. 12.56 in.
c. 12.5 in.
d. 12 in.
e. None of these

3 . 0.39 × 5.6 =

a. 2.2
b. 2.20
c. 2.19
d. 2.18
e. 2.184

4 . The three sides of a triangle are measured as 18.4, 6.68, and 19.66
centimeters long, respectively. What is the perimeter of the triangle?

a. 45 cm
b. 44.8 cm
c. 44.74 cm
d. 44.70 cm
e. 44 .7 cm

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