Posts tagged "find the value of an expression". How to find the value of an expression

Numeric expression– this is any record of numbers, signs arithmetic operations and brackets. A numerical expression can simply consist of one number. Recall that the basic arithmetic operations are “addition”, “subtraction”, “multiplication” and “division”. These actions correspond to the signs “+”, “-”, “∙”, “:”.

Of course, in order for us to get a numerical expression, the recording of numbers and arithmetic symbols must be meaningful. So, for example, such an entry 5: + ∙ cannot be called a numeric expression, since it is a random set of symbols that has no meaning. On the contrary, 5 + 8 ∙ 9 is already a real numerical expression.

Meaning numerical expression.

Let's say right away that if we perform the actions indicated in the numerical expression, then as a result we will get a number. This number is called the value of a numeric expression.

Let's try to calculate what we will get as a result of performing the actions of our example. According to the order in which arithmetic operations are performed, we first perform the multiplication operation. Multiply 8 by 9. We get 72. Now add 72 and 5. We get 77.
So, 77 - meaning numerical expression 5 + 8 ∙ 9.

Numerical equality.

You can write it this way: 5 + 8 ∙ 9 = 77. Here we used the “=” sign (“Equals”) for the first time. Such a notation in which two numeric expressions are separated by the “=” sign is called numerical equality. Moreover, if the values of the left and right sides of the equality coincide, then the equality is called faithful. 5 + 8 ∙ 9 = 77 – correct equality.
If we write 5 + 8 ∙ 9 = 100, then this will already be false equality, since the values of the left and right sides of this equality no longer coincide.

It should be noted that in numerical expression we can also use parentheses. Parentheses affect the order in which actions are performed. So, for example, let's modify our example by adding parentheses: (5 + 8) ∙ 9. Now you first need to add 5 and 8. We get 13. And then multiply 13 by 9. We get 117. Thus, (5 + 8) ∙ 9 = 117.
117 – meaning numerical expression (5 + 8) ∙ 9.

To read an expression correctly, you need to determine which action is performed last to calculate the value of a given numeric expression. So, if the last action is subtraction, then the expression is called “difference”. Accordingly, if the last action is a sum - a “sum”, division – a “quotient”, multiplication – a “product”, exponentiation – a “power”.

For example, the numerical expression (1+5)(10-3) reads like this: “the product of the sum of the numbers 1 and 5 and the difference of the numbers 10 and 3.”

Examples of numeric expressions.

Here is an example of a more complex numerical expression:

\[\left(\frac(1)(4)+3.75 \right):\frac(1.25+3.47+4.75-1.47)(4\centerdot 0.5)\]

This numerical expression uses prime numbers, ordinary and decimal fractions. Addition, subtraction, multiplication and division signs are also used. The fraction line also replaces the division sign. Despite the apparent complexity, finding the value of this numerical expression is quite simple. The main thing is to be able to perform operations with fractions, as well as carefully and accurately make calculations, observing the order in which the actions are performed.

In brackets we have the expression $\frac(1)(4)+3.75$ . Let's transform decimal 3.75 in ordinary.

$3.75=3\frac(75)(100)=3\frac(3)(4)$

So, $\frac(1)(4)+3.75=\frac(1)(4)+3\frac(3)(4)=4$

Next, in the numerator of the fraction \[\frac(1.25+3.47+4.75-1.47)(4\centerdot 0.5)\] we have the expression 1.25+3.47+4.75-1.47. To simplify this expression, we apply the commutative law of addition, which states: “The sum does not change by changing the places of the terms.” That is, 1.25+3.47+4.75-1.47=1.25+4.75+3.47-1.47=6+2=8.

In the denominator of the fraction the expression $4\centerdot 0.5=4\centerdot \frac(1)(2)=4:2=2$

We get $\left(\frac(1)(4)+3.75 \right):\frac(1.25+3.47+4.75-1.47)(4\centerdot 0.5)=4: \frac(8)(2)=4:4=1$

When do numerical expressions make no sense?

