What is the difference? How to find the difference of an arithmetic progression: formulas and examples of solutions Means the sum of numbers and the difference of numbers.

Number difference

A And b is a number which, when added to b, adds up to A. In higher analysis difference functions f(x) called expression f(x + h) - f(x), in which the letter X can be given different meanings, a h keeps the same value. Solving various problems using differences is a special branch of mathematics called. finite difference calculus(cm.). The word "final" is added here to emphasize that the above number h remains unchanged. In other parts of mathematics there are infinitesimal differences, i.e. expressions f(x+h) -f(x), in which h takes on a number of values tending to zero.

Encyclopedic Dictionary F.A. Brockhaus and I.A. Efron. - S.-Pb.: Brockhaus-Efron. 1890-1907 .

See what “Difference of numbers” is in other dictionaries:

DIFFERENCE- (1) potentials (voltage (see (2))) a quantitative characteristic of the electric field of stationary electric charges () between two of its points, equal to the work of the electric field in moving a single positive charge from one... ... Big Polytechnic Encyclopedia

Not to be confused with Symmetrical difference. The difference between two sets is a set-theoretic operation, the result of which is a set that includes all the elements of the first set that are not included in the second set. Usually... ... Wikipedia

The science of integers. The concept of an integer (See number), as well as arithmetic operations on numbers, has been known since ancient times and is one of the first mathematical abstractions. A special place among integers, i.e. numbers..., 3... Great Soviet Encyclopedia

AND; and. 1. to Miscellaneous (1 digit); difference. R. beliefs, views. Discover r. in approaches to historical facts. // The difference between the two values being compared in numerical terms. R. altitudes above sea level. R. temperature. R. water levels. R. in... ... encyclopedic Dictionary

difference- And; and. 1) a) to different 1); difference. Diversity of beliefs and views. Detect differences in approaches to historical facts. b) ott. The difference between two compared quantities in numerical terms. Difference of altitudes above sea level. Ra/ ... Dictionary of many expressions

difference- DIFFERENCE, i, g Quantitative difference between two comparative quantities in numerical terms. Difference of two numbers... Explanatory dictionary of Russian nouns

The number of numbers a and b is a number which, when added to b, gives the sum of a. In higher analysis, the difference of the function f(x) is called. expression f(x + h) f(x), in which the letter x can be given different meanings, but h retains the same meaning. Solution… … Encyclopedic Dictionary F.A. Brockhaus and I.A. Ephron

A branch of number theory in which the patterns of distribution of prime numbers (p.n.) among natural numbers are studied. The central problem is the best asymptotic solution. expressions for the function p(x), denoting the number of p.p. not exceeding x, a... ... Mathematical Encyclopedia

A complement in set theory is a family of elements that do not belong to a given set. Contents 1 Difference of sets 1.1 Definition 1.2 Examples 1.3 Properties ... Wikipedia

Several prime numbers can be members of an arithmetic progression. All sequences of prime numbers that are strictly consecutive elements of some arithmetic progression are finite, but there are arbitrarily long such... ... Wikipedia

Books

Mathematics. 4th grade. Federal State Educational Standard (CDpc), . The electronic textbook "1 C: School. Mathematics, 4th grade" was developed for students of the 4th grade of primary secondary school in accordance with the requirements of the new Federal State Educational Standard. In the guide...
Doing mathematics: for children 6-7 years old. In 2 parts. Part 2, Sorokina Tatyana Vladimirovna. The main objectives of the manual are to consolidate knowledge of the composition of numbers within 20 and skills in solving problems on addition and subtraction, familiarize the child with the mathematical concepts of “addend”,…

In elementary school, a child is first introduced to mathematics, and his first examples are simple operations such as addition or subtraction. But sometimes it is difficult to explain to a child even such seemingly simple and familiar examples to adults. How can you learn to find the sum and difference of numbers?

What is the amount and how to find it

A sum is the result of adding two numbers (terms) with a + sign between them. To get the sum, you need to add the second term to one term. In general, an example can be shown as follows: a + b = s, where a is the first term, b is the second term, and s is the result of adding these two terms. At the same time, you need to know that rearranging the terms does not change the sum - this is one of the very first rules in mathematics, which is taught in elementary school.

