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### Difference Between Math and Arithmetic

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Date: 11/06/2001 at 21:57:04
From: Vicki Kehoe
Subject: Difference between math and arithmetic

My students haven't heard the word arithmetic. No one seems to be able
to tell the difference, if there is one, between arithmetic and
mathematics. Is there a difference, and what is it?
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Date: 11/07/2001 at 08:53:42
From: Doctor Peterson
Subject: Re: Difference between math and arithmetic

Hi, Vicki.

Arithmetic is just one branch of mathematics, namely that involving
basic techniques of calculation with numbers. When you add, subtract,
multiply, divide, take square roots, and so on, you are doing
arithmetic. When you solve an equation you are doing algebra. When you
determine relations between shapes or find their area, you are doing
geometry (though the latter calculation will be done by applying
arithmetic to the geometric formulas). Most of what young children
learn in math is arithmetic.

Here are some definitions of mathematics from the Dr. Math archives,
to show how much bigger it is than arithmetic:

What is Mathematics?
http://mathforum.org/dr.math/problems/erum.09.22.00.html

What is Math?
http://mathforum.org/dr.math/problems/rob.09.14.01.html

Also, did you try a dictionary? Although lexicographers do not
always get the details of mathematical terms right, they are experts
at identifying nuances of meaning. According to Merriam-Webster
(m-w.com), arithmetic is

a branch of mathematics that deals usually with the nonnegative
real numbers including sometimes the transfinite cardinals and
with the application of the operations of addition, subtraction,
multiplication, and division to them

while mathematics is

the science of numbers and their operations, interrelations,
combinations, generalizations, and abstractions and of space
configurations and their structure, measurement, transformations,
and generalizations

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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