Let's look at another example. In the denominator of the fraction $\frac(5+5)(3\centerdot 3-9)$ the value of the expression $3\centerdot 3-9$ is 0. And, as we know, division by zero is impossible. Therefore, the fraction $\frac(5+5)(3\centerdot 3-9)$ has no meaning. Numerical expressions that have no meaning are said to have “no meaning.”

If we use letters in addition to numbers in a numerical expression, then we will get an algebraic expression.

Publication date: 08/30/2014 10:58 UTC

Geometry, a workbook for the book by Balayan E.N. "Geometry. Tasks on ready-made drawings for preparation for the Unified State Exam and Unified State Exam: grades 7-9", 7th grade, Balayan E.N., 2019
Geometry simulator, 7th grade, for the textbook by Atanasyan L.S. and others. “Geometry. 7-9 grades", Federal State Educational Standard, Glazkov Yu.A., Egupova M.V., 2019

You, as parents, in the process of educating your child, will more than once be faced with the need for help in solving homework problems in mathematics, algebra and geometry. And one of the basic skills that you need to learn is how to find the meaning of an expression. Many people are at a dead end, because how many years have passed since we studied in grades 3-5? Much has already been forgotten, and some have not been learned. The rules of mathematical operations themselves are simple and you can easily remember them. Let's start with the very basics of what a mathematical expression is.

Expression Definition

A mathematical expression is a collection of numbers, action signs (=, +, -, *, /), brackets, and variables. Briefly, this is a formula whose value will need to be found. Such formulas are found in mathematics courses since school, and then haunt students who have chosen specialties related to exact sciences. Mathematical expressions are divided into trigonometric, algebraic, and so on; let’s not get into the thicket.

Do any calculations first on a draft, and then rewrite them in workbook. This way you will avoid unnecessary crossings and dirt;
Recalculate total quantity mathematical operations that will need to be performed in the expression. Please note that according to the rules, the operations in brackets are performed first, then division and multiplication, and at the very end subtraction and addition. We recommend highlighting all the actions in pencil and putting numbers above the actions in the order in which they were performed. In this case, it will be easier for both you and your child to navigate;
Start making calculations strictly following the order of actions. Let the child, if the calculation is simple, try to perform it in his head, but if it is difficult, then write with a pencil the number corresponding to the ordinal number of the expression and carry out the calculation in writing under the formula;
As a rule, finding the value of a simple expression is not difficult if all calculations are carried out in accordance with the rules and in the right order. Most people encounter a problem precisely at this stage of finding the meaning of an expression, so be careful and do not make mistakes;
Ban the calculator. The mathematical formulas and problems themselves may not be useful in your child’s life, but that is not the purpose of studying the subject. The main thing is development logical thinking. If you use calculators, the meaning of everything will be lost;
Your task as a parent is not to solve problems for your child, but to help him in this, to guide him. Let him do all the calculations himself, and you make sure he doesn’t make mistakes, explain why he needs to do it this way and not otherwise.
Once the answer to the expression has been found, write it down after the “=” sign;
Open the last page of your math textbook. Usually, there are answers for every exercise in the book. It doesn’t hurt to check whether everything has been calculated correctly.

Finding the meaning of an expression is, on the one hand, a simple procedure; the main thing is to remember the basic rules that we went through in school course mathematics. However, on the other hand, when you need to help your child cope with formulas and solve problems, the issue becomes more complicated. After all, you are now not a student, but a teacher, and the education of the future Einstein rests on your shoulders.

We hope that our article helped you find the answer to the question of how to find the meaning of an expression, and you can easily figure out any formula!

(34∙10+(489–296)∙8):4–410. Determine the course of action. Perform the first action in the inner brackets 489–296=193. Then, multiply 193∙8=1544 and 34∙10=340. Next action: 340+1544=1884. Next, divide 1884:4=461 and then subtract 461–410=60. You have found the meaning of this expression.

