Items marked A, B, C are increasing in difficulty. Group “A” questions are
the most basic while Group “C” are
the most difficult and require higher levels of thinking skills. The level of
difficulty is only relative to the same
section. All problems include random number generation . [n] indicates n problems
types are available in the
topic. Note: Some problems use text boxes for fractions and scientific notation.
For these problems, do not
enter spaces before or after the numeric values .
Section 4.1
Objective: Students will be able to write the prime factorization of a number .
4_1 Prime Factors (3) – [10] Finding the prime factors of a number with three
prime factors.
4_1 Prime Factors (4) – [10] Finding the prime factors of a number with four
prime factors.
Section 4.2
Objective: Students will be able to find the greatest common factor.
4_2 Greatest Common Factor (4) – [10] Find the GCF when each factor has four
prime factors.
4_2 Greatest CF with variables – [4] Find the GCF of an ex pression only
involving variables.
4_2 GCF with numbers and 1 variable – [4] Find the GCF of an expression with a
number and one variable .
4_2 GCF with numbers and variables – [4] Find the GCF of an expression with a
number and multiple
variables.
Section 4.3
Objective: Students will be able to simplify fractions.
4_3 Simplify Fractions – [10] Simplify fractions by finding the GCF.
Section 4.4
Objective: Students will be able to find the least common multiple.
4_4 Find LCM of 2 numbers – [4] Finding the LCM of 2 numbers.
4_4 Find LCM of variables – [4] Finding the LCM of two variable expressions.
4_4 Find LCM of numbers and variables – [4] Finding the LCM of number and
variable expressions.
Section 4.5
Objective: Students will be able to compare and order fractions and mixed
numbers.
4_5 Review Mixed to Improper Fraction – [3] Review converting mixed numbers to
improper fractions.
4_5 Compare Fractions – [3] Use inequalities to compare fractions.
4_5 Compare Mixed Fractions – [3] Use inequalities to compare mixed fractions.
4_5 Order Fractions – [3] Order fractions from smallest to largest.
Section 4.6
Objective: Students will be able to multiply and divide expressions with
exponents.
4_6 Multiply with Exponents (A) – [2] Multiply variable only expressions.
4_6 Multiply with Exponents (B) – [2] Multiply expressions with numbers and
variables.
4_6 Multiply with Exponents (C) – [2] Multiply expressions with numbers and
multiple variables.
4_6 Divide with Exponents (A) – [2] Divide variable only expressions.
4_6 Divide with Exponents (B) – [2] Divide expressions with numbers and
variables.
4_6 Divide with Exponents (C) – [2] Divide expressions with numbers and multiple
variables.
Section 4.7
Objective: Students will be able to simplify expressions with negative
exponents .
4_7 Negative Exponents Eval – [2] Evaluate single variables with negative
exponents.
4_7 Mult Neg Exponents Vars – [2] Evaluate multiple variables with negative
exponents.
4_7 Div Neg Exponents Vars – [2] Dividing with negative exponents.
Section 4.8
Objective: Students will be able to read and write numbers using scientific
notation.
4_8 Scientific Notation – [6] Writing numbers in scientific notation.
4_8 Scientific Notation Calculations – [2] Performing calculations in scientific
notation.
Lincoln Public Schools – Math 8 – McDougal Littell Middle School Math
Course 3
Please note: This demo is a one problem sample from each topic. All problems
are random
number problems and consist of multiple types for each topic. Some fraction
problems are
not properly formatted in this demo due to the conversion to Word form. They
will appear
properly formatted when used in EDU.
4_1 Prime Factors (3) – [10] Finding the prime factors of a number with
three prime factors.
Write the prime factors of 75.
Write the value separated by a semicolon; as 3; 5; 7
Your Answer: 3; 5; 5
Correct Answer: 3; 5; 5
Comment: Write the prime factors of 75.
Write the value separated by a semicolon ; as 3; 5; 7
75 =
25 • 3 =
5 • 5 • 3
Enter the prime factors as 3; 5; 5
4_1 Prime Factors (4) – [10] Finding the prime factors of a number with
four prime factors.
