The algebraic expressions they are mathematical terms that contain numbers and letters. In combination with the symbols of mathematical operations, they allow to obtain formulas or equations, from descriptions made in words.
In turn, these letters can be added, subtracted, multiplied or divided by other numbers, which can be explicit or also represented by letters..
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For example the expression:
2x + 3
It is an algebraic expression, where the letter "x" represents a number that may be unknown or that can take different values.
What is the advantage of using an algebraic expression instead of saying: "twice a number added to 3"?
First, the algebraic expression takes up less space. And then, if x is not a fixed number, different values can be given to the "x" in order to obtain different results of this expression.
This is known as the numerical value of the algebraic expression.
For example, if x = 1 then the result is 2⋅1 + 3 = 2 + 3 = 5
Instead, making x = -2, the expression turns out to be 2⋅ (-2) + 3 = -4 + 3 = -1
In another type of application, algebraic expressions represent an equation or equality that must be solved in order to know the value of the number represented by the letter.
Here we have a simple linear equation:
2⋅x + 3 = 7
The solution to this equation, which by the way is also an algebraic expression, is:
x = 2
Since multiplying 2 by 2 gives 4 plus 3 gives the result: 7. But it is easier to understand when using an algebraic expression instead of describing everything in words.
Algebraic expressions are used extensively in Mathematics, Science, Economics, and Management.
Below is a list of expressions that appear very frequently in exercises in mathematics and other subjects, in which you are asked to express a proposition or solve an equation.
Usually an unknown or unknown number is denoted as "x", but we can use any other letter of the alphabet as appropriate..
It must also be borne in mind that an algebraic expression may have involved more than one value, unknown or variable, so each one must be assigned a different letter.
-The double or double of a number: 2x
-The double of a number plus three units: 2m + 3
-The third part of a number: z / 3
-Double a number minus its third: 2x - x / 3
-The square of a number: xtwo
-The square of a number plus twice that number: xtwo + 2x
-The double of the square of a certain number: 2xtwo
-An even number: 2n
-An odd number: 2n + 1
-Three consecutive numbers: x, (x + 1), (x + 2)
-Three consecutive even numbers: 2n, 2n + 2, 2n +4
-Three consecutive odd numbers, 2n + 1, 2n + 3, 2n + 5
-A certain number added to its consecutive: x + (x + 1) = 2x +1
-Half of the consecutive integer: (x + 1) / 2
-Triple half the square of a number: 3. (1/2) xtwo = (3/2) xtwo
-Half of one number plus one-third of another: x / 2 + y / 3
-The third part of the product between the square of a number and another number from which the unit was subtracted: (1/3) xtwo.(y-1)
-A number and its opposite: a, -a
-A number and its inverse: a, 1 / a
-The sum of a number with its consecutive squared: x + (x + 1)two
-Subtract 7 from twice a certain number squared: (2x)two - 7
-Two numbers that when multiplied give 24: p.q = 24
-The absolute value of a number: │x│
-The quotient between two numbers: x / y
-The square root of the product of two numbers: √x.y
-A number such that it exceeds another by 30 units: x = y +30
-Double a number whose half is subtracted: 2x- x / 2
Half a cow weighs 100 kg more than a quarter of the same cow. How much does the cow weigh?
For the algebraic expression of this problem, we call the weight of the cow x.
Half the cow weighs ½ x. A quarter of the cow weighs ¼ x. Finally, the algebraic expression corresponding to: "half the cow weighs 100 kg more than the fourth part" is:
½ x = ¼ x + 100
To find out how much the cow weighs, we must group the terms with x on the left side and leave 100 on the right:
(½ -¼) x = 100
¼x = 100
x = 400 kg
The cow weighs 400 kg.
On a farm the number of rabbits is twice the number of cows. If the number of cows is 10. How many rabbits are there?
If C is the number of rabbits and V is the number of cows, then the algebraic expression in the statement is:
C = 2⋅V
V = 10
Therefore, substituting the value of V in the first of the equations, we obtain:
C = 2 ⋅ 10 = 20
I mean, the farm has twenty rabbits.
What is the number that multiplied by seven and subtracting six gives twenty-nine?
If we call this unknown number x, we can raise this algebraic expression:
7x - 6 = 29
The 6 on the left side goes to the right side of the signed-changed equality:
7x = 29 + 6 = 35
It follows that x = 35/7 = 5
Double a certain number is subtracted 13 and left 7. What is the number?
If we call that number x, then its algebraic equation is:
2 x - 13 = 7
What is the value of 2x ?
The answer is that 2x has to be (13 + 7) so that by taking 13 away there is 7.
This means that 2x has to be equal to 20, that is:
2x = 20
The number x that multiplied by 2 gives 20 is 10, therefore:
x = 10
Two consecutive integers add up to 23. Formulate an algebraic equation that allows us to determine the number and find it.
Suppose that the first of the numbers is n, then the next one is n + 1 and the sum of these two is n + (n + 1). In addition, it is known that the result of the sum is 23 so the equation is written:
n + (n + 1) = 23
The solution is obtained first by simplifying the left side of the equality:
2 n + 1 = 23
Then 2 n is cleared by passing 1 to the right member with the sign changed:
2 n = 23 - 1
The right member is resolved:
2 n = 22
Next, we solve for n, passing the 2 that multiplies the member on the left by dividing the member on the right:
n = 22/2
And you get the final result:
n = 11
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