SSAT Middle Level Math : Operations

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

Example Question #1 : How To Add Variables

What is the sum of the fractions below?

Possible Answers:

Correct answer:

Explanation:

In order to solve this addition problem, a common denominator must first be found. 

 should be converted to a fraction in which the denominator is 16.

Finally, add the fractions.

Example Question #21 : Variables

Suppose you know the values of all variables in the expression 

and you want to evaluate the expression.

In which order will you carry out the operations?

Possible Answers:

Adding, multiplying, squaring

Squaring, adding, multiplying

Squaring, multiplying, adding

Adding, squaring, multiplying

Multiplying, adding, squaring

Correct answer:

Adding, squaring, multiplying

Explanation:

By the order of operations, the operation within parentheses, which is addition, is carried out first; of the remaining two, exponentiation - squaring here - precedes multiplication.

Example Question #92 : Algebra

Suppose you know the values of all variables in the expression 

and you want to evaluate the expression.

In which order will you carry out the operations?

Possible Answers:

Multiplication, addition, subtraction

Subtraction, multiplication, addition

Multiplication, subtraction, addition

Subtraction, addition, multiplication

Addition, multiplication, subtraction

Correct answer:

Subtraction, multiplication, addition

Explanation:

By the order of operations, any expressions within grouping symbols, such as parentheses and brackets, are carried out from the inside outward. Therefore, the operation in the innermost set of grouping symbols - the subtraction within parentheses - will be carried out first, followed by the remaining operation within the brackets - the multiplication. The remaining operation - the addition - is last.

Example Question #8 : How To Add Variables

Write in base ten:

Possible Answers:

Correct answer:

Explanation:

In base five, each place value is a power of five, starting with 1 at the right, then, going to the left, .

 can be calculated in base ten as

.

Example Question #9 : How To Add Variables

Add  in modulo 15 arithmetic.

Possible Answers:

Correct answer:

Explanation:

In modulo 15 arithmetic, a number is congruent to the remainder of the divison of that number by 15. Since 

and

,

.

This makes 10 the correct choice.

 

Example Question #1202 : Hspt Mathematics

Possible Answers:

Correct answer:

Explanation:

Add the numbers and keep the variable:

Answer:

Example Question #91 : Ssat Middle Level Quantitative (Math)

Possible Answers:

Correct answer:

Explanation:

Add the numbers and keep the variable:

Answer:

Example Question #1 : How To Add Variables

Simplify

Possible Answers:

Already simplified

Correct answer:

Explanation:

In order to add variables the terms must be like. In order for terms to be like, the variables must be exactly alike also being raised to the same power by the exponent.

In this case the like terms are  and . Just because there is a 1 in the exponent for the first term doesnt mean it is different from the second term. With exponents if a variable does not show an exponent, that means it is still to the first power. 

We add the coefficients of the like terms. The coefficient is the number in front of the first variable, in this case it is 1 for both terms because of the identity property of multiplication stating any variable, term, or number multiplied by 1 is itself.

    

Our last term is not like because the  variable is raised to a different power than the other two. In this case we do not combine it to the like terms, we just add it to the end of the term. 

Example Question #3 : How To Add Variables

Possible Answers:

Correct answer:

Explanation:

Remember, for exponent problems, you group together different exponents and different combinations of variables as though each were a different type of variable.  Therefore, you can group your problem as follows:

Now, just combine like terms:

Example Question #4 : How To Add Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

You should begin by distributing  through the whole group that it precedes:

Now, move your like variables next to each other:

Finally, combine the like terms:

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