Example. Find the value of the expression 2sin 30º∙cos 30º∙tg 30º∙ctg 30º. Simplify this expression. To do this, use the formula tg α∙ctg α=1. Get: 2sin 30º∙cos 30º∙1=2sin 30º∙cos 30º. It is known that sin 30º=1/2 and cos 30º=√3/2. Therefore, 2sin 30º∙cos 30º=2∙1/2∙√3/2=√3/2. You have found the meaning of this expression.

The value of the algebraic expression from . To find the value of an algebraic expression given the variables, simplify the expression. Substitute certain values for the variables. Complete the necessary steps. As a result, you will receive a number, which will be the value of the algebraic expression for the given variables.

Example. Find the value of the expression 7(a+y)–3(2a+3y) with a=21 and y=10. Simplify this expression and get: a–2y. Substitute the corresponding values of the variables and calculate: a–2y=21–2∙10=1. This is the value of the expression 7(a+y)–3(2a+3y) with a=21 and y=10.

Please note

There are algebraic expressions that do not make sense for some values of the variables. For example, the expression x/(7–a) does not make sense if a=7, because in this case, the denominator of the fraction becomes zero.

Sources:

find smallest value expressions
Find the meanings of the expressions for c 14

Learning to simplify expressions in mathematics is simply necessary in order to correctly and quickly solve problems and various equations. Simplifying an expression involves reducing the number of steps, which makes calculations easier and saves time.

Instructions

Learn to calculate powers of c. When multiplying powers c, a number is obtained whose base is the same, and the exponents are added b^m+b^n=b^(m+n). When dividing powers with the same bases, the power of a number is obtained, the base of which remains the same, and the exponents are subtracted, and the exponent of the divisor b^m is subtracted from the exponent of the dividend: b^n=b^(m-n). When raising a power to a power, the power of a number is obtained, the base of which remains the same, and the exponents are multiplied (b^m)^n=b^(mn) When raising to a power, each factor is raised to this power. (abc)^m=a^m *b^m*c^m

Factor polynomials, i.e. imagine them as a product of several factors - and monomials. Take the common factor out of brackets. Learn the basic formulas for abbreviated multiplication: difference of squares, squared difference, sum, difference of cubes, cube of sum and difference. For example, m^8+2*m^4*n^4+n^8=(m^4)^2+2*m^4*n^4+(n^4)^2. These formulas are the main ones in simplification. Use the method of isolating a perfect square in a trinomial of the form ax^2+bx+c.

Abbreviate fractions as often as possible. For example, (2*a^2*b)/(a^2*b*c)=2/(a*c). But remember that you can only reduce multipliers. If the numerator and denominator algebraic fraction multiplied by the same number other than zero, the value of the fraction will not change. You can convert expressions in two ways: chained and by actions. The second method is preferable, because it is easier to check the results of intermediate actions.

It is often necessary to extract roots in expressions. Even roots are extracted only from non-negative expressions or numbers. Odd roots can be extracted from any expression.

Sources:

simplification of expressions with powers

Trigonometric functions first emerged as tools for abstract mathematical calculations of the dependencies of quantities sharp corners V right triangle from the lengths of its sides. Now they are very widely used in both scientific and technical fields. human activity. For practical calculations trigonometric functions Depending on the given arguments, you can use different tools - several of the most accessible ones are described below.

Instructions

Use, for example, the one installed by default with operating system calculator program. It opens by selecting the “Calculator” item in the “Utilities” folder from the “Standard” subsection, placed in the “All programs” section. This section can be opened by clicking on the “Start” button to the main operating menu. If you are using the Windows 7 version, you can simply enter “Calculator” in the “Search programs and files” field of the main menu, and then click on the corresponding link in the search results.

Count the quantity necessary actions and think about the order in which they should be done. If you find it difficult this question, please note that the operations enclosed in parentheses are performed first, then division and multiplication; and subtraction are done last. To make it easier to remember the algorithm of the actions performed, in the expression above each action operator sign (+,-,*,:), with a thin pencil, write down the numbers corresponding to the execution of the actions.

