What is difference. What is the subtrahend minuend and the difference: the rule

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

The number to be subtracted from is called reduced, the number that specifies how many units to subtract from the first number, is called deductible. The number resulting from subtraction is called difference(or remainder).

Let's take subtraction as an example. There are 9 sweets on the table, if you eat 5 sweets, then there will be 4 of them. The number 9 is reduced, 5 is subtracted, and 4 is the remainder (difference):

The - (minus) sign is used to write subtraction. It is placed between the minuend and the subtrahend, while the minuend is written to the left of the minus sign, and the subtrahend is written 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 the sign = (equal), after which the result of the subtraction is written. Thus, the complete subtraction entry looks like this:

This entry reads as follows: the difference between nine and five is four, or nine minus five is four.

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

Consider how, using the natural series, you can perform a 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 to the left from it. We get the number 3:

Subtraction can also be used to compare two numbers. Wanting to compare two numbers with each other, we ask ourselves how many units one number is more or less than the other. To find out, you need to more subtract less. 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 if the subtraction was performed correctly, you can:

add the subtrahend with the difference, if it turns out to be reduced, then the subtraction was performed correctly:

The word difference can be used in many ways. It 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, weather conditions. The concept of "difference", as a mathematical term, also exists.

Arithmetic operations with numbers

The basic 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 - the result of multiplying numbers;
quotient is the result of division.

More plain language explaining the concepts of sum, difference, product and quotient in mathematics, we can simply write them down only as phrases:

amount - add;
difference - take away;
product - multiply;
private - share.

Considering definitions, what is the difference of numbers in mathematics, this concept can be denoted in several ways:

And all these definitions are true.

How to find the difference in values

Let us take as a basis the notation of 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 school curriculum, we find the rule how to find the difference:

To find the difference, subtract the minuend from the minuend.

All clear. But at the same time, we got a few more mathematical terms. What do they mean?

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

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

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

Mathematical operations with the difference of numbers

Based on the above rules, we can consider illustrative examples. Mathematics, interesting science. Here we will take only the simplest numbers for solution. By learning to subtract them, you will learn to solve more complex values, three-digit, four-digit, integer, fractional, in degrees, roots, others.

Simple examples

Example 1. Find the difference between two values.

20 - decreasing value,

15 - subtracted.

Solution: 20 - 15 = 5

Answer: 5 - the difference in values.

Example 2. Find the minuend.

48 - difference,

32 - subtracted value.

Solution: 32 + 48 = 80

Example 3. Find the value to be subtracted.

7 - difference,

17 - reduced value.

Solution: 17 - 7 = 10

Answer: the subtracted value is 10.

More complex examples

In examples 1-3, actions with simple integers are considered. But in mathematics, the difference is calculated using not only two, but also several numbers, as well as integer, fractional, rational, irrational, etc.

Example 4. Find the difference three meanings.

Integer values are given: 56, 12, 4.

56 - decreasing value,

12 and 4 are subtracted values.

The solution can be done in two ways.

Method 1 (consecutive subtraction of subtracted values):

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

Method 2 (subtracting two subtracted from the reduced sum, which in this case are called terms):

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

2) 56 - 16 = 40.

Answer: 40 is the difference of three values.

Example 5. Find the difference between rational fractional numbers.

Given fractions with the same denominators, where

4/5 - reduced fraction,

3/5 - subtracted.

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

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

Answer: 1/5.

Example 6. Triple the difference of numbers.

But how to execute such an example when you want to double or triple the difference?

Let's go back to the rules:

A double number is a value multiplied by two.
A triple number is a value multiplied by three.
The doubled difference is the difference in values multiplied by two.
A triple difference is the difference in values 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 7 and 18.

7 - reduced value;

18 - subtracted.

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

And again, there is a rule applied for a specific case:

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

Answer: - 11. This negative meaning and there is a difference between the two values, provided that the subtracted value is greater than the reduced one.

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 in any mathematical calculations. All the calculations made on them are a great help for the hurried, uninquisitive, lazy. Math for Blondes is one such resource. And we all resort to it, regardless of hair color, gender and age.

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

And even if at the beginning of the path the calculations are reduced to primitive examples, everything is ahead of you. And there is a lot to learn. We see that there are many actions with different values in mathematics. Therefore, in addition to the difference, it is necessary to study how to calculate the rest of the results. arithmetic operations:

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

Here is some interesting math.

DIFFERENCE

1. The number that makes up the remainder in subtraction (mat.). The minuend is equal to the subtrahend plus the difference.

Dictionary Ushakov. D.N. Ushakov. 1935-1940.

