COMPREHENSIVE REVIEW PRACTICE
QUESTIONS ANSWERS and EXAM
PREPARATION
An exponent shows how - CORRECT ANSWER-many times a
number should be multiplied by itself. In the factor tree, the number 54 can
be written as 2 x 3 x 3 x 3 or 2 x 3^3.
Scientific notation is a - CORRECT ANSWER-method of
representing very large and small numbers in the form a x 10^n where a is
a value between 1 and 10, and n is a nonzero integer.
For example, the number 927,000,000 is written in scientific notation as -
CORRECT ANSWER-9.27 x 10^8. Multiplying 9.27 by 10 eight times
gives 927,000,000.
When performing operations with scientific notation, - CORRECT
ANSWER-the final answer should be in the form a x 10^n.
When adding and subtracting numbers in scientific notation, -
CORRECT ANSWER-power of 10 must be the same for all number.
This results in like terms in which the a terms are added or subtracted and
the 10^n remains unchanged.
,When multiplying numbers in scientific notation, - CORRECT
ANSWER-multiply the a factors and add the exponents. For division,
divide the a factors, and subtract the exponents.
Positive numbers are - CORRECT ANSWER-greater than 0.
Negative numbers are - CORRECT ANSWER-less than 0.
Both positive and negative numbers can be - CORRECT ANSWER-
shown on a number line.
Positive and negative number can be - CORRECT ANSWER-added,
subtracted, multiplied, and divided. The sign of the resulting number is
governed by a specific set of rules.
Adding Real Numbers - CORRECT ANSWER-Positive + Positive=
Positive Example: 7+ 8=15
Negative + Negative= Negative Example: -7 + (-8)=-15
Negative + Positive=OR Example: -7+8=1
Positive + Negative = Example: 7+(-8)=-1
Keep the sign of the number with the larger absolute value and subtract the
absolute values of the numbers
,When subtracting Real Numbers - CORRECT ANSWER-Change the
subtraction to addition, change the sign of the second number, and use
addition rules.
Subtracting Real Numbers - CORRECT ANSWER-Negative -
Positive= Negative
Example: -7-8= -7+ (-8)= -15
Positive - Negative = Positive
Example: 7- (-8)= 7 + 8=15
Negative - Negative= Keep the sign of the number with the larger absolute
value and subtract the absolute values of the numbers.
Example: -7-(-8)=-7+8=1
-8-(-7)=-8+7=1
Multiplying real numbers - CORRECT ANSWER-Positive x Positive
= Positive
Example: 8 x 4= 32
Negative x Negative= Positive
Example: -8 x (-4) =32
Positive x Negative or Negative x Positive= Negative
Example: 8 x (-4)=-32
-8 x 4= -32
Dividing real numbers - CORRECT ANSWER-Positive/ Positive =
Positive
Example : 8/4=2
, Negative/ Negative= Positive
Example: -8/ (-4)=2
Positive/ Negative OR Negative/ Positive= Negative
Example: 8/(-4)=-2
-8/4=-2
When solving a multi-step equation, the - CORRECT ANSWER-
order of operations must be used to get the correct answer. Generally
speaking, the problem should be worked in the following order: 1.
Parenthesis and brackets; 2. Exponents and square roots; 3. Multiplication
and division; 4. Addition and subtraction.
The acronym PEMDAS can be used - CORRECT ANSWER-to
remember the order of operations
Always work from left to - CORRECT ANSWER-right within a step
when simplifying expressions.
A decimal is a - CORRECT ANSWER-number that contains a
decimal point. The place value for a decimal includes tenths (one place after
the decimal), hundredths (two places after the decimal), and thousandths
(three places after the decimal)
Decimals can be - CORRECT ANSWER-added, subtracted, or
divided.