Arithmetic Self Quiz-Solutions
Item 1
a. Find the greatest common divisor of 54 and 180.
b. Find the least common multiple of 54 and 180.
Solution
The prime factorization of 54 is 2 · 33 and that of 180 is 22 · 32 · 5.
a. gcd (54, 180) = 2 · 32 = 18
b. LCM (54, 180) = 22 · 33 · 5 = 540
If you had difficulty with this exercise, review the tutorials Finding the Prime Factorization of a Number, Finding the Greatest Common Divisor or Greatest Common Factor and Finding the Least Common Multiple.
Item 2
a. Round 123.77777 to the nearest hundredth.
b. Write the solution in scientific notation.
Solution
a. 123.78
b. 1.2378 x 102
If you had difficulty with this exercise, review the tutorials Working with Decimals and Arithmetic with Numbers in Scientific Notation.
Item 3
Find 
and write the answer in lowest terms.
Solution
The prime factorization of 14 is 2 · 7 and that of 12 is 22 · 3
Therefore, the least common denominator of 14 and 12 is 22 · 3 · 7 = 84
If you had difficulty with this exercise, review the tutorial Working with Fractions.
Item 4
Find 
and write the answer in lowest terms.
Solution
If you had difficulty with this exercise, review the tutorial Working with Fractions.
Item 5
What is 43% of 213?
Solution
0.43 · 213 = 91.59
If you had difficulty with this exercise, review the tutorial Working with Percents.
Item 6
Let A = {1, 3, 5, 7, 9} and B = {1, 2, 3, 4, 5}
a. What is A ∩ B?
b. What is B U A?
c. Is 
? Is 
?
Solution
a. A ∩ B 
b. B U A 
c. No, 
since 
.
No, 
since 
.
If you had difficulty with this exercise, review the tutorial An Introduction to Set Theory.
Item 7
A recipe needs 3 eggs to make 17 cookies. How many cookies can be made with a dozen eggs?
Solution
The recipe needs 3 eggs per 17 cookies. We set up the proportion:
.
Then solve for 
as follows:
68 cookies can be made with one dozen eggs.
If you had difficulty with this exercise, review the tutorial Working with Ratios and Proportions.
Item 8
a. List all the whole numbers that divide 48.
b. List three numbers that are divisible by 48.
Solution
a. 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 divide 48.
b. Since 2 · 48 = 96, 3 · 48 = 144 and 4 · 48 = 192, we know 96, 144 and 192 are divisible by 48.
If you had difficulty with this exercise, review the tutorial The Difference between Divides and Divisible.