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Simplify (10x2)/5x

  • Last Updated : 02 Nov, 2021

Algebra is the branch of mathematics in which we study numerals and variables. Numerals and variables are connected together by fundamental arithmetic operators. The main use of algebra is to find the unknowns. We also derive formulas by using algebra. For example, if we have to find the perimeter of a rectangle then the length and width of the rectangle is required. Suppose the length is ‘l’ and width is ‘b’ then the perimeter of the rectangle is formulated as 2×(l+b). For the different values of length and width, the perimeter of a rectangle can be calculated by using the above formula.

Algebraic Expression

An algebraic expression is the combination of numerals, variables, and arithmetic operators. An algebraic expression is the mathematical form of a statement. 

For example: 9 is taken away from three times a number can be written as ‘3x-9’. 

Here we suppose the unknowns as x because don’t know the exact value of that number. The term which has fix value is known as numerals and the term which do not have fix value is known as a variable. We generally represent variables by letters of the alphabet. 

In the above expression, the negative sign separates the expression into two terms. On the basis of the number of terms, an algebraic expression is categorized into the following parts.

  • Monomial: If an algebraic expression the number of terms is one then it is known as a monomial. Example: 8x, 6y, etc
  • Binomial: if the number of terms in algebraic expression is two then it is known as the binomial expression. Example: 5x+8, 9y+6z, etc
  • Trinomial: If the number of terms in an algebraic expression is three then it is known as the trinomial expression. Example: 9a+3b-6c, 8m+3n-6p, etc
  • Polynomial: If the number of terms in an algebraic expression is one or more than one then it is termed as the polynomial.

Division of the algebraic expression: 

Write the numerator and denominator of the algebraic expression in the factors form. Then find out the like terms in numerator and denominator and cancel them. The remaining term will be the answer to the given algebraic expression.

Step to solve the problem: 

Step 1: Write the numerator and denominator into the factored form.

Step 2: Find out the like term of the numerator and denominator and cancel them.

Step 3: Write the remaining term in the simplest form. That will be the answer.

Simplify (10x2)/5x.

Solution: 



Factorise the numerator and denominator. 

 The numerator can be written as = 2 × 5 × x × x

The denominator can be written as = 5 × x

Put these values in fraction form.

= (2 × 5 × x × x)/(5 × x)

Cancel out the common term of numerator and denominator.

= 2 × x

= 2x

So the simplification of (10x²)/5x is 2x.

Similar Questions

Question 1: Simplify 36x²/27x.

Solution:

Factorise the numerator and denominator. 

The numerator can be written as = 2 × 2 × 3 × 3 × x × x

The denominator can be written as = 3 × 3 × 3 × x

Put these values in fraction form.

= (2×2×3×3×x×x)/(3×3×3×x)

Cancel out the common term of numerator and denominator.

= (2 × 2 × x)/3

= 4x/3

So the simplification of 36x²/27x is 4x/3.



Question 2: Simplify 9y³/3y².

Solution:

Factorise the numerator and denominator. 

The numerator can be written as = 3×3×y×y×y

The denominator can be written as = 3×y×y

Put these values in fraction form.

= (3×3×y×y×y)/(3×y×y)

Cancel out the common term of numerator and denominator.

= 3×y

= 3y

So the simplification of 9y³/3y² is 3y.

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