Proceed with the first step, following the established order. Count in your head if the actions are easy to perform verbally. If calculations are required (in a column), write them under the expression, indicating serial number actions.

Clearly track the sequence of actions performed, evaluate what needs to be subtracted from what, divided into what, etc. Very often the answer in the expression is incorrect due to mistakes made at this stage.

Distinctive feature expression is the presence of mathematical operations. It is indicated by certain signs (multiplication, division, subtraction or addition). The sequence of performing mathematical operations is corrected with brackets if necessary. To perform mathematical operations means to find .

What is not an expression

Not every mathematical notation can be classified as an expression.

Equalities are not expressions. Whether mathematical operations are present in the equality or not does not matter. For example, a=5 is an equality, not an expression, but 8+6*2=20 also cannot be considered an expression, although it contains multiplication. This example also belongs to the category of equalities.

The concepts of expression and equality are not mutually exclusive; the former is included in the latter. The equal sign connects two expressions:
5+7=24:2

This equation can be simplified:
5+7=12

An expression always assumes that the mathematical operations it represents can be performed. 9+:-7 is not an expression, although there are signs of mathematical operations here, because it is impossible to perform these actions.

There are also mathematical ones that are formally expressions, but have no meaning. An example of such an expression:
46:(5-2-3)

The number 46 must be divided by the result of the actions in brackets, and it is equal to zero. You cannot divide by zero; the action is considered prohibited.

Numeric and algebraic expressions

There are two types of mathematical expressions.

If an expression contains only numbers and symbols of mathematical operations, such an expression is called numeric. If in an expression, along with numbers, there are variables denoted by letters, or there are no numbers at all, the expression consists only of variables and symbols of mathematical operations, it is called algebraic.

Fundamental difference numerical value from algebraic is that a numerical expression has only one meaning. For example, the value of the numerical expression 56–2*3 will always be equal to 50; nothing can be changed. An algebraic expression can have many values, because any number can be substituted. So, if in the expression b–7 we substitute 9 for b, the value of the expression will be 2, and if 200, it will be 193.

Sources:

Numeric and algebraic expressions

As a rule, children begin to study algebra in elementary school. After mastering the basic principles of working with numbers, they solve examples with one or more unknown variables. Finding the meaning of an expression like this can be quite difficult, but if you simplify it using elementary school knowledge, everything will work out quickly and easily.

What is the meaning of an expression

A numerical expression is an algebraic notation consisting of numbers, parentheses and signs if it makes sense.

In other words, if it is possible to find the meaning of an expression, then the entry is not without meaning, and vice versa.

Examples following entries are correct numeric constructions:

3*8-2;
15/3+6;
0,3*8-4/2;
3/1+15/5;

A single number will also represent a numeric expression, like the number 18 from the above example.
Examples of incorrect number constructions that do not make sense:

*7-25);
16/0-;
(*-5;

Incorrect numeric examples are just a bunch of mathematical symbols and have no meaning.

How to find the value of an expression

Since such examples contain arithmetic signs, we can conclude that they allow arithmetic calculations. To calculate the signs or, in other words, to find the meaning of an expression, it is necessary to perform the appropriate arithmetic manipulations.

As an example, consider the following construction: (120-30)/3=30. The number 30 will be the value of the numerical expression (120-30)/3.

Instructions:

Concept of numerical equality

A numerical equality is a situation where two parts of an example are separated by the “=” sign. That is, one part is completely equal (identical) to the other, even if displayed in the form of other combinations of symbols and numbers.
For example, any construction like 2+2=4 can be called a numerical equality, since even if the parts are swapped, the meaning will not change: 4=2+2. The same goes for more complex constructions involving parentheses, division, multiplication, operations with fractions, and so on.

How to find the value of an expression correctly

To correctly find the value of the expression, you must perform calculations according to a certain order actions. This order is taught in mathematics lessons, and later in algebra classes in elementary school. It is also known as arithmetic steps.