Synonyms:

See what "DIFFERENCE" is in other dictionaries:

See the difference... Dictionary of Russian synonyms and expressions similar in meaning. under. ed. N. Abramova, M.: Russian dictionaries, 1999. difference, excess, difference; difference, difference, gap, dissimilarity; diversity, difference, balance, margin, tightness, ... ... Synonym dictionary

- (difference) The change in the value of a variable between fixed points in time. If xt is the value of the variable x at time t, then the first difference is defined as Δxt=xt–xt–1. The second difference is equal to the first difference Δxt, minus the first ... ... Economic dictionary

DIFFERENCE- (1) potentials (voltage (see (2))) quantitative characteristic electric field motionless electric charges() between two of its points, equal to work electric field according to the displacement of a unit positive charge from one ... ... Great Polytechnic Encyclopedia

DIFFERENCE, difference, etc., see different. Dahl's Explanatory Dictionary. IN AND. Dal. 1863 1866 ... Dahl's Explanatory Dictionary

Subtraction result... Big Encyclopedic Dictionary

DIFFERENCE, and, wives. 1. see different. 2. Result, subtraction result. | adj. difference, oh, oh. Explanatory dictionary of Ozhegov. S.I. Ozhegov, N.Yu. Shvedova. 1949 1992 ... Explanatory dictionary of Ozhegov

difference- — [Ya.N. Luginsky, M.S. Fezi Zhilinskaya, Yu.S. Kabirov. English Russian Dictionary of Electrical Engineering and Power Industry, Moscow, 1999] Electrical engineering topics, basic concepts EN differential ... Technical Translator's Handbook

Difference is a multi-valued term: the result of subtraction. Difference (mineralogy) (for example, "medium-grained differences" or "chalk-like differences") Potential difference ... Wikipedia

AND; well. 1. to Miscellaneous (1 character); difference. R. beliefs, views. Find r. in approaches to historical facts. // Difference between two compared values in in numerical terms. R. heights above sea level. R. temp. R. water levels. R. in ... ... encyclopedic Dictionary

difference- ▲ magnitude difference difference magnitude difference; subtraction result; quantitative difference. difference. differential (# of pressure). increment. ▼ not at all, angle ↓ subtract … Ideographic dictionary Russian language

Books

A set of tables. Algebra. 7th grade. 15 tables + methodology, . The tables are printed on thick polygraphic cardboard measuring 680 x 980 mm. Brochure with guidelines for the teacher. Educational album of 15 sheets. Expressions...
Time-distributed "difference of differences" on the example of assessing the return on additional vocational training, A. V. Aistov. The paper presents an econometric model that describes the distribution of the impact effect over time, built on the basis of the “difference of differences” methodology. The model allowed...

The difference is usually called the result obtained by subtracting fewer from more. AT this case, the first number from which another is subtracted, gets the name reduced (after all, we reduce it in the process). The second number, subtracted from the first number, is called the subtracted one. In sum with the difference, the subtrahend is 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:

formula differences a-b= with
difference of squares formula a 2 - b 2 \u003d (a - b) * (a + b)
formula for the difference of cubes a 3 - b 3 \u003d (a - b) * (a 2 + ab + b 2)
potential difference formula U=Aq
difference square formula (a - b) 2 = a 2 - 2ab + b 2
difference cube formula (a - b) 3 = a 3 - 3a2b + 3ab 2 - b 3

What is difference and how to find it

You can calculate the difference using the usual, familiar to us calculator. To do this, press the "C" button, enter the numbers to be reduced, 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 the up arrow (due to this, the number goes to the stack or memory map 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 with the help of it. To do this, it is necessary to mentally reduce the subtracted by 1. After that, we translate the digits of the number into the category of additional ones, where 0 is equal to 9, 1 is equal to 8, etc. The senior digits that remain free are filled with nines. Added difference components of this kind cause the instrument counter to overflow and indicate the difference.

What is potential difference

The concept of potential difference is used by physicists. You can get the potential difference 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 generates a voltage that determines the difference in electrochemical potentials that make up the electrodes of an element of substances.

Before voltage stabilizers were invented, Weston elements allowed calibrating voltmeters. The reacting components selected in them provided high level stability of the potential difference. There is also the concept of pressure difference, used in hydraulic and air gun. This difference is analogous to the difference in electrical potentials.

How to teach your child subtraction and addition

Even before the start of school, it is desirable for a child to master elementary mathematical operations, to get an idea of \u200b\u200bwhat a difference or sum is. In order to make it easier for the baby to count, use any means at hand in the learning process. Don't be afraid to visualize the task. For example, it will be much easier for a toddler to decide how many apples he will have if he shares half with a friend on real objects, and not on a featureless piece of paper.

Children also like guessing tasks very much. For example. standard example"2+2=4" can be replaced with "2+x=4". Such an exercise will make the child think out of the box and develop logic.