Write the prime factors of 60.
Write the value separated by a semicolon ; as 3; 5; 7
Your Answer: 2; 2; 3; 5
Correct Answer: 2; 2; 3; 5
Comment: Write the prime factors of 60.
Write the value separated by a semicolon ; as 3; 5; 7
60 =
6 • 10 =
(2 • 3) • (2 • 5) =
2 • 3 • 2 • 5
Enter the prime factors as 2; 2; 3; 5
4_2 Greatest Common Factor (4) – [10] Find the GCF when each factor has
four prime factors.
Find the greatest common factor of 30 and 42.
Your Answer: 6
Correct Answer: 6
Comment: Find the greatest common factor of 30 and 42.
Find the prime factors of each number.
30 = 2 • 3 • 5
42 = 2 • 3 • 7
Multiply the common prime factors.
G.C.F. = 2 • 3 = 6
4_2 Greatest CF with variables – [4] Find the GCF of an expression only
involving variables.
Find the greatest common factor of 198 and 330.
Your Answer: 66
Correct Answer: 66
Comment: Find the greatest common factor of 198 and 330.
Find the prime factors of each number.
198 = 2 • 3 • 3 • 11
330 = 2 • 3 • 5 • 11
Multiply the common prime factors.
G.C.F. = 2 • 3 • 11 = 66
4_2 GCF with numbers and 1 variable – [4] Find the GCF of an expression
with a number and
one variable.
Find the greatest common factor of
and
Enter the exponents using the ^ key. For example
would be entered as a^5 b^6.
Your Answer: x^3 y^4 z^4
Correct
Answer: x^3 y^4 z^4
Comment: Find the greatest common factor of
and
.
Enter the exponents using the ^ key. For example
would be entered as a^5 b^6.
The GCF is the lowest power of each variable. If the variable is not present,
the
exponent is 0 and is not included in the GCF
The lowest power of x is 3, the lowest power of y is 4 and the lowest power of z
is 4.
The LCM is
entered as x^3 y^4 z^4.
4_2 GCF with numbers and variables – [4] Find the GCF of an expression
with a number and
multiple variables.
Find the greatest common factor of
and
Enter the exponents using the ^ key. For example
would be entered as a^5 b^6.
Your Answer: 4x^2
Correct Answer: 4 x^2
Comment: Find the greatest common factor of
and
Enter the exponents using the ^ key. For example
would be entered as a^5 b^6.
The GCF of 8 and 20 is 4.
The GCF is the lowest power of the variable.
The lowest power of x is 2.
The LCM is
entered as 4 x^2.
4_2 GCF with numbers and variables – [4] Find the GCF of an expression
with a number and
multiple variables
Find the greatest common factor of
and
Enter the exponents using the ^ key. For example
would be entered as a^5 b^6.
Your Answer: 4x^2 y^3
Correct
Answer: 4 x^2 y^3
Comment: Find the greatest common factor of 8x3 y10 and 20x2 y3 .
Enter the exponents using the ^ key. For example a5 b6 would be entered as a^5
b^6.
The GCF of 8 and 20 is 4.
The GCF is the lowest power of each variable. If the variable is not present,
the
exponent is 0 and is not included in the GCF
The lowest power of x is 2 and the lowest power of y is 3.
The LCM is 4x2 y3 entered as 4 x^2 y^3.
4_3 Simplify Fractions – [10] Simplify fractions by finding the GCF.
Your answer:
| Your response |
Correct response |
Simplify the fraction:
Enter a fraction such as 2/3 in the textbox.
Do not use spaces in the answer!
7/8 |
Simplify the fraction:
Enter a fraction such as 2/3 in the textbox.
Do not use spaces in the answer!
7/8 |
Comment:
Simplify the fraction:
Enter a fraction such as 2/3 in the textbox.
Find the GCF of 35 and 40.
The GCF is 5.
Divide numerator and denominator by 5.
The simplified fraction is 7/8.