To visually show your child how to add numbers, take candy or any other things. Show your child two candies, and then add two more candies to these candies. Let the child count and say that there are now four candies. Explain to him that he just added these numbers, that is, he added another number to one number and ultimately got the sum.

It is a little more difficult to explain the addition of bit terms; this topic may not be clear to a child. So, there are many categories: units, tens, thousands. Take, for example, the number 2564. If you decompose it into digits, you get: 2564 = 2000 + 500 + 60 + 4. To add to this number, for example, the number 305, use column addition. With this addition, you need to add some digits to others, starting from the end: ones to ones, tens to tens, thousands to thousands. That is, first we add 4 and 5, then 6 and 0, after 5 and 3, and finally 2 and 0. Ultimately we get the number 2869.

How to find the difference between numbers

The difference is the result of subtracting one number from another. Unlike the sum, here we cannot use the rule “the difference does not change by rearranging the terms,” since in subtraction there is always a minuend and a subtrahend. To find the subtrahend and the difference, you first need to understand these concepts. The diminished is what we “subtract” from, that is, we remove, and the subtracted is the amount of what we return from this diminished.

In general, subtraction can be written as follows: a - b = r.
Let's turn to the same candies with which we analyzed the sum of numbers. To help your child find the difference between numbers, take five candies. Let the child count and make sure there are five. Then take three candies for yourself. The child will say that there are two left. How much did they take then? Three.

As for the bit terms, here we do the same thing as with the sum, only now we do not add, but subtract. Let's take the number 6845 and subtract 4231 from it. To do this, we subtract one digit from another digit, subtracting from the end: 5-1 = 4, 4-3 = 1, 8-2 = 6, 6-4 = 2. In the answer we get 2614.

The difference is usually called the result obtained by subtracting a smaller number from a larger one. In this case, the first number from which the other is subtracted is called the minuend (after all, it is this number that we are reducing in the process). The second number, subtracted from the first number, is called subtrahend. In sum with the difference, the subtrahend becomes the minuend, and the difference between the minuend and the difference becomes the subtrahend. In cases where the subtrahend exceeds the minuend, the difference between the numbers becomes negative.

There are several difference formulas:

difference formula a-b = c
formula for difference of squares a 2 - b 2 = (a - b)*(a + b)
formula for difference of cubes a 3 - b 3 = (a - b)*(a 2 + ab + b 2)
potential difference formula U=Aq
formula for squared difference (a - b) 2 = a 2 - 2ab + b 2
difference cube formula (a - b) 3 = a 3 - 3a2b + 3ab 2 - b 3

What is the difference and how to find it

You can calculate the difference using a regular, familiar calculator. To do this, press the “C” button, enter the numbers of the minuend, then press the “-” button and enter the subtrahend. The result is obtained by pressing the “=” button. There are also less common models of calculators with reverse, so-called Polish notation. Here, to calculate the difference, instead of the “-” button, you should press the button with the image of an up arrow (due to this, the number goes to the stack or memory card of the action). After that, enter the subtrahend and press the “-” button, getting a ready answer.

There is also a certain summing device, the capabilities of which include only the addition of numbers. It is possible to find the difference using it. To do this, you need to mentally reduce the subtrahend by 1. After this, we transfer the digits of the number to the additional category, where 0 is equal to 9, 1 is equal to 8, etc. The higher digits remaining free are filled with nines. Added components of a difference of this kind cause the device counter to overflow and indicate the difference.

What is potential difference

The concept of potential difference is used by physicists. The potential difference can be obtained by connecting a voltmeter to two points of the circuit, where the voltage of the first is conditionally equal to U1, and the second is U2. In this case, the voltmeter will show the result in the form of voltage U1-U2, which is called the potential difference. Any galvanic cell produces a voltage that determines the difference in the electrochemical potentials that make up the electrodes of the substance element.

Before voltage stabilizers were invented, Weston elements made it possible to calibrate voltmeters. The reacting components selected in them ensured a high level of stability of the potential difference. There is also the concept of pressure difference, which is used in hydraulic and pneumatic weapons. This difference is an analogue of the electrical potential difference.

