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Dr. Math FAQ:
order of operations
Browse High School Basic Algebra
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Selected answers to common questions:
Solving simple linear equations.
Positive/negative integer rules.
Completing the square.
Direct and indirect variation.
Inequalities and negative numbers.
- Nonlinear Factors [10/12/1998]
I have been told that factoring the sum of two squared numbers is not
possible, but factoring x^4 + 4 is possible. Please explain.
- Non-Linear Simultaneous Equations [12/07/2003]
I have four simultaneous equations with four variables, but each one
has a non-linear term in it (e.g., ab + c + d = 3). So none of the
usual techniques will work! How can I solve the system?
- Normalization [08/01/2001]
How do I figure out: 90 + 70 + 88 + 94 + x / 5 = 85 ?
- The Nth Root of N [11/28/2000]
Is the nth root of n (a whole number other than 1) ever a rational
- Number of Equations Needed in a Simultaneous Linear System [10/29/2003]
Could you tell me why we need the same number of equations as
variables in order to get a unique solution to a system of
simultaneous linear equations?
- Number * Sum of Remaining Four Numbers [04/03/2003]
Find 5 numbers such that when each number is multiplied by the sum of
the remaining 4 numbers, the following values will result: 152, 245,
297, 320, 360.
- Objects in a Pyramid [7/8/1996]
Objects are stacked in a triangular pyramid... how many objects are in
the nth layer from the top?
- Old Test Questions Answered [1/23/1995]
I am studying for my midterm, and I've come across two questions that I
got wrong and don't understand why....
- One Variable Equations with Decimals [02/11/1997]
How do you solve 8.25x + 3 = 17.5 + x?
- Open Sentence, Statement [09/18/2001]
What is an open sentence?
- Operator Precedence [08/13/2003]
Since the following statement is true: (1+1)**(5-2) is 8, why is the
following statement true and not false: 2**1+1 is 3 and not 4, and
3*1**3 is 3 and not 27...' ?
- Ordering Exponents and Variables [04/08/2000]
Is there a rule for putting terms in descending order if the variables
have the same exponent? What about negative exponents and descending
- Ordering Products, Powers, and Parameters of Trigonometric Functions [10/31/2010]
A student wants to know how to unambiguously interpret strings of trigonometric
functions, multiplication, and exponentiation. Doctor Peterson digs into a history book
-- as well as another math doctor's conversation -- to illuminate the vagaries of the
- Order in Linear Expressions [11/20/2001]
Can you give me a convincing argument as to why, in an equation such as
y=13-7x, where y is a function of x, it should be written as y=-7x+13?
- Order of Operations [05/19/1999]
Given a, b, x, and y, find ax/by.
- Order of Operations with Percentages [04/05/2001]
Why does the order of operations exclude percentage, square roots, etc.?
- Other Ways to Get the Quadratic Formula [02/19/2010]
Doctor Jacques shares two ways to derive [-b +/- SQRT(b^2 - 4ac)]/2a
without explicitly completing the square.
- Pairs of Odd Integers [09/24/1997]
Find all pairs of odd integers a and b that satisfy the equation: a +
128b = 3ab.
- Parabola with Horizontal or Vertical Axis [05/03/2001]
How can I find the focus and directrix of a parabola whose axis is either
horizontal or vertical, like 2x^2 = -y?
- Parabolic Golf Shot Equations [01/24/2002]
Does the ball reach the green?
- Parallel and Perpendicular Lines [01/14/1999]
How do you tell without graphing whether the graphs of these equations
are parallel, perpendicular, or neither?
- Parallel Lines [12/31/1998]
What are some ways of proving lines parallel - geometrically and
- Parametric Form for Equation of a Line [6/30/1996]
How can you convert an equation such as y = -3x/4 + 7/2 to parametric
- Parity [8/2/1996]
How do I determine if the given function is odd, even or neither? What's
the symmetry of the graph?
- Partial Fractions [01/29/1998]
How do I express 3/1-(x^3) in partial fractions?
- Pascal's Triangle Pattern [04/22/1999]
What pattern does multiplying each entry by 1, 2, 3, 4, 5... in order,
and adding the products yield?
- Perfect Square: Solving Two Equations [6/14/1996]
x^2 + 5 is a perfect square, and x^2 - 5 is a perfect square.
- Perimeter Equals Area in a Triangle [4/2/1996]
When will the area and perimeter of a right triangle be numerically
- Picture Frame, Triangle Measurements [5/20/1996]
My teacher gave us ten questions to answer and I could do all except two:
1) A framed rectangular picture is 35cm long and 25cm wide... 2) The base
of a triangle is 9cm more than the perpendicular height...
- Plus or Minus Sign [03/08/2002]
What does this equation mean: y = +- k ? The - sign is directly under the
- Point Equidistant from 3 Other Points [04/11/1999]
How do you find a point that is equidistant from three other points?
- Point on a Line [03/23/2001]
Can you please tell me a formula to find if a point exists on a line?
Both are in x,y form.
- Polynomial Brain-Twisters [12/4/1995]
I'm stumped on some similar polynomial problems...
- Polynomial Degrees and Definition of a Field [03/02/1998]
The degree of polynomials added together, and definition of a field.
- Polynomial Factoring Rules [04/02/1997]
How do I apply the polynomial factoring rules to t^21+1 and 25y^2-144 =
- Polynomial Problem [3/11/1995]
A remainder of 9 results when the polynomial p(x) is divided by x-2, a
remainder of -3 when p(x) is divided by x+2, and a remainder of 3 when
divided by x-1. Find the remainder when p(x) is divided by (x-2)(x+2)(x-
- Population and Percentage [03/07/1999]
Given population data, find the number of women in two different years.
- Positive Unit Fractions [10/02/2002]
Find five different positive unit fractions whose sum is 1. (A unit
fraction is a fraction whose numerator is 1. All denominators must
also be natural numbers.)
- Precedence of Unary Operators [09/01/99]
The PEMDAS rule for order of operations ignores unary operators. Can you
explain the proper precedence for them, and give an example showing how
not knowing the rule can cause an incorrect result?
- Preparing for an Algebra Test [11/1/1995]
A 9th grade math student asks for help preparing for final exams. What is
the difference between the terms: solve and simplify? How do you find the
gradient in a graph?