![]() ![]() In this context, it’s certainly a valid question. Once you've listed all of the factors of that number, all you have to do is find the largest number repeated in both lists.Īs a teacher, you’re probably quite familiar with the age-old question students ask: “why am I even doing this?” Using our previous example of ⁹⁄₁₈, we’ll find and list all the factors of each number, starting from one. This method is similar to finding the least common denominator - you’ll find the answer by listing all possible factors. The GCF is the highest number that divides evenly into two or more numbers. Three and six can both be divided by three again, so our final answer is ½. Now that we have a simpler answer, it’s time to see if we can we simplify even further. We can’t divide nine by two evenly.Ĭan both nine and eighteen be divided by three? Yes! When we divide both by three, our fraction becomes ³⁄₆. With our answer of ⁹⁄₁₈, we can keep trying to divide by small numbers until we find one that works.Ĭan both nine and eighteen be divided by two? No. Start with two, then three, then four - and so on until you get the smallest possible answer. The two easiest methods for simplifying a fraction are: 1) Trial and errorįor this method, just keep dividing the numerator and denominator by small numbers. For example, two is a common factor of four and six, because both numbers can be divided by two. To simplify a fraction, you need a common factor: a number that will divide into both numbers evenly. This number seems a bit large, so we'll see if we can simplify it to an easier number. In our previous equation, our answer was ⁹⁄₁₈. Simplifying involves finding the smallest equivalent fraction possible. If your fraction contains high numbers, you may need to simplify it. Six plus three is nine, so our answer is ⁹⁄₁₈. Using our new equation from the common denominator method - ⁶⁄₁₈ + ³⁄₁₈ - we need to add six and three together. Add your numerators together so the sum becomes the new numerator, while the denominator stays the same. Once again, our fractions are ready to be added! Step 2: Add the numerators (and keep the denominator) For ⅙, the numbers must be multiplied by one, so the fraction stays the same. ![]() So, for ⅓, both the numerator and denominator must be multiplied by two to get ²⁄₆. This is a big adjustment for students who are already comfortable with whole number arithmetic.Īs you can see from our table, the smallest multiple that’s the same is six. Learning how to multiply and divide fractions can add even more confusion, as students must remember the differences between these operations. Many students and teachers have a limited understanding of how or why these methods are used.įractions are harder to represent with visuals or manipulatives, and the rules for adding them are more difficult to understand. Rules become much more unpredictable and confusing. ![]() ![]() The methods you use to add, subtract, multiply and divide whole numbers are different than doing the same operations for fractions. Different operations for whole numbers and fractions As a student, this is hard to wrap your head around. Whole numbers are only expressed one way, while fractions can be expressed in many ways and still represent the same amount.įor instance, there’s only one way to represent the number three, but ²⁄₄ represents the same amount as ½, 0.5 and 50%. The meaning behind fractions is confusing when you compare them to whole numbers. Fractions introduce students to rational numbers, which come with a whole new set of rules and patterns. Understanding what the numbers meanīefore fractions, students are used to working with whole numbers: basic numbers that represent whole amounts. Research has found the biggest issues are: 1. Fractions are a struggle for a few reasons. ![]()
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