The Mechanics of Working with Mixed Numbers
You multiply mixed number fractions the same way you multiply any fractions, except you convert first. That is the step most people skip and then get confused when their answer looks wrong. Take 2 1/3 times 1 3/4. You turn both into improper fractions first, so it becomes 7/3 times 7/4. Multiply straight across and you get 49/12. Convert back and it is 4 1/12. That is all there is to it. The worksheet format usually gives you eight to twelve problems per page. Some publishers include the conversion step in the instructions, others assume you already know it. I have seen both approaches fail for different reasons. When the worksheet skips the conversion reminder, students often multiply the whole numbers and fractions separately and then add them together at the end. That gives you the wrong answer every single time.
Multiplying Mixed Number Fractions Worksheet
The standard approach works for any combination. Convert each mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator. Keep the same denominator. Then multiply the numerators together and the denominators together. Simplify if the worksheet asks you to, or leave it as an improper fraction depending on the grade level. Fifth and sixth graders usually work with simpler numbers. Eighth graders get fractions with larger denominators and sometimes negative mixed numbers, which adds a whole other layer of mistakes. I ran into this exact problem last year when a student kept getting 3 3/8 instead of 2 5/8 on the third problem. The worksheet had 1 1/2 times 2 1/4. He multiplied the whole numbers to get 2, then multiplied 1/2 and 1/4 to get 1/8, and just wrote those together. It looked logical to him. I spent twenty minutes walking through why you cannot do that, using area models on scrap paper until he saw the overlap. Worksheets alone do not fix the conceptual gap. He needed to see the visual representation before the procedure made sense. Common pitfalls include forgetting to convert before multiplying, which I already mentioned, and then failing to simplify the result. Some teachers require simplified answers, some do not. If you are not sure, ask. Another pitfall is carrying over incorrectly when converting back from improper fractions. The division can get messy with larger numbers, and students often guess at the remainder.
The worksheets usually cost between three and eight dollars per packet, or you can find free versions online. The paid ones tend to have better layouts and answer keys. Free worksheets sometimes have typos in the problems or missing instructions. I have downloaded at least a dozen free packs and found errors in three or four of them. Not every site is reliable. If you prefer visual learners, pair the worksheet with fraction tiles or drawn rectangles. It takes extra time but reduces the error rate significantly. For students who just want to get through the problems quickly, the direct conversion method works fine once they understand why it is necessary. The worksheet alone will not teach the concept, but it gives you practice with the procedure.
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