ISEE Middle Level Quantitative : Algebraic Concepts
Study concepts, example questions & explanations for ISEE Middle Level Quantitative
All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #11 : Isee Middle Level (Grades 7 8) Quantitative Reasoning
Define an operation on the real numbers as follows:
For all real values of 
(a)
(b)
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(b) is the greater quantity
(a) and (b) are equal
so
and
The two are equal regardless of the value of 
Example Question #11 : Isee Middle Level (Grades 7 8) Quantitative Reasoning
(a)
(b)
(a) and (b) are equal
(a) is the greater quantity
(b) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
The two quantities are equal regardless of the values of 
and
Therefore, by the addition property of equality,
Example Question #13 : Isee Middle Level (Grades 7 8) Quantitative Reasoning
Which is the greater quantity?
(a)
(b) 18
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(b) is the greater quantity
It is impossible to determine which is greater from the information given
The information is insufficient, as we see by exploring two cases:
Case 1:
Case 2:
Remember, the three variables need not stand for whole numbers.
Example Question #1 : How To Subtract Variables
What is the value of 
To solve for 
Thus, 
Example Question #2 : How To Subtract Variables
Simplify:
It is easiest to begin by moving like terms together. Hence:
becomes
(Notice that 
Now, consider the coefficients for each term.
For 
For 
Hence, the expression simplifies to:
This can be moved around to get the correct answer (which means the same thing):
Example Question #11 : Algebraic Concepts
Simplify:
Begin by distributing the two groups. Notice that you must distribute the subtraction through the groups:
becomes
Next, you should move like terms next to each other:
(Notice that 
Now, combine terms.
For 
For 
Therefore, the final form of the expression is:
Example Question #12 : Algebraic Concepts
Solve for 
Begin by distributing. Thus,
becomes
(Don't forget that you have to distribute your subtraction for the second group.)
Combine like terms on the right side of the equation:
Next, move the 
Combine like terms on the left:
Finally, divide everything by 
This comes out to be:
or
Example Question #13 : Algebraic Concepts
Simplify:
Begin by distributing the multiplied groups:
Next, move all similar factors together:
Now, combine each set of similar factors:
Therefore, our answer is:
Example Question #2 : How To Subtract Variables
Simplify:
This problem is not too difficult. Begin by moving all common terms next to each other:
Next, simplify each group of terms that has the same set of variables:
And do not forget that you are left with 
Now, combine all of these:
Example Question #2 : How To Subtract Variables
Simplify:
Begin by moving common factors next to each other. Thus,
becomes
Now, combine each set:
Remember, there still is 
Therefore, the simplified form of the expression is:
All ISEE Middle Level Quantitative Resources
