Math Background

Comparing and Ordering Fractions: When Student Ask

  • Why do I need to learn this?
    Explain that students will need to measure things, compare measures, and compute with measures. In the United States, we use a measurement system that has many fractions in it. Challenge students to find (non-academic) examples of measurement in the classroom, on the schoolyard, and at home.
  • Why are there different ways to write fractions?
    In their math textbook, students see fractions written with a horizontal line between numerator and denominator. In some places, they might see a slash between the numerator and denominator of a fraction. The second way is easier to write, but it's sometimes hard to tell exactly what's in the numerator or denominator of a number written this way. For example, 2 1/2 could be confused with twenty-one over two and 2/3 + 5 could be confused with two over three plus five.
  • How do I know when two fractions are equivalent?
    Equivalent fractions have the same value. If you can find one number to multiply both the numerator and denominator of one fraction by that will give you the exact numerator and denominator of the other fraction, then you know they are equivalent.
  • Do I really need to use the greatest common factor when I'm trying to simplify a fraction?
    No. You can use any common factor to simplify a fraction. If you don't use the greatest common factor, then you'll have to simplify more than once to put a fraction in simplest form. For example, to simplify four-eighths, you can divide the numerator and denominator each by 2 and then again by 2, or you can use the greatest common factor, 4, and divide only once to get one-half.
  • Is there something wrong with an improper fraction?
    No. We use the word improper to indicate that the numerator is larger than the denominator. However, an improper fraction is a perfectly good fraction and, in fact, it's sometimes much easier to compute with improper fractions than with mixed numbers!
  • Do I really need to use the least common denominator when I'm looking for equivalent fractions with like denominators?
    No. Any common denominator will do, but it may be easier to compute with the least common denominator, so it's a good idea to look for it if it's easy to find.

Houghton Mifflin Math Grade 4