Factors and Fractions

• Showing students more than one way to solve a problem deepens their understanding of the concepts involved and will help them remember those concepts.

• When asked to order a set of fractions by finding equivalent fractions, suggest that students first consider the reasonable relationship of the fractions involved. For example, if students are asked to order the set of fractions , , and , they should find that < < . When discussing the results, you can point out that was the only fraction less than , so it would be the least. Similarly, since = , then < . Discussions like this will deepen students' understanding of fractions. It will also reinforce the value of checking the reasonableness of answers.

• Students frequently confuse the LCM and the GCF. Stress that factors are divisors of a number and are less than or equal to the number. Multiples of a number are products of two or more whole numbers and are generally greater than the number.

• You might want to make a poster or create a bulletin board defining least common multiple and greatest common factor and illustrating how to find each for a pair of numbers. Reviewing these two terms regularly will help students remember them.

• When students are asked what they did to change to , they will often say that they multiplied by 4. They often don't recognize that when they multiply or divide both the numerator and denominator by the same number they are multiplying or dividing by one, which does not change the value of a number.

• Students will often become confused if they are told that "reduces" to . They believe that is less than , not an equivalent fraction. Try to use the word simplify instead. A fraction in simplest form has a numerator less than its denominator, and the numerator and denominator have no factors in common.