Discussion in 'Basic Math' started by conway, Jan 4, 2024.

1. ### conway

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It is well known that in "basic" math, multiplication is addition. It is known that in higher tiers of mathematics, such as rings, that this is not the case. Yet in "basic" math multiplication is addition. So then consider...

a + 0 = a

yet...

a * 0 = 0

This case of multiplication is not addition, if anything it is subtraction. For it to be addition it should be...

a * 0 = a

So then we may say that multiplication is NOT addition in "basic" mathematics. Yet this is problematic because in every other case not involving (0). Multiplication IS addition.

I stand by to offer another solution...for those who wish to hear it.

conway, Jan 4, 2024
2. ### HallsofIvy

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Multiplying a by a positive integer, n, is the same as adding a to itself n times. But 0 is NOT a positive integer so that does not apply,

HallsofIvy, Jan 4, 2024
e.jane.aran and conway like this.
3. ### conway

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Ok, well stated. We must then still change it to multiplication is addition with only positive integers, and not zero. So then in general multiplication is NOT addition. Only in special cases is it so....So then a rewrite of many school books at the least. Yet there is a way to make the "definition" fit....with negative integers as well.

Assign all numbers a dimensional unit quantity as well as a numerical quantity. In this way, all cases of multiplication will be addition.

conway, Jan 4, 2024
4. ### conway

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Allow numbers to be defined as...

"A numerical quantity, inside a dimensional quantity. "

Allow the dimensional quantity to be notated with (_).

1 = the numerical quantity
(1_)=(_)= the dimensional quantity
(1) = the "number one"

classical 2 = novel (2) = (2,2_) = (2,_,_)
classical 3 = novel (3) = (3,3_) = (3,_,_,_)

Allow multiplication to be defined as...
"A given numerical quantity, placed into a given dimensional quantity. Then all numerical quantities are added"

Allow the definition of addition to remain unchanged.
Allow the definition for the negative symbol to remain unchanged: "The opposite of"
Allow the definition for a negative dimensional unit to exist as...
"Place the opposite of a given numerical quantity into the dimensional unit quantity."

Classical
(2*3)=6
Novel
(2*3_)=(3_*2)=(2_*3)=(3*2_)=6

2= the numerical unit
3_ = (_,_,_) = the dimensional unit

(2,2,2) = the numerical quantity given, placed into the dimensional unit quantity given.
(2 + 2 + 2) = the numerical quantity given, placed into the dimensional unit quantity given. Then all numerical quantities in all dimensional unit quantities are added.

Classical
(-2*3)
Novel
(-2 * 3_)

-2 = the numerical quantity given
3_ = the dimensional quantity given

(_,_,_) = the dimensional quantity
(-2,-2,-2) = The numerical quantity given placed into the dimensional quantity.
(-2 + -2 + -2) = (-6)

Therefore multiplication of negative integers are addition by definition.

I wish to keep this short, but I can show expressions for -(_,_,_). Or "negative" dimensional units. Upon request.

Last edited: Jan 4, 2024
conway, Jan 4, 2024
5. ### RobertSmart

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Consider the case where a+0=a, a fundamental property of addition. Yet, a×0=0, which seems contradictory to the notion that multiplication is just repeated addition. In fact, it appears more like subtraction if we aim to reconcile it with addition.

The proposed solution, a×0=a, would indeed align multiplication with addition, but it fails to address the reality where a×0=0. Thus, while in basic mathematics multiplication often resembles addition, it's clear that this simplistic view does not hold universally, especially when 00 is involved.

Mathematics, particularly at higher levels, demands a more nuanced understanding where concepts like multiplication may deviate from the simple rules observed in basic arithmetic.

Many students find it difficult to do such types of question. Many students also miss their assignment due to not knowing the basic concepts. If you are one of them facing such difficulties, I would suggest you to visit MathsAssignmentHelp website once. You can also contact them on +1 (315) 557-6473.

RobertSmart, Apr 13, 2024
6. ### conway

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I have addressed (a * 0 = 0). This mathematical construct is relative to 0 used as "space" or as "value", in the binary expression.

BOTH (a*0=a) and (a*0=0) are true. Again it is relative to zero used as a dimensional quantity, or a numerical quantity in the expression.

conway, Apr 15, 2024
7. ### tayyaba

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A grade calculator is a useful tool designed to help students and educators determine academic performance by calculating final grades based on individual assignment scores, weights, and grading criteria. This tool simplifies the often complex process of aggregating grades, ensuring accurate and transparent results. By inputting scores for quizzes, tests, homework, and other assessments, users can easily see their overall grade and identify areas needing improvement. Grade calculators are essential for effective academic planning and goal setting, providing a clear and immediate understanding of current academic standing.

tayyaba, May 28, 2024
8. ### conway

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?

conway, May 29, 2024
9. ### tayyaba

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A grade calculator is a tool designed to help students and educators determine current and projected academic performance. By inputting grades for assignments, exams, and other assessments, the calculator can compute average scores and predict final grades based on weighted categories. This tool is particularly useful for setting academic goals, understanding the impact of future grades on overall performance, and making informed decisions about study priorities. Grade calculators can vary from simple spreadsheet templates to sophisticated online platforms with advanced features.

tayyaba, May 29, 2024
10. ### tayyaba

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A grade calculator efficiently tracks and predicts academic performance by calculating weighted averages from various assessments. It aids students in setting goals and understanding how future grades will impact their overall score, promoting better study planning and time management.

tayyaba, May 29, 2024
11. ### tayyaba

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A grade calculator is a useful tool designed to help students and educators determine academic performance by calculating final grades based on individual assignment scores, weights, and grading criteria. This tool simplifies the often complex process of aggregating grades, ensuring accurate and transparent results. By inputting scores for quizzes, tests, homework, and other assessments, users can easily see their overall grade and identify areas needing improvement. Grade calculators are essential for effective academic planning and goal setting, providing a clear and immediate understanding of current academic standing.

tayyaba, May 30, 2024
12. ### tayyaba

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A grade calculator is a useful tool for students and educators to determine academic performance by computing overall grades based on individual assignment scores and their respective weights. By entering scores and weight percentages, it quickly calculates the final grade, providing immediate feedback on academic standing. This tool aids in planning and goal setting, allowing users to understand the impact of each assignment on their final grade. It also helps ensure accuracy and transparency in the grading process.

tayyaba, May 31, 2024
13. ### maryam_3

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A grade calculator is a useful tool that helps students and educators determine academic performance by computing final grades based on individual assignment scores, weights, and overall grade distribution. It automates the calculation process, allowing users to input scores for tests, quizzes, homework, and other assessments, and then calculates the overall grade. This can be particularly beneficial for tracking progress, identifying areas for improvement, and setting academic goals. By providing a clear and accurate reflection of a student's performance, grade calculators can enhance learning outcomes and streamline the grading process.

maryam_3, Jun 27, 2024

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I want to do a quiz competition

Ahmad, Jul 28, 2024 at 12:56 PM

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