My daughter was struggling with fractions. She understood how to add and subtract them, but although she understood it in theory, many of her answers are wrong. If she were in school, the class would have moved on to multiplying fractions and she would have been confused from that point on.
I sat down and made some worksheets to figure where the problems were. I am sharing my findings and methods with you.
Lesson 1: I gave her worksheets that helped me to evaluate where her problem was. I had her first write a mixed number as an improper fraction, and then simplify it. Next, I had her convert it back to a mixed number. These can be printed from any number of online websites. The worksheets were on reducing fractions, which she passed with flying colors so I know that was not the problem. The second was changing improper fractions to mixed numbers, which she did not do as well on, and the third was changing mixed numbers to improper fractions. She did miserably on this one.
Therefore, now I know that while she knows how to add and subtract fractions she has problems when it comes to dealing with improper fractions and converting them to and from mixed numbers.
Lesson 2: I wrote a worksheet that would cause her to mixed number to an improper fraction, reduce it, and then convert it back into a mixed number. This way she could check her own work, and know immediately if she got it wrong. Here are the math problems I used:
Write improper fractions as mixed numbers in simplest terms, then re-write as improper fractions.
• 5 2/8 = 42/8 = 21/4 =5 ¼ (5 2/8 = 5 ¼)
• 6 3/6
• 5 8/10
• 1 4/8
• 4 4/6
• 1 2/8
If the answer is equivalent to the original number, then it is correct, only the fraction is in its simplest form.
Lesson 3 and so forth: I will continue giving her worksheets like the one above until she consistently gets 100% on these worksheets. In addition, even after we have moved onto dividing fractions, I will continue to give her worksheets on converting, adding, and subtracting fractions to keep her skills fresh. Here is another worksheet on converting fractions:
Match the Fractions: (draw a line between the matching fractions): make two columns as shown: