Math Background

Comparing and Ordering Fractions, Mixed Numbers, and Decimals: When Students Ask

  • If I know fractions, why do I need to know about decimals?
    Students need to feel comfortable with fractions and decimals and how they relate to each other. A good example can be found at the market. You may have been asked to get a pound and a half of cheese, but the label may show the weight of the cheese as a decimal (1.50) because of the tools used to weigh the cheese and make the labels.
  • How do I know whether a fraction and a decimal are equivalent?
    Help students to think about denominators. Reading decimals as fractions will be very useful here. When you read three-tenths and 0.3, they “sound”the same, so you know they're equivalent. For a fraction like six-twentieths, write an equivalent fraction: six-twentieths = three-tenths. Then three-tenths = 0.3. For one-fourth, write an equivalent fraction: one-fourth = twenty-five-one-hundredths. Then twenty-five-one-hundredths = 0.25.
  • What is a mixed number and when would I use one?
    A mixed number is a number greater than 1 that is between two whole numbers. It is made up of a whole number part and a fraction: 1one-half is a mixed number.
  • Why don't you just let us say point six two five instead of six hundred twenty-five thousandths?
    Explain that, while the point form accurately describes what a decimal number “looks” like, it doesn't accurately convey its value. Students will be comparing and ordering decimals as well as fractions. Just as they're encouraged to say six sevenths instead of six over seven, they're encouraged to read a decimal number as a fraction to get the full sense of its value.

Houghton Mifflin Math Grade 4