Algebra Den

Subtraction of Fractions with Different Denominators

Explanation To subtract fractions with different denominators, Step 1 = Find equivalent fractions of given fraction with common denominator Step 2 = Follow the process of subtraction of fractions with same denominator (topic available in above link) As mentioned in Step 1 (above), we need to find : Common denominator = LCM of the denominators of the given fractions (LCM topic is available in this site) Equivalent Fractions = Involves following steps: Step 1 = Divide the Common Denominator by the denominator of given fractions Step 2 = Multiply the quotient with the numerator of the respective fractions. For Example = Solve (5/4) - (3/6) The above fractions have different denominators, so we need to find : Common Denominator = LCM of the denominators(4 & 6) of the given fractions = 12 Equivalent Fraction of given fraction (5/4) and (3/6): The proceed is as :- Given fraction (5/4) Step 1 = Divide the Common Denominator(12) by the denominator of given fraction(4) = 12 ÷ 4 = 3 Step 2 = Multiply the quotient(3) with the numerator of the respective fraction(5) = 5 × 3 = 15 So, Equivalent Fractions of given fraction with common denominator 5/4 = 15/12 Given fraction (3/6) Step 1 = Divide the Common Denominator(12) by the denominator of given fraction(6) = 12 ÷ 6 = 2 Step 2 = Multiply the quotient(2) with the numerator of the respective fraction(3) = 3 × 2 = 6 So Equivalent Fractions of given fraction with common denominator 3/6 = 6/12 Now, we have equivalent fractions of given fraction with same denominators (5/4) and (3/6) = 15/12 & 6/12 {Respectively} so, (5/4) - (3/6) = 15/12 - 6/12 Subtract the numerators and denominator remains same: = (15-6) / 35 Solve the Parentheses and we get: = 9/12 Divide both Numerator and Denominator by 3 and we get Fraction in Lowest Form: = 3 / 4. Alternative Method The above discussed method is for Beginners. Once you understand the concept of subtraction of fractions with different denominators, you can directly apply the addition process in following ways: (5/4) - (3/6) Find LCM of denominators and divide the LCM by denominator & multiply its quotient with respective numerators and we get: = { (5×3) - (3×2) } / 12 Solve the Parentheses and we get: = {15 - 6} / 12 Solve Braces and we get: = 9 / 12 Divide both Numerator and Denominator by 3 and we get Fraction in Lowest Form: = 3 / 4.