How to teach your child subtraction and addition

Even before starting school, it is advisable for the child to master basic mathematical operations and gain an understanding of what a difference or sum is. To make it easier for your child to count, use any available means during the learning process. Don't be afraid to visualize the task. For example, it will be much easier for a child to decide how many apples he will have left if he shares half with a friend on real objects, rather than on a faceless piece of paper.

Children also really like guessing tasks. Eg. the standard example “2+2=4” can be replaced with “2+x=4”. This exercise will force the child to think outside the box and develop logic.

The word "difference" can have many meanings. This can also mean a difference in something, for example, opinions, views, interests. In some scientific, medical and other professional fields, this term refers to various indicators, for example, blood sugar levels, atmospheric pressure, and weather conditions. The concept of “difference” as a mathematical term also exists.

In contact with

Arithmetic operations with numbers

The main arithmetic operations in mathematics are:

addition;
subtraction;
multiplication;
division.

Each result of these actions also has its own name:

sum - the result obtained by adding numbers;
difference - the result obtained by subtracting numbers;
product is the result of multiplying numbers;
the quotient is the result of division.

To explain in simpler language the concepts of sum, difference, product and quotient in mathematics, we can simply write them down only as phrases:

amount - add;
difference - subtract;
product - multiply;
private - to divide.

Looking at Definitions, what is the difference between numbers in mathematics, this concept can be defined in several ways:

And all these definitions are true.

How to find the difference between quantities

Let’s take as a basis the notation for the difference that the school curriculum offers us:

The difference is the result of subtracting one number from another. The first of these numbers, from which the subtraction is carried out, is called the minuend, and the second, which is subtracted from the first, is called the subtrahend.

Once again resorting to the school curriculum, we find a rule on how to find the difference:

To find the difference, you need to subtract the subtrahend from the minuend.

All clear. But at the same time we received several more mathematical terms. What do they mean?

The minuend is a mathematical number from which it is subtracted and it decreases (becomes smaller).
A subtrahend is a mathematical number that is subtracted from the minuend.

Now it is clear that the difference consists of two numbers that must be known to calculate it. And how to find them, we will also use the definitions:

To find the minuend, you need to add the difference to the subtrahend.
To find the subtrahend, you need to subtract the difference from the minuend.

Mathematical operations with number differences

Based on the derived rules, we can consider illustrative examples. Mathematics is an interesting science. Here we will take only the simplest numbers to solve. Having learned to subtract them, you will learn to solve more complex values, three-digit, four-digit, integer, fractional, powers, roots, etc.

Simple examples

Example 1. Find the difference between two quantities.

20 - decreasing value,

15 - subtractable.

Solution: 20 - 15 = 5

Answer: 5 - difference in values.

Example 2. Find the minuend.

48 - difference,

32 is the subtracted value.

Solution: 32 + 48 = 80

Example 3. Find the subtrahend value.

7 - difference,

17 is the value being reduced.

Solution: 17 - 7 = 10

Answer: Subtract value 10.

More complex examples

Examples 1-3 examine actions with simple integers. But in mathematics, the difference is calculated using not only two, but also several numbers, as well as integers, fractions, rational, irrational, etc.

Example 4. Find the difference between three values.

The integer values are given: 56, 12, 4.

56 - value to be reduced,

12 and 4 are subtracted values.

The solution can be done in two ways.

Method 1 (sequential subtraction of subtracted values):

1) 56 - 12 = 44 (here 44 is the resulting difference of the first two quantities, which in the second action will be reduced);

Method 2 (subtracting two subtrahends from the sum being reduced, which in this case are called addends):

1) 12 + 4 = 16 (where 16 is the sum of two terms, which will be subtracted in the next operation);

2) 56 - 16 = 40.

Answer: 40 is the difference of three values.

Example 5. Find the difference between rational fractions.

Given fractions with the same denominators, where

4/5 is a fraction to be reduced,

3/5 - deductible.

To complete the solution, you need to repeat the actions with fractions. That is, you need to know how to subtract fractions with the same denominator. How to handle fractions that have different denominators. They must be able to bring them to a common denominator.

