Begin with addition and subtraction of fractions. In addition and subtraction of fractions, the denominator stays the same so students are essentially just adding one element to what they already know. Use objects that can be divided evenly, like pies, so students can visualize what a fraction of a whole looks like. Get students up and moving by illustrating addition of fractions with the entire class. Count all members of the class to illustrate the whole. Have a certain number of students stand on the other side of the room to represent a fraction of the whole class. Add the two groups back together to demonstrate addition of fractions. Use the same visuals for subtraction of fractions.
Teach students how to make denominators the same by finding the least common multiple. This can be done easily by multiplying the two different denominators by each other. For example, if your denominators are 7 and 4, 7 x 4 is 28. Determine how many times each numerator goes into the number 28 and add that into the original numerator. This gives you two new numerators and a common denominator of 28 so students can simply add across for the answer.
Continue with multiplication after students are pretty comfortable with addition and subtraction of fractions. For quick and easy teaching of multiplying fractions, simply have students multiply across for the numerator and the denominator. In multiplication, the denominators don't have to be equal.
Divide fractions quick and easy by taking the reciprocal of the second fraction in the problem and then multiply. To find the reciprocal, just flip the second fraction over. For example, if your second fraction is ½, the reciprocal of that fraction would be 2/1.
Instruct students to express their final answer in lowest terms. This means if their final answer is 2/4, then is can be reduced to ½ by dividing both the top and bottom by 2.