4_4 Find LCM of 2 numbers – [4] Finding the LCM of 2 numbers.
Find the least common multiple of 4 and 12.
Your Answer: 12
Correct Answer: 12
Comment: Find the least common multiple of 4 and 12.
Write the multiples of each number.
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48,....
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, ....
Choose the first number which is displayed in both lists.
The LCM is 12.
4_4 Find LCM of variables – [4] Finding the LCM of two variable
expressions.
Find the lowest common multiple of x3 y8 and x8 y5
z2
Enter the exponents using the ^ key. For example a5 b6 would be entered as a^5
b^6.
Your Answer: x^8 y^8 z^2
Correct
Answer: x^8 y^8 z^2
Comment: Find the lowest common multiple of x3 y8 and x8 y5
z2
Enter the exponents using the ^ key. For example a5 b6 would be entered as a^5
b^6.
The LCM is the highest power of each variable.
The highest power of x is 8 and the highest power of y is 8. The highest power
of z is
2.
The LCM is x8 y8 z2 entered as x^8 y^8 z^2.
4_4 Find LCM of numbers and variables – [4] Finding the LCM of number and
variable
expressions.
Find the least common multiple of 6x4 y7 and 21x3 y6 .
Enter the exponents using the ^ key. For example a5 b6 would be entered as a^5
b^6.
Your Answer: 42x^4 y^7
Correct Answer: 42 x^4 y^7
Comment: Find the least common multiple of 6x4 y7 and 21x3 y6 .
Enter the exponents using the ^ key. For example a5 b6 would be entered as a^5
b^6.
The LCM of 6 and 21 is 42.
The LCM of the variables is the highest exponent of each x4 y7
Putting the these together, the LCM is 42x4 y7 entered as 42 x^4 y^7
4_5 Review Mixed to Improper Fraction – [3] Review converting mixed
numbers to improper
fractions.
Write
as an improper fraction.
Enter a fraction into the answer box as 3/5.
Your Answer: 18/5
Correct Answer: 18/5
Comment: 3
Write
as an improper fraction.
Enter a fraction into the answer box as 3/5.
3 • 5 + 3 = 18
The fraction is
entered
as 18/5.
4_5 Compare Fractions – [3] Use inequalities to compare fractions.
Replace ? with <, =, or >.
Your Answer: >
Correct Answer: >
Comment: Replace ? with <, =, or >.
The least common denominator is 77.
Multiply each fraction to get the least common denominator.
Since 14 > 11,
and
we can say
4_5 Compare Mixed Fractions – [3] Use inequalities to compare mixed
fractions.
Replace ? with <, =, or >.
Your Answer: =
Correct Answer: =
Comment: Replace ? with <, =, or >.
Convert to a mixed number.
The least common denominator is 28.
Multiply each fraction to get the least common denominator
Since 120 = 120,
and
we can say
4_5 Order Fractions – [3] Order fractions from smallest to largest.
| Your response |
Correct response |
Order the fractions from smallest to
largest: |
Order the fractions from smallest to
largest: |
 |
 |
Smallest Fraction: A (33%)
Middle Fraction: C (33%)
Largest Fraction: B (33%) |
Smallest Fraction: A
Middle Fraction: C
Largest Fraction: B |
Comment:
Order the fractions from smallest to largest.
The least common multiple is 15.
Writing each with the LCM as a common denominator:
From smallest to largest, the fractions are:
4_6 Multiply with Exponents (A) – [2] Multiply variable only expressions
Simplify the expression: x5 • x2
Write expression with an exponent. Enter x3 as x^3.
Your Answer: x^7
Correct Answer: x^7
Comment: Simplify the expression: x5 • x2
Write expression with an exponent. Enter x3 as x^3.
When multiplying with exponents, add the exponents .
x5 • x2 = x(5 + 2) = x7 entered as x^7
4_6 Multiply with Exponents (B) – [2] Multiply expressions with numbers
and variables.
Simplify the expression: 24y6 • 24y3
Write expression with an exponent. Enter x3 as x^3.