Solution: 4/5 - 3/5 = (4 - 3)/5 = 1/5

Answer: 1/5.

Example 6. Triple the difference of numbers.

How to perform such an example when you need to double or triple the difference?

Let's use the rules again:

Double a number is a value multiplied by two.
Triple a number is a value multiplied by three.
The double difference is the difference in magnitudes multiplied by two.
A triple difference is a difference in magnitude multiplied by three.

7 - reduced value,

5 - subtracted value.

2) 2 * 3 = 6. Answer: 6 is the difference between the numbers 7 and 5.

Example 7. Find the difference between values 7 and 18.

7 - reduced value;

18 - subtracted.

Everything seems clear. Stop! Is the subtrahend greater than the minuend?

And again there is a rule that applies to a specific case:

If the subtrahend is greater than the minuend, the difference will be negative.

Answer: - 11. This negative value is the difference between two quantities, provided that the quantity being subtracted is greater than the quantity being reduced.

Math for blondes

On the World Wide Web you can find a lot of thematic sites that will answer any question. In the same way, online calculators for every taste will help you with any mathematical calculations. All the calculations made on them are an excellent help for the hasty, incurious, and lazy. Math for Blondes is one such resource. Moreover, we all resort to it, regardless of hair color, gender and age.

At school, we were taught to calculate such operations with mathematical quantities in a column, and later - on a calculator. The calculator is also a handy aid. But, for the development of thinking, intelligence, outlook and other life qualities, we advise you to perform arithmetic operations on paper or even in your mind. The beauty of the human body is the great achievement of the modern fitness plan. But the brain is also a muscle that sometimes requires pumping. So, without delay, start thinking.

And even though at the beginning of your journey the calculations are reduced to primitive examples, everything is ahead of you. And you will have to master a lot. We see that there are many operations with different quantities in mathematics. Therefore, in addition to the difference, it is necessary to study how to calculate the remaining results of arithmetic operations:

the sum - by adding the terms;
product - by multiplying factors;
quotient - by dividing the dividend by the divisor.

This is some interesting arithmetic.

Subtraction is an arithmetic operation inverse to addition, by means of which as many units are subtracted (subtracted) from one number as are contained in another number.

The number from which it is subtracted is called reducible, the number that indicates how many units will be subtracted from the first number is called deductible. The number resulting from subtraction is called difference(or the remainder).

Let's look at subtraction using an example. There are 9 candies on the table, if you eat 5 candies, then there will be 4 left. The number 9 is the minuend, 5 is the subtrahend, and 4 is the remainder (difference):

To write a subtraction, use the - (minus) sign. It is placed between the minuend and the subtrahend, with the minuend written to the left of the minus sign, and the subtrahend to the right. For example, the entry 9 - 5 means that the number 5 is subtracted from the number 9. To the right of the subtraction entry, put an = (equal) sign, after which the result of the subtraction is written. So the complete subtraction notation looks like this:

This entry reads like this: the difference between nine and five equals four or nine minus five equals four.

In order to obtain a natural number or 0 as a result of subtraction, the minuend must be greater than or equal to the subtrahend.

Let's consider how, using the natural series, you can perform subtraction and find the difference of two natural numbers. For example, we need to calculate the difference between the numbers 9 and 6, mark the number 9 in the natural series and count 6 numbers from it to the left. We get the number 3:

Subtraction can also be used to compare two numbers. Wanting to compare two numbers, we ask ourselves how many units one number is greater or less than the other. To find out, you need to subtract the smaller number from the larger number. For example, to find out how much 10 is less than 25 (or how much 25 is more than 10), you need to subtract 10 from 25. Then we find that 10 is less than 25 (or 25 is more than 10) by 15 units.

Subtraction check

Consider the expression

where 15 is the minuend, 7 is the subtrahend, and 8 is the difference. To find out whether the subtraction was performed correctly, you can:

add the subtrahend with the difference, if you get the minuend, then the subtraction was performed correctly:
subtract the difference from the minuend; if you get the subtrahend, then the subtraction was performed correctly: