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.

1/5 + 2/5 = (1 + 2)/5 = 3/5.

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

1/3 + 1/5

You can write

1/3 = 5/15 and 1/5 = 3/15

so

1/3 + 1/5 = 5/15 + 3/15 = 8/15.

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

2/7 + 1/4 = 8/28 + 7/28 = 15/28

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

4 6 = 24

is a multiple of 4 and 6 but there is a smaller multiple, 12. Thus you can write

3/4 + 1/6 = 9/12 + 2/12 = 11/12.

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

4 = 2²
6 = 2 3

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

2² 3 = 12

This is the least common multiple of 4 and 6.

Penny

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