Your Answer: 256y^9
Correct Answer: 256y^9
Comment: Simplify the expression: 24y6 • 24y3
Write expression with an exponent. Enter x3 as x^3.
When multiplying with exponents, add the exponents.
256y9 entered as 256y^9
4_6 Multiply with Exponents (C) – [2] Multiply expressions with numbers
and multiple
variables.
Simplify the expression: 44w5 x3 • 43w2x3
Write expression with an exponent. Enter x3 as x^3.
Your Answer: 16384w^7x^6
Correct Answer: 16,384 w^7 x^6
Comment: Simplify the expression: 44w5 x3 • 43w2x3
Write expression with an exponent. Enter x3 as x^3.
When multiplying with exponents, add the exponents.
16,384w7x6 entered as 16,384 w^7 x^6
4_6 Divide with Exponents (A) – [2] Divide variable
only expressions.
Simplify the expression:
Write expression with an exponent. Enter x3 as x^3
Your Answer: x^3
Correct Answer: x^3
Comment: Simplify the expression:
Write expression with an exponent. Enter x3 as x^3
When dividing with exponents, subtract the exponents.
entered as x^3
4_6 Divide with Exponents (B) – [2] Divide expressions
with numbers and variables.
Simplify the expression:
Write expression with an exponent. Enter x3 as x^3
Your Answer: 9y^2
Correct Answer: 9y^2
Comment: Simplify the expression:
Write expression with an exponent. Enter x3 as x^3
When dividing with exponents, subtract the exponents.
4_6 Divide with Exponents (C) – [2] Divide expressions
with numbers and multiple variables.
Simplify the expression:
Write expression with an exponent. Enter x3 as x^3
Your Answer: 3125x^2y^2
Correct Answer: 3,125x^2 y^2
Comment: Simplify the expression:
Write expression with an exponent. Enter x3 as x^3
When dividing with exponents, subtract the exponents.
4_7 Negative Exponents Eval – [2] Evaluate single
variables with negative exponents.
Evaluate: 
Enter fractions as 1/18 or 1/x^2. 
Your Answer: 8
Correct Answer: 8
Comment: Evaluate:
Enter fractions as 1/18 or 1/x^2.
When multiplying with exponents, add the exponents.
4_7 Mult Neg Exponents Vars – [2] Evaluate multiple
variables with negative exponents.
Write with positive exponents :
Enter fractions as 1/18 or 1/x^2.
Your Answer: 1/x^6
Correct Answer: 1/x^6
Comment: Write with positive exponents :
Enter fractions as 1/18 or 1/x^2.
When multiplying with exponents, add the exponents.
When a negative exponent results, recall that
Enter the answer as 1/x^6
4_7 Div Neg Exponents Vars – [2] Dividing with negative
exponents
Simplify the expression:
Write expression with an exponent. Enter x3 as x^3
Your Answer: a^8
Correct Answer: a^8
Comment: Simplify the expression:
Write expression with an exponent. Enter x3 as x^3
When dividing with exponents, subtract the exponents.
entered as a^8
4_8 Scientific Notation – [6] Writing numbers in
scientific notation.
Your answer:
| Your response |
Correct response |
Write 0.00000251 in scientific notation
as 
Do not enter spaces in the answer
boxes. |
Write 0.00000251 in scientific notation
as
Do not enter spaces in the answer
boxes. |
Comment:
Write 0.00000251 in scientific notation as 
Do not enter spaces in the answer boxes.
The decimal place must be moved 6 places to the right. Therefore, the decimal is
2.51 and the
power of 10 is -6.
4_8 Scientific Notation Calculations – [2] Performing
calculations in scientific notation.
Your answer:
| Your response |
Correct response |
Write the answer in scientific notation:
Do not use spaces in the answer boxes.
 |
Write the answer in scientific notation:
Do not use spaces in the answer boxes.
|
Comment:
Write the answer in scientific notation:
Do not use spaces in the answer boxes.
Divide the decimals and subtract the exponents since we are dividing.
The answer is 