Arithmetic steps:

The first stage is the addition and subtraction of numbers.
The second stage is where division and multiplication are performed.
Third stage – numbers are squared or cubed.

By observing the following rules, you can always correctly determine the meaning of an expression:

Perform actions starting from the third step, ending with the first, if there are no parentheses in the example. That is, first square or cube, then divide or multiply, and only then add and subtract.
In constructions with parentheses, perform the actions in the parentheses first, and then follow the order described above. If there are several brackets, also use the procedure from the first paragraph.
In examples in the form of a fraction, first find out the result in the numerator, then in the denominator, then divide the first by the second.

Finding the meaning of an expression is not difficult if you acquire basic knowledge initial courses algebra and mathematics. Guided by the information described above, you can solve any problem, even of increased complexity.

Find out the password from VK, knowing the login

Answer: _________
2. The product cost 3200 rubles. How much did this product cost after the price was reduced by 5%?
A. 3040 rub. B. 304 p. V. 1600 rub. G. 3100 p.
3. On average, students in the class completed 7.5 tasks from the proposed test. Maxim completed 9 tasks. By what percentage is his result above average?
Answer: _________
4. The row consists of natural numbers. Which of the following statistics cannot be expressed as a fraction?
A. Arithmetic mean
B. Fashion
B. Median
D. There is no such characteristic among the data.
5. Which of the equations has no roots?
A. x =x B. x =6 C. x =0 D. x =−5
6. The numbers A and B are marked on the coordinate line (Fig. 35). Compare numbers –A and B.

A. –A< В
B. –A > B
B. –A = B
D. It is impossible to compare
7. Simplify the expression a (a – 2) – (a – 1)(a + 1).
Answer: _________
8. The values of which variables need to be known in order to find the value of the expression (5a – 2b)(5a + 2b) – 4b (3a – b) + 6a (2b – 1)?
A. a and b B. a C. b
D. The value of the expression does not depend on the values of the variables
9. Solve the equation (x – 2)2 + 8x = (x – 1)(1 + x).
Answer: _________
10. Solve the system of equations ( 3x−2y=5, 5x+6y=27.
Answer: _________
11. In a 3-hour car ride and a 4-hour train ride, the tourists traveled 620 km, and the speed of the train was 10 km/h greater than the speed of the car. What is the speed of the train and the speed of the car?
Denoting the speed of the car by x km/h and the speed of the train by y km/h, we created systems of equations. Which one is composed correctly?
A. ( 3x+4y=620, x−y=10 B. ( 3x+4y=620, y−x=10
V. ( 4x+3y=620, x−y=10 G. ( 4x+3y=620, y−x=10
12. Which point does not belong to the graph of the function y = –0.6x + 1?
A. (3; –0.8) B. (–3; 0.8) B. (2; –0.2) D. (–2; 2.2)
13. In which coordinate quadrant is there not a single point on the graph of the function y = –0.6x + 1.5?
Answer: _________
14. Use the formula to define a linear function whose graph intersects the x-axis at the point (2; 0) and the y-axis at the point (0; 7).
Answer: _________ Help

1. Find the value of the expression a a−1 if a = 0.25. Answer: _________ 2. The product cost 3200 rubles. How much did this product cost after the price was reduced by 5%?

