Fractions and Mixed Numbers

• Having students visualize what they are doing by using a model and recognizing which interpretation of a fraction is most useful for a problem will increase their understanding of operations with fractions.

• Have your students estimate the answer before performing an operation with two fractions. For example, students might estimate that the sum of + is less than one and greater than , since > and + = . Similarly, the product of (2) X (1) is close to 4, since both numbers are close to 2. The quotient of ÷ is greater than 2, since > and there are 2 fourths in .

• Students should use the numbers 0, , and 1 as benchmarks when working with fractions. For example, if they know that < and < , they should recognize that the sum of and will be less than one. However, since both numbers are very close to , their sum will be close to, but still less than, 1.

• When simplifying fractions, be sure to stress the idea of finding the GCF of both the numerator and the denominator. Similarly, for adding and subtracting fractions, remind students that they can find the LCD (least common denominator) by finding the LCM (least common multiple) of the two denominators.

• The algorithms for adding and subtracting fractions are probably more difficult than the algorithms for multiplying and dividing fractions. Students may need some time practicing these operations.

• Stress the idea that means 3 unit fractions of one fifth. Thus, + mean you have 3 one-fifths pieces and you are adding one more one-fifth piece to it, so you get 4 one-fifth pieces, or .

• Graph paper is often very helpful when students are constructing visual models for fractions.