Evaluating an algebraic expression whole numbers with two operations calculator

Quadratic Equation

In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 (and b ≠ 0) then the equation is linear, not quadratic, as there is no ax² term.) The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

The Evaluating Expressions Calculator calculates the exact value of mathematical operations between two or more fractional operations and elaborates it in an understandable form for the user. Moreover, the calculator shows the result in decimal value. 

Furthermore, this calculator evaluates the expressions that are either a sum or a difference through a pie chart. It explains the fractions as a part of a circle for the user to understand easily. 

Moreover, it is essential to note that the calculator also takes algebraic values but does not solve them for their roots or another value. It will only state it in a simplified form after completing the operations on the expression.

What Is the Evaluating Expressions Calculator?

The Evaluating Expressions Calculator is an online tool that determines the exact value of expressions under a mathematical operation. These expressions can consist of more than one term and require the fractions to have known values for the calculator to function correctly. 

The Calculator Interface consists of a single-line text box labeled “expression.” The user can write terms of expressions with mathematical operations according to his requirements. Furthermore, it is necessary to note that this calculator supports algebraic expressions, but they will only result in a more simplified expression without calculating its solution or roots. 

How To Use the Evaluating Expressions Calculator?

You can use the Evaluating Expressions Calculator by simply inputting the expression into the single-line text box. A popup window will show the detailed result of the corresponding expression. Let us take a case where we require the result of an expression $\frac{2}{5}+ \frac{4}{21}$. The following are the steps given to determine its answer::

Step 1

Enter the expression with correct mathematical operations in it as required by you. In our case, we enter the expression $\frac{2}{5}+ \frac{4}{21}$ into the text box.

Step 2

Ensure that the expression is mathematically correct and is devoid of any algebraic unknown that will give an ambiguous or vague answer. Our example has no algebraic variable. 

Step 3

Press the “Submit” button to get the results

Results

A pop-up window appears showing the detailed results in the sections explained below: 

• Input: This section shows the input expression as interpreted by the calculator. You can use this to verify whether or not the calculator has interpreted the expression inputted as you intended. 

• Exact Result: This section gives the exact answer to the entered expression. The answer is usually in the fractional form and can be shown in the integer form if the result calculates to be an exact integer. 

• Repeating decimal: This section shows the decimal representation of the exact value in fractional form.  The repetition of decimals can be denoted by a slash on top of the repeating number.

• Pie Chart: For a better representation of the fractional answer, a pie chart is used to denote the fractions as a part of a whole. This section pops up when the expressions are either summed or negated, and the pie charts show this expression in a visual form,

Solved Examples

Example 1

Given an expression below:

\[\left(\frac{3}{5} \times \frac{2}{7}\right) + \frac{1}{8} \]

Find the result by evaluating this expression.

Solution

There are three terms in this expression for which we implement the DMAS rule to find the product of the first two terms and then sum it with the third term.

The product of the first two numbers yield:

\[  \frac{6}{35} + \frac{1}{8} \]

Now we can see that the sum of the last two terms can be found using the LCM method for finding the common denominator and multiplying the numerators with the denominator of the other term. 

\[  \frac{6 \times 8 }{35 \times 8} + \frac{1 \times 35}{8 \times 35} \]

\[  \frac{48}{288} + \frac{35}{288} \]

\[ \mathbf{\frac{83}{288}} \]

Hence, the final expression is calculated, which is $\frac{83}{288}$

The decimal form can be found using the Long division method, which is 0.2964.

Example 2

Consider the expression below:

\[\left(\frac{4}{9} \div \frac{3}{5}\right) – \frac{12}{9} + \frac{23}{4} \]

Find the result by evaluating this expression.

Solution

There are four terms in this expression for which we implement the DMAS rule to find the product of the first two terms and then sum it with the third and fourth terms.

We can take the reciprocal of the 2nd term to find the result of the division of the first two terms. 

\[\left(\frac{4}{9} \times \frac{5}{3}\right) – \frac{12}{9} + \frac{23}{4} \]

\[  \frac{20}{27} – \frac{12}{9} + \frac{23}{4} \]

Now by calculating the LCM of the denominator of the terms. 

\[  \frac{20 \times 4 }{27 \times 4} – \frac{12 \times 12}{9 \times 12} + \frac{23 \times 27}{4 \times 27} \]

\[  \frac{80}{108} – \frac{144}{108} + \frac{621}{108} \]

\[ \mathbf{\frac{577}{108}} \]

Hence, the final expression is calculated, which is $\frac{577}{108}$

The decimal form can be found using the Long division method, which comes out as 5.1574.

Example 3

Consider the expression below:

\[\left(\frac{6}{11} \times \frac{4}{5}\right) – \frac{14}{11} + \frac{13}{8} \]

Find the result by evaluating this expression.

Solution

There are four terms in this expression for which we implement the DMAS rule to find the product of the first two terms and then sum it with the third and fourth terms.

The product of the first two numbers yield:

\[  \frac{24}{55} – \frac{14}{11} + \frac{13}{8} \]

Now by calculating the LCM of the denominator of the terms. 

\[  \frac{24 \times 8 }{55 \times 8} – \frac{14 \times 40}{11 \times 40} + \frac{13 \times 55}{8 \times 55} \]

\[  \frac{192}{440} – \frac{560}{440} + \frac{715}{440} \]

\[ \mathbf{\frac{347}{440}} \]

Hence, the final expression is calculated, which is $\frac{347}{440}$

The decimal form can be found using the Long division method, which comes out as 0.78863.

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