Choose three numbers out of the four:
6, -3, -5, -9,
and multiply them. Call the product P. Let a and b be the greatest and least possible values of P, respectively. What is the value of a-b?
The directions indicate A and B be the greatest and possible values of P.
P is the product of the three numbers out of the four after multiplying them.
So here we have 6, -3, -5, -9.
So we have these possible combination of P.
6*-3*-5 = 90 (2 negatives equals positive)
6*-3*-9 = 162
6*-5*-9 = 270
-3*-5*-9=-135 (3 negatives equals negative)
Of these combination, A is the greatest value of P, so 270 from 6*-5*-9.
Finding B is similar to finding A, only that B is the LEAST possible value of P.
So from the possible combination of P. B is LEAST, meaning that you want the smallest value, -135 (being negative) is the least possible value...
Since the sum is 954, you know that the integers can’t be 1, 2, 3…etc because 954 is a large sum.
We also know that each integer is distinct from one another, that means there won’t be any duplicates of the same integer.
10 numbers are chosen from 1-100.
We will start backwards…the 10 integers could be 100, 99, 98, 97, 96, 95, 94, 93, 92. Add the 9 integers together first to make sure you are within range.
SUM total: 100+99+98+97+96+95+94+93+92 = 864
To find the last number: 954-864 = 90
90 is the answer
Are these type problems giving you the blues. Do not fear. Learn these simple strategies for solving them.
The first thing you want to do is read the problem twice. Once to get familiar with the problem. A second time to understand what is being asked.
The second thing you want to do is look for important information that is in the problem. Information such as numerical values and keywords or phrases. "How many more", "total", "difference", etc. These keywords give you a hint on what approach to use to solve the problem.
Here is an example of a word problem:
Naruto and Sasuke are on a retrieval mission to collect scrolls that contain classified content. They must retrieve 25 scrolls in all and bring them back to the Hidden Leaf Village. Sasuke is more skillful in search missions than Naruto is. If Sasuke collected 16...
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Reading Formulas can make or break how a student comprehends the formula when alone - outside the presence of the teacher, instructor, tutor, or parent.
Formula For Perimeter of Rectangle: P = 2l + 2w
How To Read: The Perimeter of a Rectangle is equal to two (2) times the Length of the longer side of the rectangle (L) plus two (2) times the Width of the shorter side of the rectangle (W).
When is reading formulas like this necessary? At three particular moments, reading this formula in this manner can be effective.
When students are initially learning what the formula means
When student are learning what it means when they should already know (remediation).
When students want to remind themselves (basics learning study skill habit)
Remember, Formulas at their introduction are complete statements or thoughts. Students cannot and will not recall complete thoughts or statements...
A few years ago, I began to teach a noncredit science class at a local community college. One of the lessons was how to solve word problems. This is what the material gave us to teach the students.
1.Read questions carefully
2.Define terms, think about relationships
3.Identify key or clue words
4.Identify the problem to be answered
5.Analyze the problem
6.Plan a solution
7.Answer the question
8.Evaluate the solution
Over time I began to realize that this was too much info to give, so I began looking for better ways to explain the process. I finally stumbled on an acronym that was simple and yet explain the steps in a concise way.
The acronym was WORD which stood for:
W- What does the question give you and does it want for answer (covers points 1, 3, 4)
O- Organize the information. Most science questions have a distinct order to them that can either be organized or diagrammed to assist in ‘seeing the problem’...
When working with my math students, I find that they get intimidated very quickly by lots of words or lots of numbers. Also if it has a radical, they shut down very quickly. I try to help them by having them write down everything they already know about the problem. When they realize how much information they already have, the problems don't seem as daunting to them. They can more easily start to plug in the numbers in the problem and are able to find the answers. Also, we do several of the same type of problem, so they start to feel more comfortable with it. I will give them worked examples and extra practice problems to take home with them for independent working if they want more practice.
0. Many STEM problems involve manipulation of a set of constrained equations. Identify the set for the problem you are solving.
1. The numbers don't matter; so, ... plan on always deriving the formula or mathematical expression for your answer, first.
2. Never operate on or write dimensionless numbers in a derivation or problem solution.
3. VARIABLE = Quantity x [Units]. This is always true, even if its not presented this way in introductory courses.
4. Only variables with the same units can be added (or subtracted).
5. The result of multiplying two variables is has units that are the product of the multiplier and multiplicand:
VARIABLE_1 x VARIABLE_2 = Quantity_1 x Quantity_2 x [Units_1 x Units_2] .
Sometimes, units in the numerator(denominator) of one variable will cancel out units in the denominator(numerator) of the other.
6. For details, Google "Dimensional Analysis". That's what I'm talking about!
7. Corrects answers come from derivation...