# Algebra 1 - Find the sum of two fractions

Sum of Two Fractions

Find the sum of: 5/16 + 7/12

Enter your answer in lowest terms in the box below as a fraction, using the slash mark ( / ) for the fraction bar.

### Comments for Algebra 1 - Find the sum of two fractions

 Aug 22, 2012 Find the sum of two fractions by: Staff Answer: The answer: 5/16 + 7/12 = ? The explanation is rather long, so I am going to give you the answer first. But please read the explanation, because it explains the process. 5/16 + 7/12 = 15/48 + 28/48 = 43/48 >>> the final answer is: 43/48 -------------------------------------------------------------------------------- Explanation of process of adding two fractions with different denominators. As you already know, fractions cannot be added or subtracted unless they have the same denominator. 5/16 and 7/12 do not have the same denominator. Therefore, each fraction must be rewritten so that both fractions have the same common denominator. The new common denominator can be the least common multiple (LCM) of the two original denominators: 16 and 12 ------------------------------------------------ To find the LCM, you can use the prime factorization method (this is a method you can use to compute the LCM with any fractions) - Factor the numbers 7 and 8 into prime factors. Use exponents to show how many times each prime factor is listed. 16 = 2⁴ 12 = 2² * 3¹ - List every prime number listed as a factor of either 7 or 8. Prime Number Factors Listed: 2, 3 - List these same prime factors again, but include the highest exponent listed for each Prime Number Factors with highest exponent: 2⁴, 3¹ Multiply the factors with the highest exponent to compute the LCM: LCM = 2⁴ * 3¹ = 48 ------------------------------------------------ Convert the denominators of both fractions 48 5/16 + 7/12 “IF” the denominator of 5/16 could by multiplied by 3, the new denominator would be 48: 16 * 3 = 48 This is exactly what you want. However, there is a problem. 5/16 does not have the same value as 5/48. In order to preserve the value of the original fraction (5/16), both the numerator and denominator must each be multiplied by the same amount: the number 3. To apply this concept, multiply the original fraction by 3/3. The fraction 3/3 is equal to 1, so the original fraction is merely being multiplied by 1. As you can see by the following illustration, its value has not been changed. = [original fraction] = [original fraction] * 3/3 = [original fraction] * 1 = [original fraction] Therefore, = [original fraction] * 3/3 = 5/16 * 3/3 When multiplying two fractions, multiply the both numerators and multiply the both denominators. = 5/16 * 3/3 = (5 * 3) / (16 * 3) = (15) / (48) = 15 / 48 -----------------------------------------------------------