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Simplify (2x-6)/(21) divided by (5x – 15)/(12)

  • Last Updated : 29 Oct, 2021

In mathematics, when we talk about finding the unknown we usually use a letter from the alphabet, why not the exact number? The answer is, we directly can not find the answer, we only have an option to find this answer is by guessing, which might be correct or might be wrong. The possibility of wrong is more than correct. That is why we use a letter from the alphabet, it can take any value. When we form the equation using the given condition in the question and solve it, then that unknown will give us the exact number, which we are looking for. That letter makes our calculation easy and we termed this complete process as ‘algebra’. 

Algebraic Expression

When we use numerals and variables together with fundamental arithmetic operators then that is known as an algebraic expression. For example, we have two numbers 9 and 3, and a letter x then an algebraic expression form using these numbers and letter is 9x + 3. In this expression, there are two terms. Fundamental arithmetic operators decide the number of terms.

Based on the number of terms, the algebraic expression has been categorized into the following types.

  • Monomial: If there is only one term in an algebraic expression then that expression is known as a monomial. Example:  5x, 8y, etc.
  • Binomial: When the number of terms in an algebraic expression is two then that expression is known as the binomial algebraic expression. Example: 5x+2, 9t+8y, etc
  • Trinomial: When the number of expressions in the algebraic expression is three then that expression is known as the trinomial expression. Example: 8x+3r+9, 8t-4r-6, etc
  • Polynomial: When the number of terms in an algebraic expression is one or more than one then that expression is known as the polynomial.

Division of algebraic expression

Just like we do division in arithmetic, we can also do division in algebra. Factor terms of numerator and denominator should be the same so we can easily cancel out the common factor of numerator and denominator.  

Step to solve the problem:

Step 1: First of all, factorize the numerator and denominator of divisor and dividend and write them in the factorized form.

Step 2: If one fraction is divided by another fraction then the numerator of the first fraction multiplied by the denominator of the second fraction is divided by the denominator of the first fraction multiplied by the numerator of the second fraction.

Step 3: Take out the common factor from all the terms and cancel out the all common factor of the numerator and denominator. The remaining term will be the answer of the given problem.

Simplify (2x-6)/(21) divided by (5x – 15)/(12)

Solution:

First of all, factorized all the terms of the numerator and denominator.

= {(2x – 6)/(21)} ÷ {(5x -15) / (12)}



= {(2 × x – 2 × 3)/(3 × 7)} ÷ {(5 × x – 5 × 3)/(2 × 2 × 3)} 

Take out the common factor of numerator and denominator.

= {2(x – 3)/(3 × 7)} ÷ {5(x – 3)/(2 × 2 × 3)}

If one fraction is divided by another fraction then the numerator of the first fraction multiplied by the denominator of the second fraction is divided by the denominator of the first fraction multiplied by the numerator of the second fraction.

= {2 × (x – 3) × 2 × 2 × 3}/{3 × 7 × 5 × (x – 3)}

Cancel out the common term.

= (2 × 2 × 2)/(7 × 5)

= 8/35

Similar Questions

Question 1: Simplify: (2x-6y)/(12) divided by (5x – 15y)/(12).

Solution: 



First of all, factorized all the terms of the numerator and denominator.

= {(2x-6y)/(12)} ÷ {(5x-15y)/(12)}

= {(2×x – 2×3×y)/(2×2×3)} ÷ {(5×x – 3×5×y)/(2×2×3)}

Take out the common factor of numerator and denominator.

= {2(x – 3y)/(2×2×3)} ÷ {5(x-3y)/(2×2×3)}

If one fraction is divided by another fraction then the numerator of the first fraction multiplied by the denominator of the second fraction is divided by the denominator of the first fraction multiplied by the numerator of the second fraction.

= {2×(x-3y)×2×2×3}/{5×(x-3y)×2×2×3}

Cancel out the common term

= 2/5

Question 2: Simplify: (2x-6y)/(2y-3z) divided by (5x – 15y)/(6y-9z).

Solution:

First of all, factorized all the terms of the numerator and denominator.

= {(2x-6y)/(2y-3z)} ÷ {(5x – 15y)/(6y-9z)}

= {(2×x-2×3×y)/(2×y-3×z)} ÷ {(5×x-3×5×y)/(2×3×y-3×3×z)}

Take out the common factor of numerator and denominator.

= {2(x-3y)/(2y-3z)} ÷ {5(x-3y)/3(2y-3z)}

 If one fraction is divided by another fraction then the numerator of the first fraction multiplied by the denominator of the second fraction is divided by the denominator of the first fraction multiplied by the numerator of the second fraction.

= {2×(x-3y)×3×(2y-3z)}/{(2y-3z)×5×(x-3y)}

Cancel out the common term.

= (2×3)/5

= 6/5

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