Quandaries
and Queries 

Write the LCD for each pair of fractions. 13. 1/3,1/5 14. 2/7,1/4 15. 3/4,3/5 i dont get this question,i dont know how 2 find the lowest common denominator.please help me because this is going 2 be on a test in 2 dayz 

Hi, Adding two fractions with the same denominator is easy.
If you have two fractions with different denominators, you need to find equivalent fractions with the same denominators and then add these fractions. So for example with your first problem
You can write
so
So, how did I know to use a denominator of 15? I used 15 because 15 is a multiple of both 3 and 5, and 15 is the smallest number that is a multiple of both 3 and 5. That is, 15 is the least common multiple (LCM) of 3 and 5. Likeise in your second problem. The denominators are 7 and 4 and 28 =7 4 is a multiple of both 7 and 4 so you can write
I changed 2/7 to 7/28 by multiplying both the numerator and denominator by 4, and I changed 1/4 to 7/28 by multiplying both the numerator and denominator by 7. Smetimes it is not that easy. If you are to add 3/4 and 1/6 then
is a multiple of 4 and 6 but there is a smaller multiple, 12. Thus you can write
In this case 12 is the least common multiple of 4 and 6 so 12 is the least common denominator of 3/4 and 1/6. To find the least common multiple of two numbers first find the prime factorization of the numbers
Look at the highest power of each of the primes that appear. In this case the hightes power of 2 is 2 and the highest power of 3 is 1. Form the number
This is the least common multiple of 4 and 6. Penny 

