Steps to Solving Fractions

Video Transcript

"So what are some steps to solve fractions? Hi, I'm Jimmy Chang, I've been teaching college mathematics for nine years and we're here to address the different ways that you can solve fractions. Now it really does depend on what operation it is that we're talking about. Because sometimes the least common denominator is very important. But the least common denominator only applies to the following operations: addition and subtract. So let's explore those first. If two fractions have the exact same denominator like 3/7ths plus 2/7ths then you can just add across. All you need to do is add the numerators across and keep the denominator the same. So 3 plus 2 is 5. But don't make the mistake of adding the denominators as well, the denominators stay the same. So 3/7th plus 2/7th is 5/7ths. Now if you have a fraction that's been subtracted with another fraction but they have different denominators then you have to find the least common denominators between the two to continue on. Now all you need to do is think about what number will 4 and 2 go into and that number is 4. Now since the denominator here didn't change the numerator here wouldn't change either. Now however 2 times what number gives you 4? It has to be 2. So you have to multiply the top and bottom by the same number. So negative 1/2 is really negative 2/4ths. And then you do the subtraction 3/4ths minus 2/4ths is positive 1/4. So that is your answer. Now the idea of least common denominators do not apply to multiplication or division. If you have 1/2 times 1/3rd. All you have to do is multiply across. Multiply the top numbers, 1 times 1 is 1, 2 times 3 is 6. Multiplication is probably the most straight forward. But if you have 2/3rds divided by 1/2, division of fractions means that you; if you divide it by a fraction you have to treat this as a division problem. But you have to flip the second fraction. Well in other words multiply it by the reciprocal times 2 over 1 and then you treat it like a multiplication problem. 2 times 2 is 4. 3 times 1 is 3. So division, almost as simple as multiplication but with one adjustment. So I'm Jimmy Chang and there are some steps to solve fractions."