A. 3040 rub. B. 304 p. V. 1600 rub. G. 3100 p. 3. On average, students in the class completed 7.5 tasks from the proposed test. Maxim completed 9 tasks. By what percentage is his result above average? Answer: _________ 4. The series consists of natural numbers. Which of the following statistics cannot be expressed as a fraction? A. Arithmetic mean B. Mode C. Median D. There is no such characteristic among the data 5. Which of the equations has no roots? A. x =x B. x =6 C. x =0 D. x =−5 6. The numbers A and B are marked on the coordinate line (Fig. 35). Compare the numbers –A and B.A. –A< В Б. –А >B B. –A = B D. Cannot be compared 7. Simplify the expression a (a – 2) – (a – 1)(a + 1). Answer: _________ 8. The values of what variables do you need to know to find the value of the expression (5a – 2b)(5a + 2b) – 4b (3a – b) + 6a (2b – 1)? A. a and b B. a C. b D. The value of the expression does not depend on the values of the variables 9. Solve the equation (x – 2)2 + 8x = (x – 1)(1 + x). Answer: _________ 10. Solve the system of equations ( 3x−2y=5, 5x+6y=27. Answer: _________ 11. In a 3-hour car ride and a 4-hour train ride, tourists traveled 620 km, and the train speed was 10 km /h is greater than the speed of the car. What are the speed of the train and the speed of the car? Denoting the speed of the car by x km/h and the speed of the train by y km/h, which of them is correct? −y=10 B. ( 3x+4y=620, y−x=10 V. ( 4x+3y=620, x−y=10 G. ( 4x+3y=620, y−x=10 12. Which one points does not belong to the graph of the function y = –0.6x + 1? A. (3; –0.8) B. (–3; 0.8) B. (2; –0.2) D. (–2; 2,2) 13. In which coordinate quadrant is there not a single point on the graph of the function y = –0.6x + 1.5? Answer: _________ 14. Use the formula to define a linear function whose graph intersects the x-axis at the point (2; 0) and y axis at point (0; 7). Answer: _________ Option 2 1. Find the value of the expression x x−2 if x = 2.25. Answer: _________ 2. The product cost 1600 rubles. How much did the product cost after the price increased by 5. %? A. 1760 rub. B. 1700 rub. V. 1605 rub. G. 1680 rub. 3. During a shift, the shop’s turners processed an average of 12.5 parts. Petrov processed 15 parts during this shift. By what percentage is his result above average? Answer: ____________ 4. In the data series, all numbers are integers. Which of the following characteristics cannot be expressed as a fraction? A. Arithmetic mean B. Mode C. Median D. There is no such characteristic among the data 5. Which of the equations has no roots? A. x =0 B. x =7 C. x =−x D. x =−6 6. The numbers B and C are marked on the coordinate line (Fig. 36). Compare the numbers B and –C. A. B > –C B. B< –С В. В = –С Г. Сравнить невозможно 7. Упростите выражение х (х – 6) – (х – 2)(х + 2). Ответ: ___________ 8. Значения каких переменных надо знать, чтобы найти значение выражения (3х – 4у)(3х + 4у) – 3х (3х – у) + 3у (1 – х)? А. x Б. у В. x и у Г. Значение выражения не зависит от значений переменных 9. Решите уравнение (х + 3)2 – х = (х – 2)(2 + x). Ответ: ___________ 10. Решите систему уравнений { 2x+5y=−1, 3x−2y=8. Ответ: ___________ 11. Масса 5 см3 железа и 10 см3 меди равна 122 г. Масса 4 см3 железа больше массы 2 см3 меди на 14,6 г. Каковы плотность железа и плотность меди? Обозначив через x г/см3 плотность железа и через у г/см3 плотность меди, составили системы уравнений. Какая из систем составлена правильно? А. { 5x+10y=122, 4x−2y=14,6 Б. { 5x+10y=122, 4y−2x=14,6 В. { 10x+5y=122, 4x−2y=14,6 Г. { 10x+5y=122, 4y−2x=14,6 12. Какая из точек не принадлежит графику функции у = –1,2x – 1,4? А. (–1; –0,2) Б. (–2; 1) В. (0; –1,4) Г. (–3; 2,2) 13. В какой координатной четверти нет ни одной точки графика функции у = 1,8x – 7,2? Ответ: ___________ 14. Задайте формулой линейную функцию, график которой пересекает ось x в точке (–4; 0) и ось у в точке (0; 3). Ответ: ____________ У МЕНЯ ЗАВТРА ИТОГОВАЯ ПОЖАЛУЙСТА