Fractions can be confusing and hard to understand. It can be easy to misread or do a problem wrong that is dealing with fractions. For example, in the problem 5/3 +3/3 many may get confused and say the answer is 8/6. This is wrong because you cannot add two like denominators in the problem. Denominators are the numbers on the bottom of the fraction; in this case the denominator in 5/3 and 3/3 is 3. It is less likely to get confused if 5/3 is written as 5 thirds and 3/3 is written as 3 thirds. Clearly, you can see that the denominator is going to stay 3 or a third. You do not add the denominators (3+3=6) because that is not correct. This is a nice tip to follow especially if you are teaching younger students who have never dealt with fractions before.
Another great tip to help learn more about fractions is having the same unit. For example, if you have 2 yards + 9 feet you cannot add them because yards and feet are not the same unit. In this case you would have to convert one of the units in order to make them both have the same unit. You can do this two different ways with the example provided: yards can convert to feet and feet can convert to yards. Let’s convert 2 yards into feet. In order to do this we must know how many feet are in a yard, which is 3. So if there are 3 feet in a yard and we have 2 yards that means there are 6 feet in 2 yards. Now we can do the problem! 6 feet +9 feet = 15 feet.
I found that drawing measuring cups helps to understand the conversions between halfs and fourths. For example, if we have 3 halfs + 1 fourth it may be confusing to solve the problem if you don’t have something to look at. First of all we need to convert either halfs to fourths or fourths to halfs. I am going to solve the problem by converting halfs to fourths because a fourth is smaller than a half. I have included a picture of measuring cups to work out the problem. The end result is 6 fourths + 1 fourth= 7 fourths.