Fractions are the things that a lot of children and adults find challenging. Really, if you look at the basics of fractions you and your child will have an easier time at understanding them and working with them.
I will focus on the addition of fractions. The first thing I want to stress is that a fraction just means the breaking up of something into parts or pieces. As kids when we wanted a share of a good piece of cake we looked forward to getting a big part or fraction of it. The portion that you received when there were three kids was better than the portion you would receive if there were 6 kids who needed to get a piece of that cake.
The fraction strips (http://www.superteacherworksheets.com/fractions/fractionstrips.pdf) are useful to make comparisons of fractions. You can see how 1/2 is the big gest fraction (portion), while the other fractions are much smaller as the denominator (bottom number) increases. The denominator tells us how many ways the whole cake is divided. It tells us how many people will get a share (fraction) of the whole cake.
In the fraction, one third (1/3), the cake is divided between three (3) people. The denominator is 3. In the case of one ninth (1/9), the cake is divided between nine (9) people. The denominator is 9. A person would do better to have 1/3 of a cake than to have 1/9 of the same cake. It takes three ninths (1/9) to get one third (1/3). Look at the fraction strip.
You will have a better illustration of various fractions if you use the fraction strip (www.superteacherworksheets.com/fractions/fractionstrips.pdf). Print the strip or look on as you practice the problems below.
When you add all of the parts together you get back the whole. For example, 1/3 plus (+) 1/3 is equal to 2/3. While 1/3 + 1/3 + 1/3 equal to 3/3 (three thirds) or a whole (1). When you divide a number by itself, you get 1. In fractions you are adding only the numerators (top numbers) not the denominators (the bottom numbers).
You add thirds (1/3) with thirds, fifths (1/5) with fifths and so on. You are looking to compare the same portions or fractions when you keep the denominators the same or use a number that they both can be easily and completely divided into. You can add 1/2 plus 1/2. When you do that, you see that those two parts will always equal the “whole.”
Using the fraction strips you can add 1/8 + 1/8 and you see that they are equal to one fourth (1/4). You could have also done 1/8 + 1/8 is equal to 2/8. When you look at the sum (addition) of two eights you see that it is the same size as 1/4. Consider using highlighters of different colors to compare the fractions and see the relationships.
From the fraction strips we can see that 2/8 is another way of saying 1/4. They are equal or equivalent fractions. 1/4 is the reduced version of 2/8. If you divide the numerator by 2 and the denominator by 2, your answer would be 1/4. One forth (1/4) is just a simplified way of saying two eights (2/8).
How would you add 1/3 to 1/6? If you look shade 1/3 you see that it is much bigger than 1/6. You can also see that 1/3 is the equivalent of 1/6 + 1/6. So 1/3 plus 1/6 is equal to 3/6. Is there a number (factor) that you can use to divide into the 3 (numerator) and the 6 (denominator) evenly? The number would be 3. When you do that, your reduced fraction would be 1/2. So 3/6 is the same as 1/2. Three sixths (3/6) and one half (1/2) are equivalent fractions.
You can use another, quicker method (no need to use fraction strips) to add 1/3 plus 1/6. In school, students are taught the importance of identifying the least common denominator. Here we can identify or find a number (multiple) that both the 3 found in 1/3 and the 6 found in 1/6 can be divided into evenly. The three (3) and the 6 can evenly be divided into 6. Therefore, 6 is the smallest number (least common denominator) that both denominators can be divided (factored) into. Three (3) goes into six (6) two times and 6 goes into 6, 1 time.
Solving 1/3 + 1/6
The least common denominator is 6. Determine how many times 3 goes into 6. It is 2x. Then determine how many times 6 goes into 6. It is 1x. This method gets you to change the fractions to have the same bottom number (denominator). Since your new denominator will be 6, everything will be on top of 6. So you then multiply 2x the 1 found in 1/3 and you get 2/6. Then you multiply the 1x the 1 in 1/6 and you get 1/6. You then do 2/6 + 1/6 = 3/6 or 1/2. Look again at the strips. We came up with the same solution!
Some people just multiply the denominators of 1/3 and 1/6 and get 18 as the new denominator. So then everything would be over 18. So using the method above, they would get 6/18 + 3/18 equal 9/18. You could reduce that fraction by dividing the numerator by 9 and the denominator by 9. You would still get 1/2 again as your answer. This method leads to the use of bigger number (consider adding 1/9 + 2/18 using that method).
Remember, fractions are just portions of a whole. Use the fraction strips to familiarize yourself with the relations and how fractions compare to each other. Practice using them and see what method works best for you or your child when you encounter fractions.