When you have problems with fractions to solve, the first thing you want to think about is how you can make them easier. It's a lot easier to do arithmetic with smaller whole numbers, and fractions are the same. Reducing a fraction is really reducing your work or making it easy. For example, if you have a fraction such as 12/28, it looks pretty tough, but if you divide both the top and bottom by 2, it gets easier: (12 ÷ 2)/(28 ÷ 2) = 6/14. Wait, you can make it even easier: (6 ÷ 2)/(14 ÷ 2) = 3/7.
Addition and subtraction of fractions seem confusing because you must have a common denominator to do these operations. An easy way to remember to do this is to think of pizza pies. If your class orders three pizzas -- and everyone will get two slices -- you want those pies to be cut into the same number of pieces. Otherwise, someone will get big slices, and someone else may not get any at all. Adding and subtracting fractions is the same idea, you want it all to be even. First make it easy by reducing, then make it even.
Multiplying is already easy. You don't have to have the same numbers in the denominators. You just multiply the top, or numerator, of one fraction by the top of the other. Then do the same thing with the bottom numbers. The website Grade A Math suggests that you "Fly to Multiply." Picture two airplanes speeding across the numerators and denominators, and quickly jot down the answers. Don't forget to make it easy first by reducing, then the planes fly even faster.
Dividing fractions is often thought to be the hardest operation of the fraction operations to learn. It's really no harder than multiplication, though. First, write the equation down. Make it easy by seeing if you can divide anything out of the top and bottom numbers of the first fraction and then the second. Change the division sign into a multiplication sign and turn the second fraction upside-down. Then call in the planes and fly. Division is topsy-turvy multiplication. The first fraction stays right side up, and the second one goes topsy turvy. Then multiply.